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Nonlinear Dynamic Bifurcation and Chaos Characteristics of Piezoelectric Composite Lattice Sandwich Plates

College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, P. R. China

E-mail Address: mating19920628@163.com

College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, P. R. China

Department of Mechanics, GuangXi University, Nanning 530004, P. R. China

State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures, GuangXi University, Nanning 530004, P. R. China

E-mail Address: sandyzhang9@163.com

Corresponding author.

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Yufei Zhang

Department of Mechanics, GuangXi University, Nanning 530004, P. R. China

State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures, GuangXi University, Nanning 530004, P. R. China

E-mail Address: yufeizhang73@163.com

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A. Amer

Department of Mechanics, GuangXi University, Nanning 530004, P. R. China

State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures, GuangXi University, Nanning 530004, P. R. China

Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt

E-mail Address: asmaaamer85@science.menofia.edu.eg

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, and

C. W. Lim

https://orcid.org/0000-0003-1030-9063

Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon, Hong Kong SAR, P. R. China

E-mail Address: bccwlim@cityu.edu.hk

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https://doi.org/10.1142/S0218127424500470Cited by:2 (Source: Crossref)

Abstract

This paper investigates the nonlinear bifurcation and chaos characteristics of piezoelectric composite lattice sandwich plates at 1:3 internal resonance. The nonlinear vibration partial differential equation is first discretized to become an ordinary differential equation by applying the Galerkin method. The main resonance modulation equations and the parametric resonance for the external excitation frequency that is close to the system’s second-order modal frequency are then obtained by using the multiscale method. The Newton–Raphson method is subsequently applied to obtain the bifurcation diagram of the steady-state equilibrium of modulation equation with varying system parameters. The equilibrium stability is finally analyzed. We confirm the existence of static bifurcation such as saddle-node bifurcation, pitchfork bifurcation, and Hopf dynamic bifurcation. A detailed analysis is also conducted on the complex nonlinear jump phenomenon caused by the presence of multiple nonlinear steady-state solution regions. In the dynamic Hopf bifurcation interval, the fourth-order Runge–Kutta method is used to continue to track the dynamic periodic solution of the modulation equation in Cartesian coordinates. It is found that there are multiple boundary crises and attractor merging crises in the vibration system for piezoelectric composite lattice sandwich plates.

Keywords:

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