Nonlinear vibrations, bifurcations and chaos of piezoelectric composite lattice sandwich plate with four simply supported edges

T. Ma, W. Zhang, Y.F. Zhang and A. Amer

Chaos, Solitons & Fractals, 2024, vol. 183, issue C

Abstract: This paper is devoted to investigate the nonlinear dynamics, bifurcation and chaos of the piezoelectric composite lattice sandwich plate with 1:3 internal resonance. Galerkin method is used to discretize the nonlinear partial differential governing equations of motion into the ordinary differential equations. The multi-scale method is used to obtain the modulation equations of the piezoelectric composite lattice sandwich plate in the polar coordinates and Cartesian coordinates in the primary and parametric resonances, respectively. Using Newton-Raphson method, the bifurcation diagrams of the steady-state equilibrium solution are obtained for the modulation equation with the change of the system parameters. The stability of the steady-state equilibrium solution is analyzed for the modulation equation. The existence of the static bifurcations, such as the saddle-node bifurcation, pitchfork bifurcation and Hopf dynamic bifurcations are found. The complex nonlinear jump phenomena caused by the existence of the multiple nonlinear steady-state solution regions are analyzed in detail. Fourth-order Runge-Kutta method is used to continue tracing the nonlinear periodic solution of the modulation equation in Cartesian coordinates. The time-history diagram, phase portrait and Poincaré map are obtained for the piezoelectric composite lattice sandwich plate in the nonlinear resonance. The dynamic process of the nonlinear periodic solution is described for the modulation equation from the limit cycle oscillation to the chaotic attractor in detail.

Keywords: Piezoelectric lattice sandwich plates; Bifurcation; Chaos; Nonlinear jump phenomenon; Resonance (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077924004922
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:183:y:2024:i:c:s0960077924004922

DOI: 10.1016/j.chaos.2024.114940

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().