Analysis of bifurcation and chaos of the piezoelectric plate including damage effects

作者：Fu, Yi Ming^*; Wang, Xian Qiao

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2008, 9(1): 61-74.

• piezoelectric plates
• tensor valued internal state variables
• bifurcation and chaos
• damage
• dynamic stability

This paper presents a constitutive model for piezoelectric materials containing a substantive of distributed cracks. The model is formulated in a continuum damage mechanics framework using internal variables taken as second rank tensors. Based on the Talreja's tensor valued internal state damage variables as well as the Helmhotlz free energy of piezoelectric materials, the constitutive model is applied to analysis of bifurcation and chaos of the piezoelectric plate considering damage effects. The von Karman's plate theory is adopted to derive nonlinear dynamic equations of the piezoelectric plates with damage under a transverse periodic load. The Galerkin method and Runge-Kutta procedure are used to solve the nonlinear equations. The effect of damage value, damage position and electrical loads on the bifurcation and chaos of the piezoelectric plate are determined and discussed. Present results provide a theoretical basis for the design of dynamic stability and nondestructive testing of the piezoelectric structures.

• 出版日期2008
• 单位湖南大学