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首页> 外文期刊>Applied Mathematical Modelling >Computation of axisymmetric nonlinear low-frequency resonances of hyperelastic thin-walled cylindrical shells
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Computation of axisymmetric nonlinear low-frequency resonances of hyperelastic thin-walled cylindrical shells

机译：高弹性薄壁圆柱壳的轴对称非线性低频共振的计算

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摘要

A mathematical modeling is employed to investigate the axisymmetric nonlinear low-frequency vibrations of a class of hyperelastic thin-walled cylindrical shells subjected to axial harmonic excitations. A modified frequency domain method is presented to determine the stability of periodic solutions. Based on the variational method, the system of nonlinear governing differential equations describing the coupled axial-radial vibrations of simply supported shells is derived. Then, the harmonic balance method and the arc length method with two-point prediction are adopted to obtain the complicated steady-state solutions effectively, and the stability is discussed with the modified sorting method. Significantly, numerical results manifest that the length-diameter ratio serves a critical role in the nonlinear low-frequency vibrations, its variation should give rise to abundant nonlinear phenomena, such as the typical softening and hardening, the resonance peak shift and the isolated bubble shaped response.
机译：采用数学建模来研究经受轴向谐波激发的一类超弹性薄壁圆柱壳的轴对称非线性低频振动。提出了一种修改的频域方法以确定周期性解决方案的稳定性。基于变分方法，推导了描述简单负载壳的耦合轴向振动的非线性控制微分方程的系统。然后，采用谐波平衡方法和具有两点预测的弧长方法，以有效地获得复杂的稳态解决方案，并且用修改的分选方法讨论了稳定性。值得注意的是，数值结果表明，长度直径比在非线性低频振动中在非线性低频振动中发挥着关键作用，其变化应该产生丰富的非线性现象，例如典型的软化和硬化，共振峰值偏移和隔离的气泡形状回复。

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  • 来源
    《Applied Mathematical Modelling》 |2021年第6期|332-349|共18页
  • 作者

    Jie Xu; Xuegang Yuan; Jia Jiao; Hongwu Zhang;

  • 作者单位

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

    State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics Dalian University of Technology Dalian 116024 China School of Science Dalian Minzu University Dalian 116600 China;

    School of Science Dalian Minzu University Dalian 116600 China;

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

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Thin-walled hyperelastic cylindrical shell; Low-frequency internal resonance; Harmonic balance method; Arc length method with two-point; prediction; Stability;

    机译：薄壁超弹性圆柱壳;低频内部共振;谐波平衡法;具有两点的弧长方法;预言;稳定;

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