Multi-pulse orbits dynamics of composite laminated piezoelectric rectangular plate  

作　　者：YAO MingHui ZHANG Wei YAO ZhiGang 

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

出　　处：《Science China(Technological Sciences)》2011年第8期2064-2079,共16页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 10872010, 10732020 and 11072008);the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10425209);the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality;the Ph.D. Programs Foundation of Beijing University of Technology (Grant No. 52001015200701)

摘　　要：The multi-pulse orbits and chaotic dynamics of a simply supported laminated composite piezoelectric rectangular plate under combined parametric excitation and transverse excitation are studied in detail. It is assumed that different layers are perfectly bonded to each other with piezoelectric actuator patches embedded. The nonlinear equations of motion for the laminated composite piezoelectric rectangular plate are derived from von Karman-type equation and third-order shear deformation plate theory of Reddy. The two-degree-of-freedom dimensionless equations of motion are obtained by using the Galerkin approach to the partial differential governing equation of motion for the laminated composite piezoelectric rectangular plate. The four-dimensional averaged equation in the case of primary parametric resonance and 1:3 internal resonances is obtained by using the method of multiple scales. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on the normal form obtained, the energy phase method is utilized to analyze the multi-pulse global bifurcations and chaotic dynamics for the laminated composite piezoelectric rectangular plate. The analysis of the global dynamics indicates that there exist multi-pulse jumping orbits in the perturbed phase space of the averaged equation. Based on the averaged equation obtained, the chaotic motions and the Shilnikov type multi-pulse orbits of the laminated composite piezoelectric rectangular plate are also found by numerical simulation. The results obtained above mean the existence of the chaos in the Smale horseshoe sense for the simply supported laminated composite piezoelectric rectangular plate.

关 键 词：laminated composite piezoelectric rectangular plates multi-pulse orbit chaotic dynamics energy phase method 

分 类 号：O343.1[理学—固体力学] TN384[理学—力学]