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Large-Amplitude Oscillations of Hyperelastic Cylindrical Membrane Under Thermal-Mechanical Fields
Acta Mechanica Solida Sinica ( IF 2.2 ) Pub Date : 2021-09-18 , DOI: 10.1007/s10338-021-00278-0
Wenzheng Zhang 1 , Datian Niu 1 , Fengxia Zhao 2
Affiliation  

In this paper, the nonlinear dynamic behaviors of a hyperelastic cylindrical membrane composed of the incompressible Ogden material are examined, where the membrane is subjected to uniformly distributed radial periodic loads at the internal surface and surrounded by a thermal field. A second-order nonlinear differential equation describing the radially symmetric motion of the membrane is obtained. Then, the dynamic characteristics of the system are qualitatively analyzed in terms of different material parameter spaces and ambient temperatures. Particularly, for a given constant load, the bifurcation phenomenon of equilibrium points is examined. It is shown that there exists a critical load, and the phase orbits may be the asymmetric homoclinic orbits of the “\(\infty \)” type. Moreover, for the system with two centers and one saddle point, the dynamic behaviors of the system show softening phenomena at both centers, but the temperature has opposite effects on the stiffness of the structure. For a given periodically perturbed load superposed on the constant term, some complex dynamic behaviors such as quasiperiodic and chaotic oscillations are analyzed. With the Poincaré section and the maximum Lyapunov characteristic exponent, it is found that the ambient temperature could lead to the irregularity and unpredictability of the nonlinear system, and also changes the threshold of chaos.



中文翻译:

超弹性圆柱膜在热力场作用下的大振幅振荡

在本文中,研究了由不可压缩的 Ogden 材料组成的超弹性圆柱膜的非线性动力学行为,其中膜在内表面受到均匀分布的径向周期性载荷,并被热场包围。获得了描述膜径向对称运动的二阶非线性微分方程。然后,根据不同的材料参数空间和环境温度对系统的动态特性进行定性分析。特别地,对于给定的恒定载荷,检查平衡点的分叉现象。表明存在临界载荷,相位轨道可能是“ \(\infty \)“ 类型。此外,对于具有两个中心和一个鞍点的系统,系统的动力学行为在两个中心都表现出软化现象,但温度对结构刚度的影响相反。对于叠加在常数项上的给定周期扰动载荷,分析了一些复杂的动态行为,如准周期振荡和混沌振荡。结合庞加莱截面和最大李雅普诺夫特征指数,发现环境温度会导致非线性系统的不规则性和不可预测性,也改变混沌阈值。

更新日期:2021-09-19
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