Multiple Resonances in Fluid-Loaded Vibrating Structures

TL;DR

This paper investigates how heavy fluid loading causes a single resonance in vibrating structures to split into multiple resonances, extending classical results and using entire function theory to explain the phenomenon.

Contribution

It demonstrates that heavy fluid loading transforms each in vacuo resonance into multiple resonances, extending classical scattering frequency results to high load conditions.

Findings

Heavy fluid loading causes resonance splitting.

Single resonances become infinite multiple resonances.

The phenomenon extends classical scattering frequency results.

Abstract

This study deals with vibroacoustics under heavy fluid loading conditions. Considerable attention has been and remains focused on this subject not only because industry is very concerned but also because of mathematical difficulties that make the numerical resolution of the problem very difficult. It was recently observed in a numerical study on a high order perturbation method under heavy fluid loading that a loaded vibrating plate results in a frequency shift of the in vacuo single resonance (in both the real part because of the fluid added mass and the imaginary part because of energy lost by radiation into the fluid) as well as increase in the number of the resonance frequencies : as a result of the loading, each single in vacuo resonance frequency of the structure is transformed into a multiple resonance frequency. Here we show that this phenomenon is said to be an extension to the heavy loading condition of the Sanchez's classical result that have established that in the case of a light loading conditions "the scattering frequencies of a fluid loaded elastic structure (ie the resonance frequencies) are nearly the real eigenfrequencies of the elastic body alone and the complex scattering frequencies of the fluid with a rigid solid". Using classical results in the framework of the theory of entire functions, it is established that a single resonance of a simply supported fluid loaded rectangular plate is transformed into an infinite number of resonances.