Nonlinear dynamic responses of a truss core sandwich plate

Zhang, W.; Chen, Jianen; Cao, Dongxing; Chen, L.H.

doi:10.1016/j.compstruct.2013.09.033

Cited by 49 publications

(17 citation statements)

References 35 publications

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“…J.H.Zhang and W. zhang [9] investigated the global bifurcations and multi-pulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate under combined parametric and transverse excitations, they found that multi-pulse chaotic motions can occur in the honeycomb sandwich rectangular plate. Applying the Galerkin's approach, Zhang et al [10] investigated nonlinear dynamic behaviors of a simply supported 3D-Kagome truss core sandwich plate subjected to the transverse and the inplane excitations. The bifurcation diagrams exhibit the existence of period, muti-period and chaotic motions appear alternately.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Responses of a Honeycomb Sandwich Plate Subject to Transverse Excitations

et al. 2018

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Abstract. Nonlinear dynamic behaviors of a simply supported honeycomb sandwich plate subjected to the transverse excitations are investigated in this paper. Based on the classical thin plate theory and Von Karman large deformation theory, the governing equation of motion for the honeycomb sandwich plate is established by using the Hamilton principle. The nonlinear governing partial differential equation is discretized to the ordinary differential equations by differential quadrature method and then solved by Runge-Kutta-Fehlberg method. Based on the numerical simulations, combined with nonlinear dynamic theory, the influences of the frequency and amplitude of the transverse excitation are investigated respectively by using the bifurcation diagrams, Poincare maps and phase portraits. The results exhibit the existence of the period-1, period-2 and chaotic responses with the variation of the excitations, which demonstrate that those motions appear alternately.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Responses of a Honeycomb Sandwich Plate Subject to Transverse Excitations

et al. 2018

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“…The linear natural frequency and nonlinear response of a simply supported square truss core sandwich plate with tetrahedral core are investigated by Chen et al [8]. In [9], Zhang et al studied the nonlinear dynamic responses and periodic solutions of a truss core sandwich plate subjected to the transverse and the in-plane excitations in the presence of 1:2 internal resonance. The influence of the in-plane and transverse excitations on the frequency response curves of each mode for the truss core sandwich plate was investigated by analyzing the strong coupling of two modes.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the developed technique, the multi-pulse Shilnikov-type chaotic dynamics of the various mechanics models [20][21][22][23] have been studied widely. The studies of this paper focus on the global behaviors of the model considered in [9] by the analytical method. We use the global perturbation technique proposed by Kovacic and Wiggins [13] to investigate the Shilnikov-type single-pulse homoclinic orbits and chaotic dynamics for the truss core sandwich plate subjected to the transverse and the in-plane excitations.…”

Section: Introductionmentioning

confidence: 99%

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Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

Zhang

Chen

2017

Math Methods in App Sciences

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Communicated by T. WannerThe Shilnikov-type single-pulse homoclinic orbits and chaotic dynamics of a simply supported truss core sandwich plate subjected to the transverse and the in-plane excitations are investigated in detail. The resonant case considered here is principal parametric resonance and 1:2 internal resonance. Based on the normal form theory, the desired form for the global perturbation method is obtained. By using the global perturbation method developed by Kovacic and Wiggins, explicit sufficient conditions for the existence of a Shilnikov-type homoclinic orbit are obtained, which implies that chaotic motions may occur for this class of truss core sandwich plate in the sense of Smale horseshoes. Numerical results obtained by using the fourth-order Runge-Kutta method agree with theoretical analysis at least qualitatively.It is not difficult to show that, when the condition 3 2ˇ2 4 fI r cos c > 0 is satisfied, the fixed point p 0 is a center, and when the condition 3 2ˇ2 4 fI r cos s < 0 is satisfied, the fixed point q 0 is a saddle, which is connected to itself by a homoclinic orbit. The phase portrait of system (37) is given in Figure 3(a). Following the analysis presented by Kovacic and Wiggins, it is found that for sufficiently small , the

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“…Awrejcewicz et al [24] utilized the BubnovGalerkin approach with high-order approximations and finite difference method to investigate the complex nonlinear vibrations and bifurcations of a transversally and axially excited thin plate strip. Zhang et al [25] investigated the nonlinear dynamic responses of a truss core sandwich plate. Amabili et al [26] investigated the nonlinear vibrations of composite laminated plates with different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Subharmonic Melnikov method of four-dimensional non-autonomous systems and application to a rectangular thin plate

et al. 2015

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The existence and bifurcations of the subharmonic orbits for four-dimensional non-autonomous nonlinear systems are investigated in this paper. The improved subharmonic Melnikov method is presented by using the periodic transformations and Poincaré map. The theoretical results and the formulas are obtained, which can be used to analyze the subharmonic dynamic responses of four-dimensional nonautonomous nonlinear systems. The improved subharmonic Melnikov method is used to investigate the subharmonic orbits of a simply supported rectangular thin plate under combined parametric and external excitations for verifying the validity and applicability of the method. The theoretical results indicate that the subharmonic orbits can occur in the rectangular thin plate with 1:1 and 1:2 internal resonances. The results of numerical simulation also indicate the existence of the subharmonic orbits for the rectangular thin plate, which can verify the analytical predictions.

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Nonlinear dynamic responses of a truss core sandwich plate

Cited by 49 publications

References 35 publications

Nonlinear Dynamic Responses of a Honeycomb Sandwich Plate Subject to Transverse Excitations

Nonlinear Dynamic Responses of a Honeycomb Sandwich Plate Subject to Transverse Excitations

Global bifurcations and single‐pulse homoclinic orbits of a plate subjected to the transverse and in‐plane excitations

Subharmonic Melnikov method of four-dimensional non-autonomous systems and application to a rectangular thin plate

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