Radiation of leaky Lamb waves: relation between attenuation and power flux

Abstract

Lamb waves are guided elastodynamic waves in a free plate. When the plate is in contact with a fluid, the mechanical waves may leak energy in the form of acoustic waves, thereby fundamentally changing their physical nature. These leaky waves are described by an intricate nonlinear eigenvalue problem, which we have previously shown to be reducible to a linear one by an appropriate change of variables. This allows us to reliably compute the full set of eigensolutions.

It is the aim of this contribution to discuss the radiation of all wave solutions in a consistent manner. We show that balance of power flux leads to a simple relationship between attenuation and power flux of the waves. This result is non-trivial in that it imposes a strong relationship between the eigenvalues and the eigenvectors as well as between the axial and transversal wavenumbers. In particular, the analysis holds also for the highly attenuated branches related to the nonpropagating waves in the free plate. Although neither leakage nor damping are involved, these nonpropagating waves do exhibit attenuation. In contrast to this, our analysis shows that attenuation in the nondissipative fluid-coupled plate is entirely due to radiation.

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.