Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate

Zhang, Wei; Gao, Mei-juan; Yao, Minghui; Yao, Zhigang

doi:10.1007/s11433-009-0225-8

Cited by 28 publications

(23 citation statements)

References 27 publications

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“…Based on the research presented by Zhang et al [6][7][8][9][10] and Zhang [11], we consider a four edge simply supported rectangular thin plate whose edge lengths are a and b, and thickness is h, respectively. The thin plate is subjected to the transverse and in-plane excitations simultaneously.…”

Section: Equations Of Motion Of the Buckled Thin Platementioning

confidence: 99%

“…Moreover, we consider the case of α 1 = β 1 = α in (10). We want to study the resonant nonlinear dynamics of (10) using the perturbation method.…”

Section: Perturbation Analysis and Exponential Dichotomiesmentioning

confidence: 99%

“…The modal interaction on the first two modes of the rectangular thin plate is studied using the exponential dichotomy and an averaging approach for system (10).…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Based on the study presented in [2], Zhang et al [6,7] extended the Melnikov method to study the multi-pulse chaotic dynamics of a buckled thin plate and laminated composite piezoelectric rectangular plate. Recently, a series of works about the multi-pulse chaotic dynamics for some highdimensional physical systems is presented in [8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Resonant chaotic motions of a buckled rectangular thin plate with parametrically and externally excitations

Zhang

2010

Nonlinear Dyn

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Resonant chaotic motions of a simply supported rectangular thin plate with parametrically and externally excitations are analyzed using exponential dichotomies and an averaging procedure for the first time. The formulas of the rectangular thin plate are derived by a von Karman type equation and the Galerkin's approach. The critical condition to predict the onset of chaotic motions for the full system is obtained by developing a Melnikov function containing terms from the non-hyperbolic mode. We prove that the non-hyperbolic mode of the thin plate does not affect the critical condition for the occurrence of chaotic motions in the resonant case. Simulations also show that the chaotic motions of the hyperbolic subsystem are shadowed by the chaotic motions for the full system of the rectangular thin plate.

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Section: Equations Of Motion Of the Buckled Thin Platementioning

confidence: 99%

“…Moreover, we consider the case of α 1 = β 1 = α in (10). We want to study the resonant nonlinear dynamics of (10) using the perturbation method.…”

Section: Perturbation Analysis and Exponential Dichotomiesmentioning

confidence: 99%

“…The modal interaction on the first two modes of the rectangular thin plate is studied using the exponential dichotomy and an averaging approach for system (10).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Resonant chaotic motions of a buckled rectangular thin plate with parametrically and externally excitations

Zhang

2010

Nonlinear Dyn

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“…Yao et al [16] investigated the Shilnikov type multi-pulse orbits and chaotic dynamics of a four-edge simply supported laminated composite piezoelectric rectangular plate subjected to the in-plane, transverse and piezoelectric excitations by using the energy phase method. The method of multiple scales is utilized to obtain the four-dimensional averaged equation in the case of primary parametric resonance and 1:3 internal resonances Zhang et al [17] analyzed the Shilnikov type multi-pulse chaotic dynamics of a six-dimensional nonlinear system, which represents the averaged equation of a composite laminated piezoelectric rectangular plate subjected to the transverse, in-plane excitations and the excitation loaded by piezoelectric layers. The case of 1:2:4 internal resonances are considered.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Mousa

Sayed

Eldesoky

et al. 2014

Int. J. Dynam. Control

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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 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 multivalued amplitudes and hence to jump phenomena. A comparison with the available published work is reported.

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Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

Zhou

Zhang

2017

Appl. Math. Mech.-Engl. Ed.

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Higher-dimensional chaotic dynamics of a composite laminated piezoelectric rectangular plate

Cited by 28 publications

References 27 publications

Resonant chaotic motions of a buckled rectangular thin plate with parametrically and externally excitations

Resonant chaotic motions of a buckled rectangular thin plate with parametrically and externally excitations

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

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