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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。
This paper analyzes the free vibration of circular cross-section cantilever beams in non-viscous, incompressible waters. In the case of ignoring the influence of the surface wave, the vibrational differential equation of the beam coupled with the water body is solved, and the analytical expression of the frequency and mode shape of the free vibration of the cantilever beam in the water is obtained, and an example is given. Finally, applying the concept of additional mass, a simple formula for calculating the natural vibration frequency of the beam in water was obtained. The result of the simple formula and the analytical expression is very good.