弹性半空间地基上预应力中厚矩形板的横向振动

基于Reissner-Mindlin一阶剪切变形理论,讨论在预加面内机械荷载作用下,弹性半空间地基上四边自由中厚矩形板的横向振动问题。把地基看作三维弹性半空间体,考虑地基变形的衰减。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-Ritz法求得四边自由中厚矩形板的自振频率和在横向简谐荷载作用下的动力响应。讨论了板的长宽比、宽厚比及弹性地基和板的相对刚度对板的自振频率的影响。

Vibration of Initially Stressed Moderately Thick Rectangular Plates on Elastic Half Space Foundation

Based on Reissner-Mindlin first order shear deformation theory,the free and forced vibration analysis for an initially stressed,moderately thick rectangular plate with four free edges on elastic half space foundation was presented.Initial stresses were induced by in-plane mechanical loads.The foundation was regarded as a three dimensional elastic half space entity while its weakening deformation was considered.A set of pb-2 eigenfunctions,which effectively satisfies the free dege condition was adopted and Rayleigh-Ritz method was employed to determine the natural frequencies and dynamic responses of the plate under harmonic load.Numerical results are given in tabular and graphical forms.The effects played by plate aspect ratio,transverse shear deformation,plate-foundation stiffness ratio,and initial membrane stresses were studied.