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提出了一种区域分解法来分析不同组合边界条件的薄壁回转壳的自由振动。首先沿壳体母线方向将壳体分解为一些自由壳段,并采用广义变分和最小二乘加权残值法将壳体分区界面上的位移协调方程引入到壳体的势能泛函中;然后将壳段位移变量以Fourier级数和Chebyshev多项式展开,对总的势能泛函变分后得到回转壳的离散动力学方程。采用区域分解法分析了不同边界条件的圆柱壳、圆锥壳、抛物壳的自由振动,并将计算结果与其它文献值及ANSYS结果对比,结果表明:随着回转壳分区数目的增大,区域分解法计算出的壳体频率很快收敛;本文结果与其它方法计算结果非常吻合(相对误差不超过0.4%)。采用该方法可高效计算不同组合边界条件回转壳体的低阶和高阶振动频率。
A method of regional decomposition is proposed to analyze the free vibration of the thin-walled shell with different combinations of boundary conditions. Firstly, the shell is decomposed into some free shell segments along the direction of the generatrix of the shell, and the displacement coordination equation on the shell partition interface is introduced into the potential energy functional shell of the shell by using generalized variational method and least-squares weighted residual method. Then, Displacement variables of shell segment are expanded by Fourier series and Chebyshev polynomial, and the discrete dynamic equations of the shell are obtained by functional variation of the total potential energy. The free vibration of cylindrical shell, conical shell and parabolic shell with different boundary conditions is analyzed by the method of regional decomposition. The results of the calculation are compared with those of other literature and ANSYS. The results show that with the increase of the number of shell of rotating shell, The shell frequency calculated by the method converges very fast. The results in this paper are in good agreement with those calculated by other methods (the relative error is less than 0.4%). Using this method, the low-order and high-order vibration frequencies of gyrotron shells with different combinations of boundary conditions can be calculated efficiently.