Global and Local Dynamics of a Bistable Asymmetric Composite Laminated Shell

Zhenkun Guo,Guoqing Jiang,Ting Dong

doi:10.3390/sym13091690

Abstract

As bistable composite laminated plate and shell structures are often exposed to dynamic environments in practical applications, the global and local dynamics of a bistable asymmetric composite laminated shell subjected to the base excitation is presented in this paper. Temperature difference, base excitation amplitude, and detuning parameters are discussed. With the change of temperature difference, the super-critical pitchfork bifurcation occurs. Three equilibrium solutions corresponding to three equilibrium configurations (two stable configurations and one unstable configuration) can be obtained. With the increase of excitation amplitude, local and global dynamics play a leading role successively. The global dynamics between the two stable configurations behave as the periodic vibration, the quasi-periodic vibration, the chaotic vibration and dynamic snap-through when the excitation amplitude is large enough. The local dynamics that are confined to a single stable configuration behave as 1:2 internal resonance, saturation and permeation when the excitation amplitude is small. Dynamic snap-through and large-amplitude vibrations with two potential wells for the global dynamics will lead to a broad application prospect of the bistable asymmetric composite laminated shell in energy harvesting devices.

Highlights

Bistable composite laminates possess many distinctive features regarding their two stable equilibrium configurations, which have been proposed to generate new deformable and deployable structures in a series of engineering fields
In this paper, the global and local dynamics of a bistable asymmetric composite laminated shell subjected to the base excitation are investigated
When subjected to the base excitation with small amplitude, the shell vibrates around just one stable configuration, which is dominated by the local dynamics while when subjected to the base excitation with large amplitude, the shell vibrates between the two stable configurations, which is dominated by the global dynamics

Summary

Introduction

Bistable composite laminates possess many distinctive features regarding their two stable equilibrium configurations, which have been proposed to generate new deformable and deployable structures in a series of engineering fields. Moore et al [13] investigated the thermal response and stability of the asymmetric laminated plate and shell structures for static snap-through through a varying temperature field. The local dynamics through theoretical modeling of bistable composite laminated plate and shell structures have been investigated by Arrieta et al [24,25]. The bistable composite laminated plate and shell structures prove to be a good candidate for broadband-frequency energy harvesters owing to the dynamic snap-through that exhibits large strains and in turn generates more power compared with the oscillation around a single well [34]. The snap-through of bistable composite laminated plate and shell structures using smart materials such as piezoelectric transducer (PZT) and microfiber composite (MFC) was studied [35].

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Three Equilibrium Configurations

Global Dynamics

Local Dynamics

Conclusions