水中悬臂梁的自振频率的简便计算公式

本文分析了无粘性的、不可压缩水域中的圆截面的悬臂梁的自由振动。在忽略水面波影响的情况下,求解梁与水体耦联的振动微分方程,得到悬臂梁在水中自由振动的频率和振型的解析表达式,并给出了算例。最后应用附加质量的概念,得到了计算梁在水中的自振频率的简易公式,该简易公式和解析表达式的结果吻合极好。

Formula for Free Vibration Frequencies of Cantilever Cylinder in Water

An exact analysis of free vibration of a cantilever cylinder in an inviscid incompressible water, including hydrodynamic interaction, is presented. The cylinder is treated as a one-dimentional structure governed by beam theory. Ignoring surface wave effects, the analytic solution is obtained by solving the coupled differential equations of the water-structure interaction. In order to reduce the computational effort involved when using the exact expression to evaluate the natural frequencies of a cylinder in water, a simplified formula using the added mass representation is derived. Excellent agreement is observed in the predictions made by the simplified formula and the analytical expression.