| Abstract: | Thermally induced vibrations of functionally graded material rectangular plates are investigatedin this research. The thermomechanical properties of the plate are assumed to be temperature and positiondependent. Dependency on temperature is expressed based on theTouloukian formula, and position dependencyis written as a power-law function. The ceramic-rich surface of the plate is subjected to temperature rise orheat flux, whereas the metal rich surface is kept at reference temperature or thermally insulated. Temporalevolution of the temperature profile across the plate thickness is obtained by the solution of one-dimensionalheat conduction equation. This equation is originally nonlinear since temperature dependency of thermalconductivity is taken into account. The solution of this equation is obtained by means of the generalizeddifferential quadrature (GDQ) accompanied with the successive Runge–Kutta algorithm in time domain. Themotion equations of the plate are obtained based on the first-order shear deformation theory of plates under smallstrains 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 resultingequations are linear time-dependent coupled equations which are traced in time by means of the Newmarktime-marching method. Conducting comparison studies to assure the validity and accuracy of the proposedmodel, parametric studies are carried out to examine the influences of temperature dependency, thermal andmechanical boundary conditions, power-law index, plate geometry and boundary conditions. It is shown thatthermally induced vibrations exist for thin plates. |
