求解混合边值振动问题的辅助函数法

Auxiliary functions method for solving mixed-boundary vibration problems

提出辅助函数方法,为混合边值振动问题求解提供一种手段。以圆柱第2类边值出平面简谐振动问题为例阐述辅助函数的基本思想和定义;以半空间凹陷地形出平面散射问题为例讨论辅助函数的构造原则和正确方式;利用辅助函数法给出圆柱一般混合边值出平面简谐振动问题解答;讨论采用辅助函数法在位移和应力边界交接处级数解答的收敛情况;给出若干算例,说明辅助函数法的可行性和有效性。

An auxiliary functions method for solving the vibration problems of mixed-boundary values is presented in the paps r. The basic idea and definition of the auxiliary functions are explained by a simple example of the antiplane harmonic vibration of a cylinder with stress-boundary value. The antiplane scattering problem by a cylindrical canyon in a half-space is taken as an example to demonstrate the construction principle and pattern of auxiliary functions. The solution for the antiplane harmonic vibration of a cylinder with general mixed-boundary value is presented by using the auxiliary functions and, the convergence condition of the solution in the connection of the displacement boundary and the stress boundary is discussed. Some successful practices in the scattering problems show that the auxiliary functions method presented in the paper is effective.