本文研究水下结构物的复杂应力状态对结构固有频率的影响，克服以往研究中只考虑整体均匀分布应力的局限性。水下结构因外部环境特殊常常处于复杂应力状态，复杂应力与流固耦合的共同作用使结构的固有频率求解变为一个耦合非线性特征值问题，以往求解流固耦合的方法不再适用于此类问题。有限元方法也能处理此类问题，但存在处理过程复杂、计算量大、不能明确说明结构应力与动力特性之间的本质物理联系等缺点。针对该问题本文用理论方法进行了分析，首先基于Flügge壳体理论、考虑流固耦合作用、利用特定模态之间的正交性建立复杂应力结构自由运动方程，然后采用多项式近似结合二次型矩阵线性化的方法对此类结构的固有频率进行求解。在数值算例中，计算了某水下圆柱壳的固有频率，并对比和分析了不同类型的复杂应力对于水下结构固有频率的影响特点。
Abstract
Study the influence of underwater structure complex stress on the natural frequency, overcome the limitation that only consider the overall uniform stress distribution in the former study. The underwater structure often has complex stress because of their working environment, the complex stress and fluid structure interaction make it become a nonlinear eigenvalue problem which is difficult to solve. We take a cylindrical shell as an example and, based on the Flügge shell theory, consider the fluid structure interaction， make use of the orthogonality of specific order modes to derive the dynamic equation of an underwater complex stress structure. The stress-caused coupled fluid-loaded structural modes are calculated by means of a polynomial approximation and quadratic matrix linearization. In the case study, we calculate the natural frequency of different type of stress structure, compare and analyze the influence characteristic of different type stress.
关键词
复杂应力 /
流固耦合 /
结构振动 /
固有频率
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Key words
complex stress /
fluid-structure interaction /
structure vibration /
natural frequency
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