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Axisymmetric 3: 1 internal resonance of thin-walled hyperelastic cylindrical shells under both axial and radial excitations

薄壁超弹性圆柱壳在轴向和径向组合激励作用下的轴对称3:1内 共振

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Abstract

Nonlinear vibration with axisymmetric 3: 1 internal resonance is investigated for an incompressible neo-Hookean hyperelastic cylindrical shell under both axial and radial harmonic excitations. A full nonlinear strain-displacement relation is derived from the large deflection theory of thin-walled shells. A set of nonlinear differential equations describing the large deflection vibration are formulated by the Lagrange equation and the assumption of small strains. Steady-state responses of the system are predicted via the harmonic balance method with the arc length continuation, and their stabilities are determined via the modified sorting method. The effects of excitations on the steady-state responses are analyzed. The results reveal a crucial role played by the phase difference in the structural response, and the phase difference can effectively control the amplitude of vibration.

摘要

本文研究了不可压缩neo-Hookean超弹性圆柱壳在轴向和径向简谐激励作用下的轴对称3:1内共振问题. 基于薄壳大挠度理论, 导出了考虑所有非线性项的位移-应变关系. 通过Lagrange方程以及小应变假设得到了描述大挠度振动的非线性微分方程组. 采用谐波 平衡法和弧长连续法, 计算了系统的稳态响应, 并且结合改进的排序方法对其稳定性进行了判断. 分析了激励对于稳态响应的影响. 结 果表明, 组合激励的相位差对于结构响应有着非常重要的影响, 通过调节相位差可以有效地控制振动幅值.

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Authors and Affiliations

  1. College of Science, Dalian Minzu University, Dalian, 116600, China

    Jia Jiao  (焦佳) & Xuegang Yuan  (袁学刚)

  2. State Key Laboratory for Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

    Jie Xu  (许杰) & Xuegang Yuan  (袁学刚)

  3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Li-Qun Chen  (陈立群)

Authors
  1. Jia Jiao  (焦佳)
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  2. Jie Xu  (许杰)
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  3. Xuegang Yuan  (袁学刚)
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  4. Li-Qun Chen  (陈立群)
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Corresponding author

Correspondence to Xuegang Yuan  (袁学刚).

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11672069, 11872145, 11872159, 12172086, and 12101106).

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Jiao, J., Xu, J., Yuan, X. et al. Axisymmetric 3: 1 internal resonance of thin-walled hyperelastic cylindrical shells under both axial and radial excitations. Acta Mech. Sin. 38, 521417 (2022). https://doi.org/10.1007/s10409-022-09006-x

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  • DOI: https://doi.org/10.1007/s10409-022-09006-x

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