Vibrations of a floating bean on marine waves

Abstract

Small vertical vibrations of a horizontal floating towed beam under action of marine waves is studied. The beam bending stiffness, the attached mass of water and the restriction forces are taken in consideration. To describe the waves action the theory of small gravity waves is accepted and it is supposed that the water motion is plane harmonic or random stationary, and the directions of waves propagation and of the towing coincide. To the motion description the one-dimensional Bernoully-Euler beam model is used, and the problem is solved in the linear approximation. The solution is presented as a partial sum of series in system of orthogonal beam functions with unknown time-depending coefficients. In the case of harmonic waves the amplitude-frequency dependences for these coefficients are found in an explicit form. The dependence of resonance frequency on the towing velocity is established. For the random stationary waves the spectral densities and dispersions for the mentioned time-depending coefficients are found. Comparison of results for harmonic and random waves is performed. It is established that compared with the harmonic waves the random waves under identical conditions lead to the essential diminishing of amplitudes especially at resonance zones of the first two vibration modes describing the beam motion as a rigid body. Refs 11. Figs 6.

Keywords:

floating beam, towing, waves excitation, harmonic and random vibrations