中文摘要：

将准Green函数方法应用于求解夹支任意形状底扁球壳的自由振动问题。即利用问题的基本解和边界方程构造一个准Green函数,这个函数满足了问题的齐次边界条件。采用Green公式将夹支任意形状底扁球壳自由振动问题的振型控制微分方程化为第二类Fredholm积分方程。通过边界方程的适当选择,克服了积分方程核的奇异性。最后通过离散化方程求得数值结果。数值算例表明：该方法具有较高的精度、计算量小、收敛速度快,是一种新型有效的数学方法。

英文摘要：

The quasi-Green′s function method is employed to solve the free vibration of slip clamped shallow spherical shell with arbitrary boundary shape.A Green quasi-function is established by using the fundamental solution and boundary equation of the problem.This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the free vibration problem of slip clamped shallow spherical shell with arbitrary boundary shape is reduced to Fredholm integral equation of the second kind by Green′s formula.Irregularity of the kernel of integral equation is overcome by choosing a suitable form of the normalized boundary equation.Finally,the numerical results can be obtained from the discretization equations.Numerical examples demonstrate that the method has high precision,small amount of calculation,and fast convergence rate,and it is a new kind of effective mathematical methods.