Slow-fast dynamics in the truss core sandwich plate under excitations with high and low frequencies

Chen, Zhenyang; Chen, Fangqi; Zhou, Liangqiang

doi:10.1016/j.apm.2020.06.055

Applied Mathematical Modelling

2020

DOI: 10.1016/j.apm.2020.06.055

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Slow-fast dynamics in the truss core sandwich plate under excitations with high and low frequencies

Zhenyang Chen

Fangqi Chen

Liangqiang Zhou

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Cited by 2 publications

References 41 publications

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Numerical analysis of a degenerate generalized Hopf bifurcation

Xue

et al. 2021

Int. J. Mod. Phys. C

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In this paper, we present a numeric bifurcation analysis of the normal form of degenerate Hopf bifurcation truncated up to seventh order with an equilibrium point located at the origin. By applying the genericity nondegenerate conditions and normal form theory, we study the bifurcation analysis of the codimension-3 Takens–Hopf bifurcation for the difficult case, where a rich bifurcation scenario is displayed. The third Lyapunov coefficient is used to distinguish the different cases of a codimension-3 Takens–Hopf bifurcation point, which can be efficiently computed with the aid of a software program based on the symbolic package Maple, presented in Appendix A. The normal form analysis results can be used to depict the complete bifurcation diagrams and phase portraits. In order to investigate the mechanism of the transitions between equilibrium and limit cycles, the methods of two scales in frequency domain are employed to study the evolutions.

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Numerical analysis of a degenerate generalized Hopf bifurcation

Xue

et al. 2021

Int. J. Mod. Phys. C

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Chaotic Dynamics of Non-Autonomous Nonlinear System for a Sandwich Plate with Truss Core

Zhang

2022

Mathematics

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This paper deals with the multi-pulse chaotic dynamics of a sandwich plate with truss core under transverse and in-plane excitations. In order to analyze the complicated nonlinear behaviors of the sandwich plate model by means of the improved extended Melnikov technique, the two-degrees non-autonomous system is transformed into an appropriate form. Through theoretical analysis, the sufficient conditions for the existence of multi-pulse homoclinic orbits and the criterion for the occurrence of chaotic motion are obtained. The damping coefficients and transverse excitation parameters are considered as the control parameters to discuss chaotic behaviors of the sandwich plate system. Numerical results and the maximal Lyapunov exponents are performed to further test the existence of the multi-pulse jumping orbits. The theoretical predictions and numerical results demonstrate that the chaos phenomena may exist in the parametrical excited sandwich plate.

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Slow-fast dynamics in the truss core sandwich plate under excitations with high and low frequencies

Cited by 2 publications

References 41 publications

Numerical analysis of a degenerate generalized Hopf bifurcation

Numerical analysis of a degenerate generalized Hopf bifurcation

Chaotic Dynamics of Non-Autonomous Nonlinear System for a Sandwich Plate with Truss Core

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