应用瑞利—里滋法分析储箱内液体晃动模态

Modal analysis of liquid filled in tank applying Rayleigh-Ritz method

将瑞利—里滋法进一步拓展到储箱内液体晃动的模态分析中,结合瑞利商给出储箱内带自由液面液体晃动基频的计算方程,使得瑞利—里滋计算模态的方法得到进一步的扩展,同时对液体晃动基频计算提出更为有效的计算方法.此外,应用有限元程序ADINA,对圆柱形储箱内带自由液面的晃动频率和模态进行数值模拟.研究了液面半径和深度对液体晃动固有频率和模态的影响.模拟得出的结论与瑞利商和里滋法的计算结论基本相符,从而验证了所提出的瑞利—里滋法解析解的有效性.所给出的解析方法适合任意储箱内液体晃动的模态分析.

Rayleigh-Ritz method is developed for the modal analysis of liquid filled in tank with free surface. The equation calculating the lowest frequency of liquid with free surface is presented. The applications of this method is expanded, and the method which is more valid is put forward to calculate the lowest frequency of liquid filled in the tank with free surface. In addition, the frequency and mode of vibration of liquid with free surface are calculated with the finite cell procedure ADINA. The effects of the radius and the height of surface of liquid for inherent frequency and mode of vibration of liquid are researched. The result is consistent with numerical result by Rayleigh-Ritz method. So the validity of analytical result by Rayleigh-Ritz method is validated. The analytical method this paper deduced is suitable for modal analysis of liquid filled in any tank.