为提高圆柱壳水下振动数值计算的快速性和准确性，对截断模态选取的规律性进行研究。首先以35个不同尺度的圆柱壳为计算样本，以圆柱壳表面均方振速级为收敛目标，基于瑞利-里兹法求解圆柱壳振动方程，计算结果表明：轴向截断模态m值与长径比和环频率均相关。长径比相同，随着环频率的增大，截断模态m逐渐降低，且下降趋势逐渐平缓；环频率相同，长径比越大，截断模态m值越高。环向截断模态n仅与环频率相关。随着环频率的增大，n值逐渐减小。环频率以下均方振速级满足高精度计算条件时，截断模态对应的轴向波长与环向波长之比大概满足2倍的关系。固有频率和均方振速解析解与有限元仿真对比验证了理论计算的正确性和截断模态选取的合理性。
In order to improve the rapidity and accuracy of numerical calculation on underwater vibration of cylindrical shell, the selection rules of truncated mode are studied. At first, a sample of 35 cylindrical shells with different scales was calculated, the mean square velocity of the cylindrical shell was defined as the convergence target, and the Rayleigh-ritz method was applied to solve the vibration equation of cylindrical shell. The calculated results show that the axial truncation mode m is related to both the aspect ratio and the ring frequency. As the aspect ratio is consistent, with the increasing of ring frequency, the value of truncation mode m decreases gradually and the downward tend to flat. When the ring frequency is consistent, the larger the aspect ratio, the higher the value of truncation mode. The circumferential truncation mode n is only related to the ring frequency, and with the increasing of ring frequency, the value of truncation mode n decreases gradually. Under the condition of high precision calculation on the mean square velocity, the axial wavelength corresponding to the truncation mode is about two times that of the circumferential wavelength. The analytical results of natural frequency and mean square velocity are compared with that of finite element simulation, which verifies the accuracy of the theoretical calculation and the rationality of the truncation mode selection.
2018,40(12): 22-26,32 收稿日期：2017-11-26
DOI：10.3404/j.issn.1672-7649.2018.12.005
分类号：U661.3
基金项目：国家自然科学基金资助项目（50979110）
作者简介：仝博(1989-),男,博士研究生,研究方向为船体结构振动声辐射控制
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