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把惯性力和地基反力看成广义载荷,板的挠曲面微分方程与振型函数微分方程在数学形式上是完全一致的,基于此提出了弹性地基板振动分析的一种解析方法.为简便,选择与实际系统的尺寸及材料性质一样,受单位集中力作用的简支矩形板为基本系统,将实际系统的非简支边界进行适当的简化,就可比较方便地得到具有常见约束的矩形板的固有频率.算例表明,用此方法求得的结果与已有的解析解完全一致.
Considering the inertia force and the foundation reaction as the generalized load, the differential equation of the flexural plate and the vibration function differential equation are exactly the same in the mathematical form. Based on this, an analytical method of the vibration analysis of the elastic foundation is proposed. , Choose the same as the size and material properties of the actual system, the simple supported rectangular plate concentrated by the unit as the basic system, the non-simplified boundary of the actual system is simplified appropriately, you can easily get a rectangular constraint with common constraints The natural frequencies of the plates are shown.Examples show that the results obtained by this method are completely consistent with the existing analytical solutions.