Natural vibration of a beam-water interaction system

The dynamical behaviour of a flexible beam-water interaction system is examined. The coupled system is subject to an undisturbed boundary condition at infinity in the water domain and a zero surface wave or linear surface disturbance condition on the free surface. The governing equations describing the behaviour of the system are analyzed by using the separation of variables method and their solutions presented. The eigenvalue equation of the natural vibration of the beam-water system is derived and exact solutions for each combination of boundary conditions are obtained. Calculations show that for the undisturbed condition at infinity in the water domain, the natural frequencies of the coupled dynamic system are lower than those of the flexible dry beam, indicating that the influence of water on the beam has the effect of an additional mass. It is further shown that the free surface wave disturbance plays a more important role in the determination of vibration characteristics in the lower frequency region of the coupled system and that fluid compressibility is more influential and higher frequencies. The orthogonality relation of the natural vibration forms of the coupled fluid-structure interaction system are derived and the case of this coupled system subject to the radiation condition at infinity proposed by Sommerfield [1] is discussed