Chaotic response of a Galerkin shell to constant load and periodic excitation

Abstract

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 Poincaré maps.

Keywords

Galerkin principle elastic shell chaos Melnikov function residue theory non-linear vibration

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