Static and free vibration response analysis of a functionally graded piezoelectric material plate under thermal, electric, and mechanical loads is done in this study. The displacement field is acquired using the first-order shear deformation theory, and the Hamilton principle is applied to deduce the motion equations. Temperature-dependent material properties of the functionally graded material plate are used, and these properties follow the power-law distributions along the thickness direction. However, the properties of piezoelectric material layers are assumed to be independent of the electric field and temperature. Finite element formulation for the functionally graded piezoelectric material plate is done using the combined effect of mechanical and electrical loads. The effects of parameters like electrical loading, volume fraction exponent N, and temperature distribution on the static and free vibration characteristics of the functionally graded piezoelectric material square plate are analyzed and presented. Responses are obtained in terms of the centerline deflection, axial stress and the nondimensional natural frequency with various boundary conditions. It is observed that the centerline deflection and nondimensional natural frequency increases as exponent N increases. At the same time, the axial stress decreases with an increase in exponent N. The findings of the static and the free vibration analysis suggest the potential application of the functionally graded piezoelectric material plate in the piezoelectric actuator as well as for sensing deflection in bimorph.
Free vibration analysis of a functionally graded material beam: evaluation of the Haar wavelet method
