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A thin cylinderical shell under thermal and mechanical shocks is considered. In cases that the characteristic times of structural and thermal disturbances are of comparable magnitudes, simultaneus solution of temperature and stress fields is required. For this purpose, the classical equations of coupled dynamic thermoelasticity of thin cylinderical shell are derived. These
equations include the dynamics
equilibrium equations of shells and
energy equations. Since there is no closed form solution for this problem, finite element method is used. The technique used is based on weak formulation of Galerkin weighted residual and Kantrovich approximation for space and time domains. Then governing dynamic equations of an element is derived and assembled for total domain in matrix form. Next, Newmark method is used for solving equations and from that radial and axial displacements, rotations and temperature distributions along cylinder length at various times are calculated. Some other unknowns such as forces, moments, axial and circumferential stresses and radial shear stresses may be found from nodal parameters. In this study, the effect of axial displacement is considered in governing equations. Second order thermal distributions through thickness is applied. Applied pressure, shear and thermal shocks are variables in term of time and longitudinal component of space. In this study, it was shown that the effects of coupling of equations could be considerable. Also, in some cases, neglecting axial displacement from equations was seen to produce large errors. The overall results compared well with previous works in special cases.