Introduction of frequency, angular, longitudinal, and transverse quality factors to characterize the resonances of a water-loaded elastic plate

Abstract

The frequency derivative of the phase of the immersed elastic plate reflection coefficient is related to its derivatives with respect to the longitudinal and transverse phase velocities in the plate and to the phase velocity in the surrounding fluid. In this relation, products, composed of one of these variables and of the corresponding phase partial derivative, appear. At a resonance frequency, the frequency phase derivative amplitude corresponds to the inverse of the resonance half-width; the frequency-frequency phase derivative product can be identified to a frequency quality factor, denoted as Qx. By analogy, all the other products correspond to quality factors. It is shown that the product assigned to the fluid phase velocity corresponds to an angular quality factor, denoted as Qy. The products assigned to the longitudinal and tranverse phase velocities are naturally qualified as longitudinal and transverse quality factors, denoted as Ql and Qt. It is established that the sum of Qx and Qy equates the sum of Ql and Qt. Moreover, each of these quality factors is shown to be related to a stored kinetic energy, associated either to a normal displacement, to a parallel displacement, to a longitudinal or to transverse displacement.