Dynamic Behavior And Stability Of Thermal-elastic Circular Thin Plate Under The Action Of Non-conservative Forces

In this paper, dynamic Behavior and Stability of elastic non-conservative circular thin plate, subjected to tangentially uniformly distributed follower forces, is analyzed. The main research work is as follows:(l)By the analysis of force-balance of elements, the axisymmetric governing equations of circular thin plate with movable and unmovable supports in the middle plane, subjected to tangentially uniformly distributed follower forces, are derived. The governing equation is a order four partial differential equation with variable coefficient. On the assumption of oscillation form, the mixed initial-boundary value problem is converted into corresponding two point boundary value problem of ordinary differential equation. Then numerical solutions for the eigenvalue problem of the ordinary differential equation with variable coefficients are obtained by shooting method. Moreover, the characteristic curves between self-excited frequencies and critical loads and their critical divergence load of the circular plate with movable and unmovable simple supports and clamped supports along edges are plotted, and the effect of Possion' s ratio on the self-excited frequencies and critical loads of the circular plate is analyzed.(2) On the basis of the above study, by the Kantorovich averaging method and shooting method, the vibration and the stability of varying thickness thermal-elastic circular thin plate and varying thermal circular thin plate, subjected to non-conservative forces, are studied. Based on the numerical solutions for the eigenvalue problem of the ordinary differential equation, the characteristic curves, under those two conditions, between self-excited frequencies and critical loads and their critical divergence load of the circular plate with unmovable simple supports and clamped supports along edges are plotted. Besides, the effect of the variation of coefficient of thickness and the variation coefficient of thickness temperature on the self-excited frequencies and critical loads of the circular plate is analyzed.(3)At last, based on large deflection theory of circular thin plate, the dynamic governing equation of nonlinear vibration of thermal-elastic circular plate subjected to distributed forces in terms of the displacement of the middle plate are derived. By numerical calculation, the vibration response of thermal-elastic thin plate with unmovable simple supports and clamped supports along edges are obtained. Furthermore, the characteristic curves of fundamental frequencies versus amplitudes for some specific values of follower force are plotted..