The influence of welding residual stress on the vibration characteristics of circular thin plate is investigated herein, with which to solve the non-uniform pre-stress distribution problem. According to the strain-stress relationship equations, the differential formula of thin circular plate with pre-stress distribution is derived. Based on the Rayleigh-Ritz method, the Lagrange energy formulation is constructed. The pre-stress distribution function and vibration displacement trial function are expanded into the cosine trigonometric series, and the approximate solutions of structural free vibration for circular plate is proposed. The thin circular plate with simply-support boundary for example, the influence of different type’s distribution of welding residual stress on the natural frequency and mode shape are compared. The effectiveness and convergence of the proposed method are verified through numerical calculations; and the proposed approach can be used to deal with the arbitrary pre-stress distribution problem.
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