无拉力弹性半空间地基上预应力四边自由中厚板的动力响应

DYNAMIC RESPONSE OF INITIALLY STRESSED MODERATELY THICK PLATES WITH FOUR FREE EDGES RESTING ON TENSIONLESS ELASTIC HALF-SPACE FOUNDATIONS

基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载和温度场作用下,无拉力弹性半空间地基上四边自由中厚板在动荷载作用下的动力特性。把地基看作三维弹性半空间体,考虑地基变形衰减,用一组数学上完备的二元多项式作为位形函数,采用pb-2 Rayleigh-Rizt法求得四边自由中厚板的动力响应,并讨论了初应力对板的动挠度和动弯矩的影响。

Based on Reissner-Mindlin first order shear deformation plate theory, the dynamic response of an initially stressed, moderately thick plate with four free edges resting on a tensionless elastic half-space foundation is presented. Initial stresses are induced by in-plane mechanical loads or temperature changes. The foundation is regarded as a three dimensional elastic half-space entity while its weakening deformation is considered. A set of pb-2 eigenfunctions, which effectively satisfies the free edge condition, is adopted, and Rayleigh-Ritz method is employed to determine the deflections and bending moments of the plate. Finally, the effects of initial membrane stress and thermal stress are studied.