Green functions for hydroelastic analysis of vibrating free–free beams and plates

Abstract Closed form expressions for the Green function of flexural vibrations of uniform beams are well known, giving the response at any point in the beam due to harmonic point excitation at any position along the beam. The expressions involve trigonometric and hyperbolic functions. The present work first develops alternative forms for the free–free beam, in terms of the sinusoidal eigenmodes of a pinned–pinned beam plus the rigid body modes. Convergence is assessed by comparison with the well-known classical results for a free–free beam. The analysis is then extended to the case of free–free rectangular plates of arbitrary aspect ratio. The work is motivated by the desirability of employing sinusoidal modes for the structure when undertaking hydroelastic analysis (e.g. for a flexible beam or plate floating in the sea).