弹性地基板振动分析的一种解析方法

An Analytical Approach to Study the Vibration of Plates on Plastic Foundation

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.

The deflection equation and vibration modal equation are similar for inertial force and foundation force are generalized load. In this paper, an analytical approach based on the Betty's reciprocal theorem of work is presented to study the vibration of plates on plastic foundation. For rectangular plates, one can choose a basic system that has four simply supported edges and is loaded with a unit force. It is necessary for one to simplify those edges of real systems which are not simply supported. From results obtained here, one can find that the method is valid. It is more important that the approach is also applicable to more complicated cases.