Abstract This study proposed an efficient analytical framework to achieve exact stochastic responses of circular cylindrical shells under various stationary excitations. By introducing the exact modal shapes of closed and open cylindrical shells based on the Flugge theory, the analytical power spectral densities of responses for the two shells were derived via the pseudo excitation method (PEM), where the calculus operation in the spatial domain and the integral in frequency domain were involved. To take full advantage of PEM for matrix operation and improve computational efficiency, the discrete analytical method (DAM), implementing analytically the calculus operation in the spatial domain and discretizing the frequency domain, was proposed. Furthermore, the exact stationary stochastic responses of three shell examples under point, surface, base acceleration and spacecraft specification spectrum excitations were achieved. By comparing the root mean squares of responses, especially twisting moment and membrane shear force with those by finite element analysis software, the high accuracy and efficiency of DAM were demonstrated. The remarkable effect of frequency bandwidth of excitation on stochastic responses was also revealed. The exact stochastic responses calculated by DAM can be taken as benchmark solutions to verify the numerical methods for the high-frequency wideband random vibration problem.

中文翻译：

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不同稳态激励下薄圆柱壳的解析随机响应

摘要 本研究提出了一种有效的分析框架，以实现圆柱壳在各种静止激励下的精确随机响应。通过引入基于 Flugge 理论的封闭和开放圆柱壳的精确模态形状，通过伪激发方法 (PEM) 推导出两个壳响应的解析功率谱密度，其中空间域中的微积分运算和涉及频域积分。为了充分利用PEM进行矩阵运算，提高计算效率，提出了在空间域中解析地实现微积分运算并在频域中离散化的离散分析法(DAM)。此外，三个壳实例在点、面、实现了基本加速度和航天器规格频谱激发。通过将响应的均方根，特别是扭转力矩和膜剪力与有限元分析软件的响应进行比较，证明了DAM的高精度和高效率。还揭示了激励频率带宽对随机响应的显着影响。DAM 计算的精确随机响应可以作为基准解来验证高频宽带随机振动问题的数值方法。还揭示了激励频率带宽对随机响应的显着影响。DAM 计算的精确随机响应可以作为基准解来验证高频宽带随机振动问题的数值方法。还揭示了激励频率带宽对随机响应的显着影响。DAM 计算的精确随机响应可以作为基准解来验证高频宽带随机振动问题的数值方法。