无拉力弹性地基板振动分析的一种方法

An approach to the study of the vibration of plates on the tensionless Winkler foundation

基于薄板挠曲面微分方程与振型函数微分方程在数学形式上的一致性,应用贝蒂功互等定理,引入阶梯函数,给出了解决无拉力W ink ler地基板振动分析的一种方法.在此,惯性力和地基反力被视为广义荷载.可选择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,因而可比较方便的得到具有常见约束的矩形板的固有频率,因接触区的边界不能预先确定,故需使用迭代法获得解答.

As the differential equation of deflection and one of the vibration model function are identical in mathematical function to thin plates, an approach based on the Betty＇s reciprocal theorem of work and step function is presented for studing the vibration of plates on tensionless Winkler foundation. In this paper, inertial force and foundation counterforce are regarded as generalized loads. A rectangular plate, which is loaded with a unit force ,with four simply supported edges is regarded as a basic system. It is necessary to simplify those edges of real systems which are not simply supported. So, we may easily obtain the inherent frequency of rectangular plates with general binding, iterative procedures are used to obtain the solution because the boundaries of contact region can not be given beforehand.