Effect of a thermal gradient on the natural frequencies of a rectangular plate

Abstract The effect of a constant thermal gradient on the transverse vibrational frequencies of a simply supported rectangular plate is investigated. Bounds for the eigen-frequencies are obtained for various plate width-to-length ratios as functions of a parameter related to the temperature dependence of the modulus of elasticity of the material. The upper bounds are calculated by the Rayleigh-Ritz method and the lower bounds by the Bazley-Fox second projection method. In all instances, the gap between the bounds over their average is less than one-half of 1 per cent.