Fundamental thermo-elasticity equations for thermally induced flexural vibration problems for inhomogeneous plates and thermo-elastic dynamical responses to a sinusoidally varying surface temperature

Abstract

Equations of motion governing thermally induced vibration of plates with inhomogeneous material properties through the thickness direction are presented. Equations of motion for thermally induced flexural vibration for inhomogeneous rectangular plates in which the material properties are given in the form of a power of the thickness coordinate are derived from the above-mentioned fundamental equations. An exact solution of the one-dimensional temperature change is presented for an inhomogeneous plate in which one surface is exposed to a sinusoidally varying temperature, and the other is kept at zero temperature change. The associated quasi-static and dynamic solutions pertinent to deflection and thermal stresses in the inhomogeneous rectangular plate are derived under the condition of simply supported edges. Numerical calculations are performed, and the effects of material inhomogeneity such as Young’s modulus, coefficient of linear thermal expansion, and mass density, angular frequency in cyclic heating, and aspect ratio on the thermo-elastic response of the rectangular plate are shown in graphical form. Comparing the dynamic solutions with quasi-static ones, the effect of inertia on the thermo-elastic response of the inhomogeneous rectangular plate is evaluated.