Thermally Induced Flexural Vibration Problem of Inhomogeneous Rectangular Plates: When Temperature Change at the Bottom Surface Is Kept at Zero

Abstract

Herein, a thermally induced flexural vibration problem of inhomogeneous rectangular plates in which the material constants are given as a power of the coordinate in the thickness direction is considered. Assuming that the top surface of the plate uniformly receives cyclic heat supply and that the bottom surface is kept at zero temperature change, a problem of 1D heat conduction in an unsteady state in the inhomogeneous plate is analyzed theoretically. Analytical solutions of temperature change, deflection, and stresses in the plate with simply supported edges in which power exponents in the material constants are free from any constraints are derived. Performing numerical calculations, an effect of inhomogeneity in the specific heat capacity on amplitude and phase shift in temperature change inside of plate is clarified. To evaluate the influence of inhomogeneity in the material constants on the inertia effect in the thermoelastic response of the plate, amplification factors are defined as ratios of maximum amplitudes in dynamic solutions of deflection and stresses to those in quasistatic solutions. It is clarified that amplification factors in deflection and stresses of the plate are significantly affected by inhomogeneity in the Young's modulus of elasticity and the mass density.