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作者:

Ma, T. (Ma, T..) | Zhang, W. (Zhang, W..) | Zhang, Y. F. (Zhang, Y. F..) | Amer, A. (Amer, A..)

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EI Scopus SCIE

摘要:

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 NewtonRaphson 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. Fourthorder 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 Poincare 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.

关键词:

Piezoelectric lattice sandwich plates Bifurcation Resonance Chaos Nonlinear jump phenomenon

作者机构:

  • [ 1 ] [Ma, T.]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China
  • [ 2 ] [Zhang, W.]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China
  • [ 3 ] [Zhang, W.]GuangXi Univ, Dept Mech, Nanning 530004, Peoples R China
  • [ 4 ] [Zhang, Y. F.]GuangXi Univ, Dept Mech, Nanning 530004, Peoples R China
  • [ 5 ] [Amer, A.]GuangXi Univ, Dept Mech, Nanning 530004, Peoples R China
  • [ 6 ] [Zhang, W.]GuangXi Univ, State Key Lab Featured Met Mat & Life Cycle Safety, Nanning 530004, Guangxi, Peoples R China
  • [ 7 ] [Zhang, Y. F.]GuangXi Univ, State Key Lab Featured Met Mat & Life Cycle Safety, Nanning 530004, Guangxi, Peoples R China
  • [ 8 ] [Amer, A.]GuangXi Univ, State Key Lab Featured Met Mat & Life Cycle Safety, Nanning 530004, Guangxi, Peoples R China
  • [ 9 ] [Amer, A.]Menoufia Univ, Fac Sci, Dept Math & Comp Sci, Shibin Al Kawm, Egypt

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来源 :

CHAOS SOLITONS & FRACTALS

ISSN: 0960-0779

年份: 2024

卷: 183

7 . 8 0 0

JCR@2022

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SCOPUS被引频次: 4

ESI高被引论文在榜: 0 展开所有

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