Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations  

作　　者：Yan ZHOU Wei ZHANG 

机构地区：[1]Mathematics Science College,Inner Mongolia Normal University [2]Beijing Key Laboratory on Nonlinear Vibrations and Strength of Mechanical Structures,College of Mechanical Engineering,Beijing University of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2017年第5期689-706,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11402127,11290152 and 11072008)

摘　　要：The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.

关 键 词：double Hopf bifurcation composite laminated piezoelectric plate periodic solution quasi-periodic solution 

分 类 号：O175[理学—数学]