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Author:

Mousa, A.A. (Mousa, A.A..) | Sayed, M. (Sayed, M..) | Eldesoky, I.M. (Eldesoky, I.M..) | Zhang, W. (Zhang, W..)

Indexed by:

EI Scopus

Abstract:

The aim of this paper is to investigate the stability of a simply supported laminated composite piezoelectric rectangular plate under combined excitations. Analysis of the amplitude and phase modulation equations with the associated nonlinear interaction coefficients, as provided by the multiple scale analyses of various 1:1 internal resonance conditions and primary resonance case, where ω 2≅ ω 1 and Ω 3≅ ω 1 is considered. The method of multiple time scale is applied to solve the non-linear differential equations describing the system up to the second-order approximation. All possible resonance cases at this approximation order are extracted. The stable/unstable periodic solutions are determined and are presented through frequency response plots. The analytical results are verified by comparing them with those of numerical integration of the modal equations. The influence of different parameters on the dynamic behavior of the composite laminated piezoelectric rectangular plate is studied. Variation of the some parameters leads to multi-valued amplitudes and hence to jump phenomena. A comparison with the available published work is reported. © 2014, Springer-Verlag Berlin Heidelberg.

Keyword:

Piezoelectricity Resonance Laminated composites Numerical methods Convergence of numerical methods Frequency response Laminating Differential equations Nonlinear equations Difference equations Bifurcation (mathematics)

Author Community:

  • [ 1 ] [Mousa, A.A.]Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shibin El-Kom, Egypt
  • [ 2 ] [Mousa, A.A.]Department of Mathematics and Statistics, Faculty of Science, Taif University, P. O. Box 888, El-Taif, Saudi Arabia
  • [ 3 ] [Sayed, M.]Department of Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf; 32952, Egypt
  • [ 4 ] [Sayed, M.]Department of Mathematics and Statistics, Faculty of Science, Taif University, P. O. Box 888, El-Taif, Saudi Arabia
  • [ 5 ] [Eldesoky, I.M.]Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shibin El-Kom, Egypt
  • [ 6 ] [Zhang, W.]College of Mechanical Engineering, Beijing University of Technology, Beijing; 100124, China

Reprint Author's Address:

  • [sayed, m.]department of mathematics and statistics, faculty of science, taif university, p. o. box 888, el-taif, saudi arabia;;[sayed, m.]department of engineering mathematics, faculty of electronic engineering, menoufia university, menouf; 32952, egypt

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Source :

International Journal of Dynamics and Control

ISSN: 2195-268X

Year: 2014

Issue: 4

Volume: 2

Page: 494-508

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count: 16

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 12

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