Temperature dependent vibration analysis of functionally graded rectangular plates

A theoretical method is developed to investigate vibration characteristics of initially stressed functionally graded rectangular plates made up of metal and ceramic in thermal environment. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Two types of thermal condition are considered. The first type is that one value of the temperature is imposed on the upper surface and the other (or same) value on the lower surface. The second is that the heat flows from the upper surface to the lower one held at a prescribed temperature. Material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The third-order shear deformation plate theory to account for rotary inertia and transverse shear strains is adopted to formulate the theoretical model. The Rayleigh–Ritz procedure is applied to obtain the frequency equation. The analysis is based on an expansion of the displacements in the double Fourier series that satisfy the boundary conditions. The effect of material compositions, plate geometry, and temperature fields on the vibration characteristics is examined. The present theoretical results are verified by comparing with those in literature.