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选用弹性半空间地基模型分析四边自由各向异性矩形地基板的弯曲和稳态振动解析解。将异性薄板控制微分方程与基于弹性半空间地基位移解建立的板与地基变形协调方程相结合,先按对称性分解,然后采用三角级数法得出了弹性半空间地基上四边自由各向异性矩形薄板的弯曲和稳态振动解析解,包括地基反力(幅值)、板的挠度(幅值)、板的内力(幅值)的解析表达式。克服了数值法的弊端,取消了对地基反力的假设,得到了板的内力(幅值)及地基反力(幅值)更切实际的分布规律。算例结果不但与文献结果吻合良好,而且表明对于异形板,对称载荷能引起反对称的内力和变形。该方法使得半空间地基上各向异性矩形薄板这一复杂的接触问题的求解统一化、简单化、规律化。
Elastic Half Space Foundation Model Analysis of Bending and Steady-State Vibration Analysis of Rectangular Free-Form Baseboards with Four Ends. The governing equations of the heterosexual sheet are combined with the equations of the foundation deformation deformation based on the displacement of the elastic half-space foundation. The first is the symmetry decomposition and the third is the free-form anisotropy of the elastic half-space foundation Rectangular thin plate bending and steady-state vibration analysis, including the foundation reaction (amplitude), plate deflection (amplitude), plate internal force (amplitude) analytic expression. It overcomes the drawbacks of numerical method, cancels the hypothesis of foundation reaction force, and obtains the more realistic distribution rule of internal force (amplitude) and reaction force (amplitude). The results of the example not only agree well with the results in the literature, but also show that the symmetrical load can cause the antisymmetric internal forces and deformations for profiled plates. This method makes the solution of the complicated contact problem of the anisotropic rectangular thin plate on the half space foundation uniform, simplified and regular.