水中双向加肋圆柱壳体的自由振动

Free Vibration from Orthogonally Stiffened Infinite Cylindrical Shell in Water

以浸没于水中的双向加肋弹性薄圆柱壳为研究对象 ,考虑介质与结构振动的耦合效应 ,研究流固耦合系统的自由振动。基于 Kennard薄壳理论、Helmholtz方程以及壳壁外表面的运动协调条件 ,并借助 Dirac- δ函数引进肋骨对壳体的作用 ,从而建立耦合系统的运动方程。通过傅氏积分变换 ,引进算子函数 ,并利用算子函数的周期性 ,进而得出系统的频率方程。采用沿实波数轴搜索求根的方法 ,重点计算了无限长双向加肋薄圆柱壳的自由传播波频率系数。

In the context of the coupling effect between medium and structure, the free vibration of an immerged orthogonally stiffened thin elastic shell is investigated. In the discussion, the coupling conditions on the surface of the shell and Dirac δfunctions are used to deduce the motion differential equations of free vibration of the coupling system, in which Kennard's thin shell theory and Helmholtz equation are employed. Further, the equations are solved by means of Fourier integral transformation, and then by the use of an operator function with periodicity, the dispersion equation of the system is derived. Using a method of searching along the real wavenumber axis, the free propagation vibrations in the structure are obtained.