MULTI-PULSE ORBITS AND CHAOTIC DYNAMICS OF A COMPOSITE LAMINATED RECTANGULAR PLATE  

作　　者：Xiangying Gu Wei Zhang Minghui Yao 

机构地区：[1]College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China

出　　处：《Acta Mechanica Solida Sinica》2011年第5期383-398,共16页固体力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10732020 and 11072008);the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB)

摘　　要：This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy＇s third-order shear deformation plate theory and the model of the yon Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton＇s principle. Then, using the second-order Galerkin dis- cretization, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1：1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The theoretic results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation, which also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy＇s third-order shear deformation plate theory and the model of the yon Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton＇s principle. Then, using the second-order Galerkin dis- cretization, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1：1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The theoretic results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation, which also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

关 键 词：composite laminated plate third-order shear theory multi-pulse homoclinic orbit CHAOS 

分 类 号：O415.5[理学—理论物理] TS653[理学—物理]