Spectrum of a fluid-loaded vibrating plate: the multiple resonance phenomenon

TL;DR

This paper investigates how fluid loading causes a single resonance of a vibrating plate to split into multiple resonances, refining classical results and providing a theoretical explanation for this phenomenon.

Contribution

It demonstrates that fluid loading transforms each in vacuo resonance into an infinite set of resonances, extending classical asymptotic analysis with a theoretical framework.

Findings

Single in vacuo resonance becomes multiple resonances under fluid loading

The phenomenon is explained using classical entire function theory

Each resonance transforms into an infinite set of resonances

Abstract

It was recently observed in a numerical study on a high order perturbation method under heavy fluid loading that a loaded vibrating plate results, not only in the classical 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), but also in an increase in the number of the resonance. As a result of the loading, a single in vacuo resonance of the structure is transformed into a multiple resonance. Here we show that this phenomenon is a refinement of the Sanchez's classical result where it was established, using asymptotic analysis, 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 ". A theoretical explanation of the multiple resonances is given using classical results on theory of entire functions. It is established that every single in vacuo resonance of a simply supported rectangular plate is transformed into an infinite number of resonances under fluid-loading condition.