Green函数法解非均匀弹性地基板的自由振动

APPLICATION OF THE GREEN'S FUNCTION METHOD TO THE FREE VIBRATION PROBLEMS OF PLATES ELASTICALLY SUPPORTED ON A NONHOMOGENEOUS FOUNDATION

把板在特定域中的Green函数当作影响函数,根据实际板的边界条件首先求出虚拟域中的Green函数“源”,继而确定板内任意点的挠度及内力。在板的振动问题中及板的分布惯性力的影响后就可得到其自振频率的本征方程,从而计算出其各阶自振频率的值。文中附有算例,并把其计算结果与已有解析解作了比较,表明它们之间具有良好的吻合。

The Green's function of plate in a particularly chosen region may be seen as the influence function, according to the boundary conditions of real plate it is necessary firstly, to calculate the values of the Green's function 'sources' in the fictitious region, and then the deflections and inner forces at any point in plates are easy to determine. In plate vibration problems, after considering the influence of the distributed forces of inertia of plate, the eigenvalue equation of the plate vibration frequency may be obtained, then the values of each order frequency may be solved.There are some examples calculated in this paper. The results are compared with those of the analytical solutions. They are seen in good agreement.