Multi-pulse chaotic dynamics of non-autonomous nonlinear system for a honeycomb sandwich plate

Abstract

The global bifurcations and multi-pulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate under combined parametric and transverse excitations are investigated in this paper for the first time. The extended Melnikov method is generalized to investigate the multi-pulse chaotic dynamics of the non-autonomous nonlinear dynamical system. The main theoretical results and the formulas are obtained for the extended Melnikov method of the non-autonomous nonlinear dynamical system. The nonlinear governing equation of the honeycomb sandwich rectangular plate is derived by using the Hamilton's principle and the Galerkin's approach. A two-degree-of-freedom non-autonomous nonlinear equation of motion is obtained. It is known that the less simplification processes on the system will result in a better understanding of the behaviors of the multi-pulse chaotic dynamics for high-dimensional nonlinear systems. Therefore, the extended Melnikov method of the non-autonomous nonlinear dynamical system is directly utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the two-degree-of-freedom non-autonomous nonlinear system for the honeycomb sandwich rectangular plate. The theoretical results obtained here indicate that multi-pulse chaotic motions can occur in the honeycomb sandwich rectangular plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the honeycomb sandwich rectangular plate. It also demonstrates the validation of the theoretical prediction.

Free Vibration and Hardening Behavior of Truss Core Sandwich Beam

“…In the study, the influences of the structural parameters on the dimensionless linear natural frequencies of the truss core sandwich beam are studied at first by neglecting the nonlinear terms in (20). The face sheets and the truss of the sandwich beam are made of the same material.…”

“…represents the coupled relation between the different modes and the coupled term does not appear when the single mode response is considered. The coefficients in (20) are presented in the Appendix.…”

“…Li and Zhu [19] studied the free vibration of honeycomb sandwich plates by using the improved Reddy third-order shear deformation plate theory. J. H. Zhang and W. Zhang [20] investigated the global bifurcations and multipulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate by using the extended Melnikov method. Yang et al [21] investigated the transverse vibrations and stability of an axially moving sandwich beam.…”

Dynamic properties of truss core sandwich plate with tetrahedral core

“…Liu et al [14] studied the free vibration of the sandwich plate with square honeycomb cores by using a semi-analytical method. Zhang et al [15] investigated the global bifurcations and multi-pulse chaotic dynamics of a simply supported honeycomb sandwich rectangular plate by using the extended Melnikov method.…”

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

“…We have found two papers on bifurcations and chaotic dynamics of sandwich plates. 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.…”