TWI762856B - Bell plate with harmonics sound, percussion instrument with the bell plate, and design method of the bell plate - Google Patents

Abstract

A bell plate with harmonics sound, a percussion instrument with the bell plate, and a design method of the bell plate are provided to overcome the problem that the conventional bell plate is unable to produce harmonic sound. The bell plate includes a striking face symmetric about a central axis and having a first edge perpendicular to the central axis. The first edge has two end points connected to a second edge. The striking face further has two inclined edges extending towards the central axis. Each inclined edge has two end points respectively connected to the second edge and a third edge. The striking face has a fourth edge connected to two end points of the second and third edges. The bell plate further includes a plurality of through-holes extending through the striking face which can be hit to generate harmonic sound.

Description

Bell board with harmonic octave tone, percussion instrument with the bell board and the Design method of bell board

The present invention relates to a bell board with simple harmonic multiplier tones, a percussion instrument with the bell board, and a design method of the bell board, especially a device capable of making the bell board emit simple harmonic multiplier tones.

In a symphony orchestra, Percussion Instrument is an indispensable instrument for playing various beautiful melodies. The natural frequencies of its vibration modes include Fundamental Frequency (the first natural frequency) and Overtones (Overtones, namely The 2nd, 3rd, 4th, ... natural frequencies), when the overtone has an integer proportional relationship with the fundamental tone, it is called "Harmonics Sound", which can make the sound more harmonious and soft.

However, the core technology used to create a good-sounding and pleasant bell board has been gradually lost, so that the later produced bell board cannot produce harmonious and soft timbre (octave tone), resulting in limited applicable sound styles.

In view of this, it is necessary to propose a bell board with simple harmonic multiplier tones, a percussion instrument with the bell board, and a design method of the bell board, so as to meet the actual needs and improve its practicability.

In order to solve the above-mentioned problems, the object of the present invention is to provide a kind of sound with simple harmonic multiplier tones. A bell board, which can be struck to produce simple harmonic multiplier tones.

Another object of the present invention is to provide a percussion instrument with the bell plate, which can be used to generate harmonic harmonics by striking.

Another object of the present invention is to provide a method for designing a bell board with harmonic multiplier tones, so as to design a bell board with simple harmonic multiplier tones that can be generated by knocking.

The "harmonics sound" mentioned in the whole of the present invention refers to the ratio between the fundamental sound and the overtone that is equal to or close to an integer multiple, which can be understood by those with ordinary knowledge in the art.

The "nodal line position" mentioned in the whole text of the present invention refers to the position that does not affect the vibration of the mode shape, that is, the position where the modal displacement is equal to zero (fixed point), and the nodal line position cannot excite the corresponding sound frequency , which can be understood by those with ordinary knowledge in the field.

The directionality or similar terms used throughout the present disclosure, such as "front", "back", "left", "right", "top (top)", "bottom (bottom)", "inside", "outside" , "side surface", etc., mainly refer to the directions of the attached drawings, each directionality or its similar terms are only used to assist the description and understanding of the various embodiments of the present invention, and are not intended to limit the present invention.

The use of the quantifier "a" or "an" for the elements and components described throughout the present invention is only for convenience and provides a general meaning of the scope of the present invention; in the present invention, it should be construed as including one or at least one, and a single The concept of also includes the plural case unless it is obvious that it means otherwise.

Similar terms such as "combined", "combined" or "assembled" mentioned in the whole text of the present invention mainly include the components that can be separated without destroying the components after the connection, or the components can not be separated after being connected, which are common knowledge in the field. It can be selected according to the material of the components to be connected or the assembly requirements.

The bell board with simple harmonic multiplier tone of the present invention comprises: a striking surface, which is located in XY A plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length, the two end points of the first base edge are symmetrical to a central axis, and the central axis system is parallel to the The Y axis of the plane coordinate system, one of the end points of the first base edge is connected to a second base edge, the second base edge and the first base edge together form a right angle and have a second length, the second length and The dimension ratio of the first length is equal to 0.14, starting from the end of the second base edge away from the first base edge, and extending a hypotenuse near the central axis and away from the first base edge, and the two end points of the hypotenuse are respectively Connect the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third length, the ratio of the third length to the first length is equal to 0.35, the first base edge The other end point is connected to another second base edge, and is connected to another hypotenuse and another third base edge in sequence, and the central axis is used as the axis of symmetry to form two second base edges and two oblique edges that are symmetrical to each other. side and two third base sides, a fourth base side extends along the X-axis direction, two end points of the fourth base side are symmetrical to the central axis, and one end point of the fourth base side is connected to one of the third base sides The edge is far from one end of the hypotenuse on the same side, the other end of the fourth base edge is connected to the other end of the third base edge away from the hypotenuse on the same side, the first base edge, the two second base edges The edge, the two hypotenuse edges, the two third base edges and the fourth base edge can be together to form the appearance shape of the striking surface, and there is a shortest distance between the fourth base edge and the first base edge, The dimension ratio of the shortest distance to the first length is equal to 0.97, the fourth base edge has a fourth length, the dimension ratio of the fourth length to the first length is equal to 0.14; and a plurality of perforations pass through the striking surface , the plurality of perforations have a first perforation, a second perforation and a third perforation, the first perforation and the second perforation are arranged opposite to the central axis, the first perforation and the second perforation are respectively There is a first distance between the first base edges, and the ratio of the first distance to the first length is equal to 0.14. distance, the size ratio of the second distance to the first length is equal to 0.25, the third through hole is located on the central axis and has a third distance from the fourth base edge, the third distance and the first length The size ratio is equal to 0.12.

The bell board with simple harmonic multiplier tone of the present invention comprises: a striking surface, which is located in XY A plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length, the two end points of the first base edge are symmetrical to a central axis, and the central axis system is parallel to the The Y axis of the plane coordinate system, one of the end points of the first base edge is connected to a second base edge, the second base edge and the first base edge together form a right angle and have a second length, the second length and The dimension ratio of the first length is equal to 0.41, starting from the end of the second base edge away from the first base edge, and extending a hypotenuse near the central axis and away from the first base edge, and the two end points of the hypotenuse are respectively Connect the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third length, the ratio of the third length to the first length is equal to 0.39, the first base edge The other end point is connected to another second base edge, and is connected to another hypotenuse and another third base edge in sequence, and the central axis is used as the axis of symmetry to form two second base edges and two oblique edges that are symmetrical to each other. side and two third base sides, a fourth base side extends along the X-axis direction, two end points of the fourth base side are symmetrical with the central axis, one end point of the fourth base side is connected to one of the third base sides The base edge is away from one end of the hypotenuse on the same side, the other end of the fourth base edge is connected to the other end of the third base edge away from the hypotenuse on the same side, the first base edge, the two second base edges The base edge, the two hypotenuse edges, the two third base edges and the fourth base edge can be together to form the appearance shape of the striking surface, and there is a shortest distance between the fourth base edge and the first base edge , the size ratio of the shortest distance to the first length is equal to 1.09, the fourth base edge has a fourth length, and the size ratio of the fourth length to the first length is equal to 0.15; surface, the plurality of perforations have a first perforation, a second perforation and a third perforation, the first perforation and the second perforation are arranged opposite to the central axis, the first perforation and the second perforation are respectively There is a first distance with the first base edge, the ratio of the first distance to the first length is equal to 0.15, the first through hole and the second through hole and the second base edge have a first Two distances, the ratio of the second distance to the first length is equal to 0.24, the third through hole is located on the central axis and has a third distance from the fourth base edge, the third distance and the first length The size ratio is equal to 0.15.

The percussion instrument with the bell plate of the present invention further comprises: a body; and a plurality of suspensions A piece is passed through the plurality of through holes of the bell plates, and the bell plates are suspended on the frame body.

The method for designing a bell board with simple harmonic multiplier tone of the present invention includes: inputting a design parameter group into a computer system to establish a mathematical model of a bell board, the bell board having a striking surface , is located in the XY plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length, the two end points of the first base edge are symmetrical to a central axis, the center The axis system is parallel to the Y-axis of the plane coordinate system, one of the end points of the first base edge is connected to a second base edge, the second base edge and the first base edge together form a right angle and have a second length, the The ratio of the second length to the first length is equal to 0.14, starting from the end of the second base edge away from the first base edge, and extending a hypotenuse close to the central axis and away from the first base edge, and the hypotenuse is Two end points are respectively connected to the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third length, and the size ratio of the third length to the first length is equal to 0.35, the The other end point of the first base edge is connected to another second base edge, and sequentially connected to another hypotenuse and another third base edge, and the central axis is used as the axis of symmetry to form two mutually symmetrical second base edges , two hypotenuses and two third base edges, a fourth base edge extends along the X-axis direction, the two end points of the fourth base edge are symmetrical to the central axis, and one of the end points of the fourth base edge is connected to it One end of a third base edge far from the hypotenuse on the same side, the other end of the fourth base edge is connected to one end of the third base edge away from the hypotenuse on the same side, the first base edge, the The two second base edges, the two hypotenuse edges, the two third base edges and the fourth base edge can be together to form the appearance shape of the striking surface, and there is a space between the fourth base edge and the first base edge. a shortest distance, the ratio of the shortest distance to the first length is equal to 0.97, the fourth base edge has a fourth length, the ratio of the fourth length to the first length is equal to 0.14, the bell board has a number of A through hole penetrates the striking surface, the plurality of through holes have a first through hole, a second through hole and a third through hole, the first through hole and the second through hole are arranged opposite to the central axis, the first through hole There is a first distance between the second through hole and the first base edge, the ratio of the first distance to the first length is equal to 0.14, the first through hole and the second through hole are respectively and the second base There is a second distance between the edges, the second distance and The size ratio of the first length is equal to 0.25, the third through hole is located on the central axis, and has a third distance from the fourth base edge, and the size ratio of the third distance to the first length is equal to 0.12; the The computer system performs finite element analysis on the mathematical model to obtain a number of mode shapes and corresponding natural frequencies of the mathematical model; the computer system sets a number of target frequencies for the mathematical model for correcting the number natural frequencies; the computer system revises the design parameter set according to the revised natural frequencies; and the computer system revises the shape structure of the mathematical model according to the revised design parameter set, so that the ringing board is Tap to produce simple harmonic multiplier sound.

The method for designing a bell board with simple harmonic multiplier tone of the present invention includes: inputting a design parameter group into a computer system to establish a mathematical model of a bell board, the bell board having a striking surface , is located in the XY plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length, the two end points of the first base edge are symmetrical to a central axis, the center The axis system is parallel to the Y-axis of the plane coordinate system, one of the end points of the first base edge is connected to a second base edge, the second base edge and the first base edge together form a right angle and have a second length, the The ratio of the second length to the first length is equal to 0.41, starting from the end of the second base edge away from the first base edge, and extending a hypotenuse close to the central axis and away from the first base edge, the hypotenuse of Two end points are respectively connected to the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third length, and the dimension ratio of the third length to the first length is equal to 0.39, the The other end point of the first base edge is connected to another second base edge, and sequentially connected to another hypotenuse and another third base edge, and the central axis is used as the axis of symmetry to form two mutually symmetrical second base edges , two hypotenuses and two third base edges, a fourth base edge extends along the X-axis direction, the two end points of the fourth base edge are symmetrical to the central axis, and one of the end points of the fourth base edge is connected to it One end of the third base edge far from the hypotenuse on the same side, the other end of the fourth base edge is connected to the other end of the third base edge away from the hypotenuse on the same side, the first base edge, The two second base edges, the two hypotenuse edges, the two third base edges and the fourth base edges can be together to form the appearance shape of the striking surface, and the fourth base edge and the first base edge are has a shortest distance that is the same as The dimension ratio of the first length is equal to 1.09, the fourth base edge has a fourth length, the dimension ratio of the fourth length to the first length is equal to 0.15, the bell plate has a plurality of perforations penetrating the striking surface, The plurality of perforations have a first perforation, a second perforation and a third perforation, the first perforation and the second perforation are disposed opposite to the central axis, and the first perforation and the second perforation are respectively connected to the There is a first distance between the first base edges, the ratio of the first distance to the first length is equal to 0.15, and the first through hole and the second through hole respectively have a second distance from the second base edge , the size ratio of the second distance to the first length is equal to 0.24, the third through hole is located on the central axis and has a third distance from the fourth base edge, the third distance and the size of the first length The ratio is equal to 0.15; the computer system performs finite element analysis on the mathematical model to obtain several mode shapes of the mathematical model and corresponding several natural frequencies; the computer system sets several target frequencies for the mathematical model, for revising the natural frequencies; the computer system revises the design parameter set according to the revised natural frequencies; and the computer system revises the shape structure of the mathematical model according to the revised design parameter set, so that The bell board emits simple harmonic multiplier tones after being struck.

Accordingly, the bell board with simple harmonic multiplier, the percussion instrument with the bell board, and the design method of the bell board of the present invention can make the bell board be struck to generate a simple harmonic multiplier tone, harmonic double or harmonic treble, and the first perforation, the second perforation and the third perforation are located at the nodal line position of the mode shape of the ringing board, and will not affect the The sounding mode of the ringing board, and the audio frequency of the simple harmonic frequency sound can be designed through the parameter conditions of the design variable group, which can make the ringing board emit simple harmonic frequency sound, and it is easy to adjust the sound of the ringing board. Simple harmonic octave tone, can be used in performance occasions that require rich percussion skills, and the music style suitable for performance is not limited.

〔this invention〕

1: Tap the surface

11: First base edge

12: Second base edge

13: Bevel

14: Third base edge

15: Fourth base edge

16: Tap the center point

2: perforation

2a: first perforation

2b: Second perforation

2c: third perforation

C: Suspension

A: Central axis

D1: first distance

D2: Second distance

D3: The third distance

D4: Fourth distance

D5: Fifth distance

F: frame

L1: first length

L2: second length

L3: third length

L4: Fourth length

P: bell board

S1: Shortest distance

[FIG. 1] A top view of the first embodiment of the bell board with harmonic multiplier tone according to the present invention.

[FIG. 2] A top view of the second embodiment of the bell board with harmonic multiplier tones of the present invention.

[FIG. 3] A combination diagram of the percussion instrument having the bell plate according to the present invention.

[Fig. 4a] The eighth mode shape diagram of the scale F ^# 5 of the design method of the ringing plate with harmonic multiplier tone of the present invention.

[Fig. 4b] The 10th mode shape diagram of the scale F ^# 5 of the design method of the ringing plate with harmonic multiplier tone of the present invention.

[Fig. 4c] The 12th mode shape diagram of the scale F ^# 5 of the design method of the ringing plate with harmonic multiplier tones of the present invention.

In order to make the above-mentioned and other objects, features and advantages of the present invention more obvious and easy to understand, the preferred embodiments of the present invention are exemplified below, and are described in detail as follows in conjunction with the accompanying drawings:

Please refer to FIG. 1 , which is a first embodiment of a bell board P with harmonic multiplier tones of the present invention, which includes a striking surface 1 and a plurality of perforations 2 penetrating the Tap face 1.

The bell plate P can be processed from various metal materials to make a structure with the same thickness, such as copper, iron or stainless steel. In this embodiment, the material of the bell plate P is made of stainless steel. The following description is given by taking the density ρ=7871.74kg/m ³ , Young's Modulus E=192.95GPa, Poisson's ratio ν=0.27 and thickness=3mm as an example, but not limited thereto.

The bell plate P has the striking surface 1, and the striking surface 1 can be struck by a striking member (eg, a striking hammer), so as to force the striking surface 1 to vibrate and emit a harmonic multiplier sound. Specifically, the striking surface 1 is located in the XY plane coordinate system. The striking surface 1 has a first base edge 11 extending along the X-axis direction of the plane coordinate system and has a first length L1. The first base edge The two endpoints of 11 are symmetrical to A central axis A, the central axis A is parallel to the Y axis of the plane coordinate system, and the two end points of the first base edge 11 are respectively connected to a second base edge 12 . The second base edge 12 and the first base edge 11 together form a right angle and have a second length L2, and a size ratio of the second length L2 to the first length L1 is between 0.1 and 0.45.

The striking surface 1 also has two hypotenuses 13 and two third bases 14 , the second bases 12 , the hypotenuses 13 and the third bases 14 are symmetrically formed on the other side of the central axis A Another set of the second base edge 12, the hypotenuse 13 and the third base edge 14, the hypotenuse 13 is close to the central axis A and away from the end of the second base edge 12 away from the first base edge 11 The first base edge 11 extends, and two end points of the oblique edge 13 are respectively connected to the second base edge 12 and the third base edge 14 . The third base edge 14 is parallel to the central axis A and has a third length L3, and a size ratio of the third length L3 to the first length L1 is between 0.3 and 0.45.

A fourth base edge 15 extends along the X-axis direction. Two end points of the fourth base edge 15 are symmetrical to the central axis A, and are respectively connected to one end of the two third base edges 14 away from the hypotenuse 13 . There is a shortest distance S1 between the four base sides 15 and the first base side 11 , and the size ratio of the shortest distance S1 to the first length L1 is between 0.85 and 1.15. The fourth base edge 15 has a fourth length L4, and a size ratio of the fourth length L4 to the first length L1 is between 0.13 and 0.17. In this way, the first base edge 11 , the two second base edges 12 , the two hypotenuse edges 13 , the two third base edges 14 and the fourth base edge 15 can be together to form the external shape of the striking surface 1 . .

In this embodiment, in order to enable the ringing board P to emit a double frequency tone of the fundamental frequency, it is preferable to make the size ratio of the second length L2 and the first length L1 equal to 0.14, and the third length L3 and the The size ratio of the first length L1 is equal to 0.35, the size ratio of the shortest distance S1 to the first length L1 is equal to 0.97, and the size ratio of the fourth length L4 to the first length L1 is equal to 0.14.

The plurality of perforations 2 are used for fixing the bell board P to a percussion instrument, and the plurality of perforations The holes 2 penetrate through the striking surface 1. In this embodiment, the plurality of through holes 2 are described below by taking a first through hole 2a, a second through hole 2b and a third through hole 2c as an example.

Specifically, the first through hole 2a and the second through hole 2b are disposed opposite to the central axis A, and the first through hole 2a and the second through hole 2b have a first hole between the first base edge 11 and the first base edge 11 respectively. A distance D1, the size ratio of the first distance D1 and the first length L1 is between 0.13-0.16; in addition, the first through hole 2a and the second through hole 2b, respectively, have a distance between the second base edge 12 and the second base edge 12 . A second distance D2, the size ratio of the second distance D2 and the first length L1 is between 0.2-0.3; the third through hole 2c is located on the central axis A and has a gap between the fourth base edge 15 The third distance D3, the size ratio of the third distance D3 and the first length L1 is between 0.05-0.2.

In this embodiment, in order to prevent the first through hole 2a, the second through hole 2b and the third through hole 2c from affecting the vibration of the mode shape of the ringing plate P, the first distance D1 is preferably set. The size ratio to the first length L1 is equal to 0.14, the size ratio of the second distance D2 to the first length L1 is equal to 0.25, and the size ratio of the third distance D3 to the first length L1 is equal to 0.12.

It is worth mentioning that, under the condition that the material parameters (such as: density, Young's coefficient) and thickness of the ringing plate P remain unchanged, the scale frequencies generated by the above-mentioned embodiment of the ringing plate P can be scaled by equal proportions. The first base edge 11 , the second base edge 12 , the hypotenuse 13 , the third base edge 14 and the fourth base edge 15 of the striking surface 1 enable the fundamental tone of the ringing board P to conform to the natural frequencies of other scales. Please refer to Table 1, taking the first base edge 11 as the scaling standard as an example, when the length of the first base edge 11 is scaled from 16.3 cm to 14.1 cm, in this embodiment, the The two base sides 12 , the hypotenuse 13 , the third base side 14 and the fourth base side 15 are scaled in equal proportions, so that the fundamental tone of the ringing board P is transformed from the scale G5 to the scale C6 .

The striking surface 1 of the ringing board P with simple harmonic multiplier tone of the present invention may also have a knocking area, so that the knocking area can excite the vibration of the modal shape of the ringing board P, The knocking area is preferably located on the knocking surface 1 except for the first through hole 2a, the second through hole 2b and the third through hole 2c. In this embodiment, the knocking area is an area formed by the first through hole 2a, the second through hole 2b and the third through hole 2c. The first through hole 2a and the second through hole 2b are connected to form an area. For a straight line, the striking area takes the intersection of the central axis A and the straight line as a striking center point 16 .

Furthermore, in order to excite the fundamental tone and the double frequency tone when the striking center point 16 is struck, there is a fourth distance D4 between the striking center point 16 and the first base edge 11 . The size ratio of the distance D4 to the first length L1 is between 0.13 and 0.32, and preferably equal to 0.31. In addition, there is a fifth distance D5 between the knock center point 16 and the fourth base edge 15 , and the size ratio of the fifth distance D5 to the first length L1 is between 0.7 and 0.9, and preferably equal to 0.84.

When the bell board P with simple harmonic multiplier tone of the present invention is in use, the user can make the bell board P excite several natural frequencies by tapping the striking area of the striking surface 1, and the number of The lowest frequency among the natural frequencies is a fundamental tone, that is, the frequency of a standard note (eg, the frequency of C6 is 1047Hz), and the natural frequencies other than the fundamental tone form an overtone (eg, the frequency of C7 is 2093Hz), so that The frequency ratio of each of the overtones to the fundamental tone can form the effect of simple harmonic multipliers in a proportional relationship close to an integer multiple.

Please refer to FIG. 2 , which is a second embodiment of the ringing board P with simple harmonic multipliers of the present invention. In this embodiment, the ringing board P can emit a triple frequency of the fundamental frequency. It is preferable to make the size ratio of the second length L2 to the first length L1 equal to 0.41, the size ratio of the third length L3 to the first length L1 to be equal to 0.39, and the shortest distance S1 to the first length L1 The size ratio of the fourth length L4 is equal to 1.09, and the size ratio of the fourth length L4 to the first length L1 is equal to 0.15.

In the second embodiment of the present invention, in order to make the first through hole 2a, the second through hole 2b and the third through hole 2c will not affect the sounding mode of the ringing board P, preferably the ratio of the first distance D1 to the first length L1 is equal to 0.15, the second distance D2 to the first The size ratio of the length L1 is equal to 0.24, and the size ratio of the third distance D3 to the first length L1 is equal to 0.15.

In the second embodiment of the present invention, in order to excite the fundamental tone and the triple frequency tone when the striking center point 16 is struck, the size ratio of the fourth distance D4 to the first length L1 is preferably equal to 0.15 , the size ratio of the fifth distance D5 to the first length L1 is preferably equal to 0.78.

It is worth mentioning that, under the condition that the material parameters (such as: density, Young's coefficient) and thickness of the ringing plate P remain unchanged, the scale frequencies generated by the above-mentioned embodiment of the ringing plate P can be scaled by equal proportions. The first base edge 11 , the second base edge 12 , the hypotenuse 13 , the third base edge 14 and the fourth base edge 15 of the striking surface 1 enable the fundamental tone of the ringing board P to conform to the natural frequencies of other scales. Please refer to Table 1. Taking the first base edge 11 as the scaling standard as an example, when the length of the first base edge 11 is scaled from 15.9 cm to 13 cm, in this embodiment, the second base edge 11 can be The base side 12 , the hypotenuse side 13 , the third base side 14 and the fourth base side 15 are scaled in equal proportions, so that the fundamental note of the ringing board P is transformed from the scale F5 to the scale C6 .

Please refer to Fig. 3, which is a percussion instrument with a bell plate according to the present invention, which includes several bell plates P, a frame body F and a plurality of suspension parts C as described in the foregoing embodiments. The component C is used for suspending the plurality of bell boards P on the frame F. In detail, the suspension member C can penetrate through the perforation 2 on the striking surface 1, so as to suspend the bell board P on the frame body F, for example, but not limited to, the suspension member C Can be fishing line, wire, or a combination thereof. Wherein, the scales that can be generated by the several ringing boards P may be the same or different. In this embodiment, the several ringing boards P are G ^# 6, A6, A ^# 6, B6, C7, C ^# 7, D7, D ^# 7, E7, F7 and other fundamental scale sequences are used as the implementation of the percussion instrument, but not limited to this.

The percussion instrument with the bell plate of the present invention may also have a percussion member (eg, a percussion hammer), which is used by the player to strike the bell plate P to emit harmonic multiplier tones.

A preferred embodiment of the method for designing a bell board with harmonic multiplier tones of the present invention, the design method can utilize a computer system to connect a database as an execution framework, and the computer system executes a design operation software, such as : Dedicated application program or finite element analysis software (eg ANSYS) with its internal function library, etc. The design method includes the following steps.

Input a set of design parameters into the computer system to establish a mathematical model of the aforementioned ringing board P, the set of design parameters may include parameters such as the appearance size, thickness, material density, Young's coefficient and Poisson's ratio of the striking surface 1 , and the setting positions of the plurality of perforations 2 on the striking surface 1, in this embodiment, the material of the ringing plate P is stainless steel, the density of the stainless steel ρ=7871.74kg/m ³ , the Young’s coefficient ( Young's Modulus) E=192.95GPa, Poisson's ratio (Poisson's ratio) ν=0.27 and thickness=3mm, but this is not a limitation of the present invention.

After establishing the mathematical model, the computer system performs finite element analysis on the mathematical model to obtain several mode shapes and corresponding several natural frequencies of the mathematical model. In this embodiment, whether the computer system uses the finite element analysis software to establish the mathematical model, or executes finite element analysis to obtain several mode shapes and corresponding natural frequencies of the mathematical model, all are the invention. Those with ordinary knowledge in the technical field can understand it, and details are not described here.

Please refer to Figures 4a to 4c, which are the 8th, 10th and 12th mode shape diagrams of the scale F ^# 5, respectively. In the present invention, in order to make the first perforation 2a, the second perforation 2b and the The third through-hole 2c will not affect the sounding mode of the ringing board P, the first through-hole 2a, the second through-hole 2b and the third through-hole 2c are preferably set on the modal vibration of the striking surface 1. The nodal line position of the mode shape, that is, the position where the modal displacement of the mode shape diagram is equal to zero. In this way, the computer system can overlap the three-mode mode shape diagrams to obtain a plurality of fixed point regions, and the plurality of fixed point regions are located at the nodal line positions of each of the mode shape diagrams. Therefore, the computer system can respectively set the first through hole 2a, the second through hole 2b and the third through hole 2c in the fixed point regions, and establish the mathematical model accordingly.

On the other hand, since the striking area can be struck to generate harmonic octave tones, the striking area must be set at a place other than the nodal line position of the mode shape. In this way, the computer system can overlap the three-mode mode shape diagrams to obtain a plurality of dynamic point regions, and the plurality of dynamic point regions are all located outside the nodal line positions of each of the mode shape diagrams. Therefore, the computer system can use the plurality of moving point areas as the striking area, preferably the moving point area closer to the center of the striking surface 1 as the striking area, and establish the mathematical model accordingly. .

The computer system can set several target frequencies for the mathematical model for correcting the several natural frequencies; then, the computer system can correct the design parameter group according to the corrected several natural frequencies, and according to the corrected several natural frequencies The design parameter group modifies the shape structure of the mathematical model, so that the mathematical model can be used as a basis for the subsequent casting and processing of the bell plate P, and the bell plate P can be struck to emit a simple harmonic frequency tone.

，其中，F(D)為該數個自然頻率與該數個目標頻率的誤差平方平均根；f _N為第N個自然頻率的頻率，f _objN為第N個目標頻率的頻率，N為該自然頻率與該目標頻率的編號，且N=1,2,3,…,i，i為該自然頻率與該數個目標頻率的數量，且i≧2。 Specifically, the computer system can use a numerical approximation method (Approximation Method) to calculate the minimum error square mean root of several natural frequencies and several target frequencies of the mathematical model, and the numerical approximation method can be, for example, a Newton method ( Newton's method) or the optimization function of the finite element analysis software (such as: SUBP, SWEEP of ANSYS); the computer system uses the minimum square mean root of error as an objective function (Objective) to optimize the design parameter set Function) to correct the several natural frequencies, wherein the formula of the objective function can be shown in the following (1):

, where F(D) is the square mean root of the error between the natural frequencies and the target frequencies; f _N is the frequency of the Nth natural frequency, f _objN is the frequency of the Nth target frequency, and N is the frequency of the Nth target frequency. The numbers of the natural frequency and the target frequency, and N=1,2,3,...,i, i is the number of the natural frequency and the number of target frequencies, and i≧2.

，其中，ε _r 為第r個自然頻率與第r個目標頻率之誤差百分比，r=1,2,3,…，f _r為第r個自然頻率的頻率，f _objr為第r個目標頻率的頻率，r為該自然頻率與該目標頻率的編號。 Preferably, in order to enable the mathematical model to generate simple harmonic octave tones that are closer to the proportional relationship of integer multiples, the computer system can make the error percentage between the natural frequency and the target frequency less than 5%, and the formula for the error percentage is It can be shown in the following formula (2):

, where ε _r is the error percentage between the r-th natural frequency and the r-th target frequency, r=1,2,3,…, f _r is the frequency of the r-th natural frequency, and f _objr is the r-th target frequency frequency, r is the number of the natural frequency and the target frequency.

In this embodiment, the ringer of the double-frequency tone is described below by taking two target frequencies and two natural frequencies as examples. The two target frequencies are in a proportional relationship close to an integer multiple, as shown in Table 3. , among which, the modal number system recorded in Table 2 is expressed as the generation sequence of the modal shape of the ringing plate P, for example: F-08 is the eighth modal shape. On the other hand, three target frequencies and three natural frequencies are used as an example for the following description of the ringer of triple frequency tone. The three target frequencies are in a proportional relationship close to an integer multiple, as shown in Table 4.

In order to verify the reliability of the design method of the ringing board with simple harmonic octave tone of the present invention, the computer system is an experimental modal analysis software (eg: SIGLAB), and the mathematical model of the ringing board P is executed. modal analysis to obtain several mode shapes and corresponding natural frequencies of the mathematical model. Take the natural frequencies of finite element analysis and experimental modal analysis recorded in Table 4 as the target frequency and natural frequency of the above formula (2), respectively, to obtain the difference between the natural frequency of the mathematical model of the ringing board P and the target frequency. The average square root of the minimum error, and the error range of the average square root of the minimum error falls between 1.88 and 3.82. In this way, the natural frequencies and modal shapes of the finite element analysis and experimental modal analysis of the mathematical model of the ringing plate P correspond well, and the frequency ratios of the experimental modal analysis in Tables 5 and 6 are close to 1, respectively. : 2 and 1: 2: 3 integer multiples of multiplier tones, which can prove the reliability of the design method of the ringing board with simple harmonic multiplier tones of the present invention.

Preferably, the computer system can convert the set of design parameters of the mathematical model into an output file, which can be processed by the manufacturer (eg, using laser processing technology, etc.) to manufacture the aforementioned bell board P, so as to make the bell board P. P can be tapped to produce simple harmonic octave tones with a proportional relationship close to an integer multiple.

To sum up, the bell board with simple harmonic multiplier tone, the percussion instrument with the bell board, and the design method of the bell board of the present invention can make the bell board generate simple harmonics after being struck Octave tone, simple harmonic double or simple harmonic triple tone, and the first perforation, the second perforation and the third perforation are located at the nodal line position of the mode shape of the ringing board, and will not Affect the sounding mode of the bell board, and the audio frequency of the harmonic multiplier can be designed through the parameter conditions of the design variable group, which can make the bell board emit a simple harmonic multiplier sound and easy to adjust the bell The simple harmonic multiplier tone of the board can be used in applications that require rich The performance of percussion skills and the style of music suitable for performance are not limited.

Although the present invention has been disclosed by the above-mentioned preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make various changes and modifications relative to the above-mentioned embodiments without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the patent application attached hereto.

1: Tap the surface

11: First base edge

12: Second base edge

13: Bevel

14: Third base edge

15: Fourth base edge

16: Tap the center point

2: perforation

2a: first perforation

2b: Second perforation

2c: third perforation

A: Central axis

D1: first distance

D2: Second distance

D3: The third distance

D4: Fourth distance

D5: Fifth distance

L1: first length

L2: second length

L3: third length

L4: Fourth length

P: bell board

S1: Shortest distance

Claims (5)

A bell board with simple harmonic multiplier tone, comprising: a striking surface, which is located in an XY plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length , the two end points of the first base edge are symmetrical to a central axis, the central axis system is parallel to the Y axis of the plane coordinate system, one of the end points of the first base edge is connected to a second base edge, the second base edge It forms a right angle with the first base edge and has a second length, the ratio of the second length to the first length is equal to 0.14, starting from the end of the second base edge away from the first base edge, close to the The central axis extends a hypotenuse away from the first base edge, two end points of the hypotenuse are respectively connected to the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third base edge length, the ratio of the third length to the first length is equal to 0.35, and the other end point of the first base edge connects to another second base edge, and sequentially connects another hypotenuse and another third base edge, The central axis is the axis of symmetry to form two second base edges, two hypotenuses and two third base edges that are symmetrical to each other, a fourth base edge extends along the X-axis direction, and the two end points of the fourth base edge Symmetrical to the central axis, one end of the fourth base edge is connected to one end of the third base edge away from the hypotenuse on the same side, and the other end of the fourth base edge is connected to the other third base edge. The base edge is far from one end of the hypotenuse on the same side, the first base edge, the two second base edges, the two hypotenuse edges, the two third base edges and the fourth base edge can be together to form the knock The appearance shape of the surface, there is a shortest distance between the fourth base edge and the first base edge, the ratio of the shortest distance to the first length is equal to 0.97, the fourth base edge has a fourth length, the first The ratio of the size of the four lengths to the first length is equal to 0.14; and a plurality of perforations penetrate through the striking surface, the plurality of perforations have a first perforation, a second perforation and a third perforation, the first perforation and the The second through holes are disposed opposite to the central axis, the first through holes and the second through holes respectively have a first distance from the first base edge, and the ratio of the first distance to the first length is equal to 0.14 , there is a second distance between the first through hole and the second through hole and the second base edge respectively, the size ratio of the second distance to the first length is equal to 0.25, the third through hole The hole is located on the central axis and has a third distance from the fourth base edge, and a size ratio of the third distance to the first length is equal to 0.12. A bell board with simple harmonic multiplier tone, comprising: a striking surface, which is located in an XY plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length , the two end points of the first base edge are symmetrical to a central axis, the central axis system is parallel to the Y axis of the plane coordinate system, one of the end points of the first base edge is connected to a second base edge, the second base edge It forms a right angle with the first base edge and has a second length, and the ratio of the second length to the first length is equal to 0.41, starting from the end of the second base edge away from the first base edge, close to the The central axis extends a hypotenuse away from the first base edge, two end points of the hypotenuse are respectively connected to the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third base edge length, the ratio of the third length to the first length is equal to 0.39, the other end point of the first base edge connects to another second base edge, and connects the other hypotenuse and another third base edge in sequence, The central axis is the axis of symmetry to form two second base edges, two hypotenuses and two third base edges that are symmetrical to each other, a fourth base edge extends along the X-axis direction, and the two end points of the fourth base edge Symmetrical to the central axis, one end of the fourth base edge is connected to one end of the third base edge away from the hypotenuse on the same side, and the other end of the fourth base edge is connected to the other third base edge. The base edge is far from one end of the hypotenuse on the same side, the first base edge, the two second base edges, the two hypotenuse edges, the two third base edges and the fourth base edge can be together to form the knock The appearance shape of the surface, there is a shortest distance between the fourth base edge and the first base edge, the ratio of the shortest distance to the first length is equal to 1.09, the fourth base edge has a fourth length, the first The ratio of the size of the four lengths to the first length is equal to 0.15; and a plurality of perforations penetrate through the striking surface, the plurality of perforations have a first perforation, a second perforation and a third perforation, the first perforation and the The second through holes are disposed opposite to the central axis, the first through holes and the second through holes have a first distance from the first base edge respectively, and the ratio of the first distance to the first length is equal to 0.15 , between the first through hole and the second through hole and the second base edge respectively There is a second distance, and the ratio of the second distance to the first length is equal to 0.24, the third through hole is located on the central axis and has a third distance from the fourth base edge, the third distance and the The dimension ratio of the first length is equal to 0.15. A percussion instrument with a bell board, which has the bell board with simple harmonic octave tone as described in any one of items 1 to 2 of the scope of the application, further comprising: a body; and a plurality of suspensions A piece is passed through the plurality of through holes of the bell plates, and the bell plates are suspended on the frame body. A method for designing a bell board with simple harmonic octave tone, comprising: inputting a design parameter group into a computer system to establish a mathematical model of a bell board, the bell board having a striking surface, Located in the XY plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length, the two end points of the first base edge are symmetrical to a central axis, the central axis system Parallel to the Y axis of the plane coordinate system, one end point of the first base edge is connected to a second base edge, the second base edge and the first base edge together form a right angle and have a second length, the second base edge The ratio of the length to the first length is equal to 0.14, starting from the end of the second base edge away from the first base edge, extending a hypotenuse near the central axis and away from the first base edge, and the two ends of the hypotenuse The points are respectively connected to the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third length, and the ratio of the third length to the first length is equal to 0.35, and the first base edge is equal to 0.35. The other end point of the base edge is connected to another second base edge, and sequentially connected to another hypotenuse and another third base edge, and the central axis is used as the axis of symmetry to form two second base edges, two base edges that are symmetrical to each other. A hypotenuse and two third base edges, a fourth base edge extends along the X-axis direction, two end points of the fourth base edge are symmetrical with the central axis, and one end point of the fourth base edge is connected to one of the One end of the third base edge away from the hypotenuse on the same side, the other end of the fourth base edge is connected to the other end of the third base edge away from the hypotenuse on the same side, the first base edge, the two The second base edge, the two hypotenuse edges, the two third base edges and the fourth base edge can be surrounded together The appearance shape of the striking surface is formed. There is a shortest distance between the fourth base edge and the first base edge. The ratio of the shortest distance to the first length is equal to 0.97. The fourth base edge has a fourth base edge. length, the ratio of the fourth length to the first length is equal to 0.14, the bell plate has a plurality of perforations running through the striking surface, and the plurality of perforations have a first perforation, a second perforation and a third perforation , the first through hole and the second through hole are arranged opposite to the central axis, and there is a first distance between the first through hole and the second through hole and the first base edge, the first distance and the first The dimension ratio of a length is equal to 0.14, the first through hole and the second through hole respectively have a second distance from the second base edge, and the dimension ratio of the second distance to the first length is equal to 0.25, the third The through hole is located on the central axis and has a third distance from the fourth base edge, and the size ratio of the third distance to the first length is equal to 0.12; the computer system performs finite element analysis on the mathematical model to obtain Several mode shapes and corresponding several natural frequencies of the mathematical model; the computer system sets several target frequencies for the mathematical model for correcting the several natural frequencies; the computer system determines the corrected several natural frequencies according to the The natural frequency modifies the design parameter group; and the computer system modifies the shape structure of the mathematical model according to the modified design parameter group, so that the ringing board emits a simple harmonic octave tone when struck. A method for designing a bell board with simple harmonic octave tone, comprising: inputting a design parameter group into a computer system to establish a mathematical model of a bell board, the bell board having a striking surface, Located in the XY plane coordinate system, the striking surface has a first base edge extending along the X-axis direction of the plane coordinate system and has a first length, the two end points of the first base edge are symmetrical to a central axis, the central axis system Parallel to the Y axis of the plane coordinate system, one end point of the first base edge is connected to a second base edge, the second base edge and the first base edge together form a right angle and have a second length, the second base edge The ratio of the length to the first length is equal to 0.41, starting from the end of the second base edge away from the first base edge, and extending a hypotenuse near the central axis and away from the first base edge. Two end points are respectively connected to the second base edge and a third base edge, the third base edge is parallel to the central axis and has a third length, and the dimension ratio of the third length to the first length is equal to 0.39, the The other end point of the first base edge is connected to another second base edge, and sequentially connected to another hypotenuse and another third base edge, and the central axis is used as the axis of symmetry to form two mutually symmetrical second base edges , two hypotenuses and two third base edges, a fourth base edge extends along the X-axis direction, the two end points of the fourth base edge are symmetrical to the central axis, and one of the end points of the fourth base edge is connected to it One end of the third base edge far from the hypotenuse on the same side, the other end of the fourth base edge is connected to the other end of the third base edge away from the hypotenuse on the same side, the first base edge, The two second base edges, the two hypotenuse edges, the two third base edges and the fourth base edges can be together to form the appearance shape of the striking surface, and the fourth base edge and the first base edge are having a shortest distance, the ratio of the shortest distance to the first length is equal to 1.09, the fourth base edge has a fourth length, the ratio of the fourth length to the first length is equal to 0.15, the bell board has A plurality of perforations penetrate the striking surface, the perforations have a first perforation, a second perforation and a third perforation, the first perforation and the second perforation are arranged opposite to the central axis, the first perforation There is a first distance between the through hole and the second through hole and the first base edge, respectively, and the ratio of the first distance to the first length is equal to 0.15. The first through hole and the second through hole are respectively connected to the second There is a second distance between the base edges, the ratio of the second distance to the first length is equal to 0.24, the third through hole is located on the central axis and has a third distance from the fourth base edge, the first The size ratio of the three distances to the first length is equal to 0.15; the computer system performs finite element analysis on the mathematical model to obtain several mode shapes and corresponding several natural frequencies of the mathematical model; The mathematical model sets a number of target frequencies for correcting the number of natural frequencies; the computer system corrects the design parameter set according to the corrected number of natural frequencies; and the computer system corrects the design parameter set according to the corrected design parameter set The shape structure of the mathematical model is modified, so that the bell board emits a simple harmonic octave tone when struck.

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