PERTURBATION SOLUTION TO THE DYNAMIC RESPONSE OF ORTHOTROPIC CYLINDRICAL SHELLS USING THE GENERALIZED THEORY OF THERMOELASTIC1TY

Abstract

The generalized theory of thermoelasticity with one thermal-mechanical coupling coefficient and three thermal relaxation time coefficients is used to solve a boundary value problem of a simply supported orthotopic cylindrical shell subjected to sudden temperature changes and mechanical loadings by the application of a perturbation method. Various techniques of expanding the perturbation coefficients are discussed, and difficulties are identified. The problem of singularities in long time solutions is shown, and a solution procedure is demonstrated. The approximate solution uses Galerkin's method and the Laplace transform. Numerical values of frequencies and displacements are displayed graphically and in tabular form. These results quantitatively show that, for ultrastrength materials with relatively high Young's modulus and thermal expansion coefficients, the coupling effect between strain and temperature fields is not negligible and can be demonstrated with a perturbation method solution.