From Lamb waves to quasi-guided waves: On the wave field and radiation of elastic and viscoelastic plates

Abstract

Leaky Lamb waves are elastodynamic quasi-guided waves propagating in plates which are in contact with a fluid. They are usually perceived and studied as perturbations to waves in the free plate. Recent advances in solving the nonlinear eigenvalue problem that describes these waves allow to reliably and efficiently obtain all solutions. The resulting wavenumbers in the plate and in the fluid as well as the wave field account for the exact fluid-structure interaction. A classification of the solutions based on the transversal wavenumber spectrum is proposed. The properties of each kind of quasi-guided wave are discussed. Moreover, we analyze the relationship between radiation rate and attenuation. The free, perfectly elastic plate exhibits wave propagation without losses. Nontheless, attenuated modes exist in this case and are known as nonpropagating modes. We show that – in contrast to the free plate – attenuation of waves is solely due to radiation, that all waves propagate energy and that subsonic radiation is possible. The radiation rate of the waves can be calculated using their eigenvector. This allows to split the total attenuation of waves in viscoelastic plates into a contribution due to radiation and one due to damping. Lastly, we present and discuss the dispersion curves of a strongly fluid-loaded plate.

Daniel A. Kiefer

Researcher at Institut Langevin

Research in guided elastodynamic waves, fluid-structure interaction, simulation and signal processing for ultrasonic sensors and nondestructive testing.