The phenomena of bifurcation and chaos are studied for a class of second order nonlinear nonautonomous ordinary differential equations, which may be formulated by the nonlinear radially symmetric motion of the dynamically loaded hyperelastic spherical membrane composed of the Rivlin–Saunders material model with a noninteger power-law exponent. Firstly, based on the variational principle, the governing equation describing the problem is obtained with the spherically symmetric deformation assumption. Then, the dynamic characteristics of the system are qualitatively analyzed in detail in terms of different values of material parameters. Particularly, for a given constant load, the parameter spaces describing the bifurcation behaviors of equilibrium curves are established and the characteristics of equilibrium points are presented; for a periodically perturbed load, the quasi-periodic and chaotic behaviors are discussed for the systems with two and three equilibrium points, respectively.

中文翻译：

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基于非整数幂律本构模型的动态加载超弹性球膜的分岔与混沌现象

研究了一类二阶非线性非自治常微分方程的分岔和混沌现象，该方程可以由具有非整数幂的 Rivlin-Saunders 材料模型组成的动态加载的超弹性球膜的非线性径向对称运动表示。律指数。首先，基于变分原理，利用球对称变形假设得到描述问题的控制方程。然后，根据材料参数的不同取值，对系统的动态特性进行了详细的定性分析。特别是对于给定的恒定载荷，建立了描述平衡曲线分岔行为的参数空间，并给出了平衡点的特征；