Green functions for hydroelastic analysis of vibrating free-free beams andplates

Closed form expressions for the Green function of flexural vibrations of un iform beams are well known, giving the response at any point in the beam du e to harmonic point excitation at any position along the beam. The expressi ons involve trigonometric and hyperbolic functions. The present work first develops alternative forms for the free-free beam, in terms of the sinusoid al eigenmodes of a pinned-pinned beam plus the rigid body modes. Convergenc e is assessed by comparison with the well-known classical results for a fre e-free beam. The analysis is then extended to the case of free-free rectang ular plates of arbitrary aspect ratio. The work is motivated by the desirab ility of employing sinusoidal modes for the structure when undertaking hydr oelastic analysis (e.g. for a flexible beam or plate floating in the sea). (C) 2000 Elsevier Science Ltd. All rights reserved.