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首页> 外文期刊>Proceedings of the Institution of Mechanical Engineers. Part K, Journal of Multi-body Dynamics >Chaotic response of a Galerkin shell to constant load and periodic excitation
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Chaotic response of a Galerkin shell to constant load and periodic excitation

机译：Galerkin壳对恒定载荷和周期性激励的混沌响应

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摘要

This study intends to investigate the dynamic behaviour of a non-linear elastic shallow shell of large deflection subjected to constant boundary loading and harmonic lateral excitation. The general governing equation for the shell is established using the Galerkin Principle. Three types of dynamic equation of the shell are developed, corresponding to certain geometry and loading conditions. Melnikov functions are considered for each type. Non-linear responses of the shell to the loads are analysed theoretically. Centre points, saddle points, and homoclinic orbits are determined and analysed on the basis of the governing equations established. The critical conditions for chaos to occur are provided for the vibrations of the shell. Numerical analysis is also performed for the non-linear elastic shell. Chaotic and regular vibrations of the shell are analysed with presentations of time history plots, phase diagrams, and Poincare maps.
机译：本研究旨在研究在恒定边界载荷和谐波横向激励作用下大挠度的非线性弹性浅壳的动力学行为。使用Galerkin原理建立壳体的一般控制方程。根据特定的几何形状和载荷条件，开发了三种类型的壳体动力学方程。每种类型都考虑了梅尔尼科夫函数。理论上分析了壳体对载荷的非线性响应。根据建立的控制方程确定并分析中心点，鞍点和同斜轨道。为壳体的振动提供了发生混沌的临界条件。还对非线性弹性壳体进行了数值分析。通过时间历史图，相图和庞加莱图的显示来分析壳体的混沌振动和规则振动。

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