固流耦合振动问题的加权残值法

利用最小二乘配点法计算充液圆柱壳体的固有频率，结果与考题相符。假设圆柱壳体内的液体为不可压缩无粘无旋的理想注体，其速度热函数满足Ｌａｐｌａｃｅ方程试函数取重三角函数。通过配点离散化后，最后将固有频率问题回归结为四次特征值问题，通过一些变换，将四次特征值问题化为一次标准特征值问题，再由ＱＲ法求解。

Study on Solid-fluid Coupled Dynamic Problem in the Method of Weighted Residuals

This paper calculates the natural frequencies of circular cylindrical shell filled with liquid by least square collocation method(LSCM). The results of the computation coincide with the examination example. When liquid is assumed to be incompressible, inviscid, inwhirl and ideal, velocity potential functions in the shell accord with LAPLACE equations. The dynamic equations of the circular cylindrical shell are based upon an exact moment theory. Trial functions are approached by double trigonometric functions. After collocationg to the shell and the liquid, the problem of the natural frequencies of the filled liquid cylindrical shell is reduced to the problem of four dimensioned generalized algebra eigenvalue. Then the problem is changed to the problem of normal algebra eigenvalue problem by some alternations and the eigenvalues are obtained with QR method.