Thermal vibrations of beams and plates with temperature-dependent properties

Rapidly applied intense thermal loadings may produce mechanical vibrations of thin structural components. Thermal conductivity and the modulus of elasticity of high-temperature materials such as graphite or silicon carbide are functions of temperature. Thus for accurate design of components operating in a high temperature range, it is necessary to account for the effects of the temperature dependent material properties. An analysis is made of beams and plates in which temperature-dependent conductivity and elasticity are included. The beam and plate equations of motion are modified to account for thermal loading and temperature-dependent material properties. The modified equations consist of homogeneous differential equations with variable coefficients and nonhomogeneous boundary conditions. The solutions are based on the fact that the solutions can be separated into quasistatic solutions satisfying the nonhomogeneous boundary conditions and dynamic solutions satisfying the homogeneous boundary conditions. Temperature histories throughout the material are obtained by the finite-difference (Crank-Nicolson) method. Comparisons are made of temperatures, stresses, and deflections for different materials in which the modulus may exhibit a positive or negative change with increasing temperature