Modeling and chaotic dynamics of the laminated composite piezoelectric rectangular plate
type: Item
instance of: scholarly article
title: Modeling and chaotic dynamics of the laminated composite piezoelectric rectangular plate
zbMATH Open document ID: 1407.74065
DOI: 10.1155/2014/345072
author: Xianqiang Yang
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: This paper investigates the multipulse heteroclinic bifurcations and chaotic dynamics of a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. According to the von Karman type equations, Reddy's third-order shear deformation plate theory, and Hamilton's principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. The method of multiple scales and Galerkin's approach are applied to the partial differential governing equation. Then, the four-dimensional averaged equation is obtained for the case of 1\ :\ 3 internal resonance and primary parametric resonance. The extended Melnikov method is used to study the Shilnikov type multipulse heteroclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multipulse chaotic dynamics are analytically obtained. From the investigation, the geometric structure of the multipulse orbits is described in the four-dimensional phase space. Numerical simulations show that the Shilnikov type multipulse chaotic motions can occur. To sum up, both theoretical and numerical studies suggest that chaos for the Smale horseshoe sense in motion exists for the laminated composite piezoelectric rectangular plate.
Mathematics Subject Classification ID: 74M05
Mathematics Subject Classification ID: 74H60
Mathematics Subject Classification ID: 74F15
Mathematics Subject Classification ID: 74H45
zbMATH DE Number: 7016201
Wikidata QID: Q59064374
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/345072
OpenAlex ID: W2090060294
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description: scientific article; zbMATH DE number 7016201