傾斜機能性圧電薄膜における熱弾性挙動の特性曲線法による数値解析

抄録

This study deals with a one-dimensional dynamic thermoelastic problem in a functionally graded piezoelectric thin film. It is assumed that all response quantities are initially zero. The top surface of the thin film is kept at the reference temperature and the bottom surface is subjected to a sudden temperature rise. For the elastic field, the top surface is fixed to a flat rigid body and the bottom surface is free of stress. For electric field, a voltage is applied between the top and bottom surfaces. The variation of material properties is assumed to be expressed as exponential functions of the space-variable. First, the transient heat conduction equation is solved under the thermal initial and boundary conditions. Solving the equation of electrodynamics under the electrical initial and boundary conditions, the dielectric flux density is derived. The elastic constitutive equation and the equation of motion which govern the particle velocity and thermal stress are solved by employing the method of characteristics. Numerical results are obtained when the material at the top surface of the thin film is taken to be PZT-4. Time histories of thermal stresses at the middle of the thin film are illustrated graphically. The effect of the applied voltage on the thermal stress is discussed.