点支撑预应力中厚矩形板的横向振动

基于Reissner-Mindlin一阶剪切变形板理论,讨论在预加面内机械荷载或温度场作用下,点支撑中厚矩形板的横向振动。温度场假定沿板表面为均布,沿板厚方向为线性分布的。利用考虑剪切变形影响的Timoshenko梁函数,采用Rayleigh-Ritz法给出不同边界条件下点支撑中厚板的自振频率。结果表明,温度升高与预加面内压力将使板的自振频率下降,支撑点位置的变化、边界约束条件和横向剪切变形效应都对板的自振频率有显著影响。

VIBRATIONS OF INITIALLY STRESSED MODERATELY THICK RECTANGULAR PLATES WITH POINT SUPPORTS

Based on Reissner-Mindlin first-order shear deformation plate theory, the free vibration analysis of an initially stressed, moderately thick rectangular plate with point supports is presented. The initial stresses are induced by in-plane mechanical loads or temperature field, which is assumed to be a uniform distribution over the plate surface and a linear through-the-thickness temperature gradient. A set of Timoshenko beam eigenfunctions, which satisfies different kinds of geometric boundary conditions, is adopted and Rayleigh-Ritz method is employed to determine the natural frequencies of the plate. Numerical results are given in tabular forms, showing the effects of locations of points, boundary conditions and transverse shear deformation on the vibration characteristics of the plate. The results reveal that the frequencies are reduced by increasing temperature and initial compressive loads.