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Dynamical modeling and analysis of hyperelastic spherical shells under dynamic loads and structural damping

机译：动态载荷下超弹性球壳的动力学建模与分析，结构阻尼

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摘要

This paper investigates the effects of dynamic loads and structural damping on the nonlinear behaviors of incompressible hyperelastic spherical shells modeled by the Yeoh strain energy function. Firstly, the dynamical modeling is formulated for the nonlinear behaviors of the shells by the variational principle, and the second order nonlinear ordinary differential equation describing the radially symmetric motion is obtained. Then, the dynamic behaviors, such as periodic, quasiperiodic and chaotic motions, are discussed under different loading types. Particularly, for constant loads, the first integral of the integrable Hamiltonian system without damping is given and it is numerically proved that there exists an asymmetric "∞" homoclinic orbit for the prescribed material parameters obtained in experiments; moreover, it is found that for different prestretches, the structural parameter has a completely different role on the nonlinearity of the system, and the basins of attraction are given with the structural damping. For periodic loads, there exist some interesting dynamic phenomena, i.e., quasiperiodic oscillation in the approximately integrable Hamiltonian system, limit cycles and chaos with the damping. The criterion for chaos is discussed by the Melnikov method combined with the numerical calculation and the chaos is further analyzed with the Poincare section and the phase plane.
机译：本文研究了动态载荷和结构阻尼对由Yeoh菌株能量函数建模的不可压缩超弹性球形壳的非线性行为的影响。首先，通过变分原理为壳体的非线性行为配制动态建模，获得描述径向对称运动的二阶非线性常微分方程。然后，在不同的负载类型下讨论了诸如周期性，QuaSiodic和混沌运动的动态行为。特别地，对于恒定载荷，给出了不抑制的可集成哈密顿系统的第一积分，并且在数量上证明存在不对称的“∞”的同性轨道，用于实验中获得的规定材料参数;此外，发现针对不同的普拉斯，结构参数对系统的非线性具有完全不同的作用，并且具有结构阻尼的吸引力盆地。对于周期性负载，存在一些有趣的动态现象，即QuaSiperiodic振荡，在大约可排序的哈密顿系统中，限制循环和混乱，随着阻尼。 Celnikov方法讨论了混沌的标准与数值计算结合，并进一步分析了庞的部分和相面的混乱。

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  • 来源
    《Applied Mathematical Modelling》 |2021年第7期|468-483|共16页
  • 作者

    Zhentao Zhao; Xuegang Yuan; Wenzheng Zhang; Datian Niu; Hongwu Zhang;

  • 作者单位

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

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

    School of Science Dalian Minzu University Dalian 116600 PR China;

    School of Science Dalian Minzu University Dalian 116600 PR China;

    State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics Faculty of Vehicle Engineering and Mechanics Dalian University of Technology Dalian 116024 PR 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

    Hyperelastic spherical shell; Structural damping; Dynamic load; Asymmetric "∞" homoclinic orbit; Melnikov method;

    机译：超弹性球形壳;结构阻尼;动态负荷;不对称“∞”同型轨道;Melnikov方法;

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