Rapid heating of FGM rectangular plates

Abstract

Thermally induced vibrations of functionally graded material rectangular plates are investigated in this research. The thermomechanical properties of the plate are assumed to be temperature and position dependent. Dependency on temperature is expressed based on theTouloukian formula, and position dependency is written as a power-law function. The ceramic-rich surface of the plate is subjected to temperature rise or heat flux, whereas the metal rich surface is kept at reference temperature or thermally insulated. Temporal evolution of the temperature profile across the plate thickness is obtained by the solution of one-dimensional heat conduction equation. This equation is originally nonlinear since temperature dependency of thermal conductivity is taken into account. The solution of this equation is obtained by means of the generalized differential quadrature (GDQ) accompanied with the successive Runge–Kutta algorithm in time domain. The motion equations of the plate are obtained based on the first-order shear deformation theory of plates under small strains and small deformations assumptions. Hamilton’s principle is used to establish the motion equations. These equations are discreted in the plate domain bymeans of the two-dimensional GDQ method. The resulting equations are linear time-dependent coupled equations which are traced in time by means of the Newmark time-marching method. Conducting comparison studies to assure the validity and accuracy of the proposed model, parametric studies are carried out to examine the influences of temperature dependency, thermal and mechanical boundary conditions, power-law index, plate geometry and boundary conditions. It is shown that thermally induced vibrations exist for thin plates.