Multiple Resonances in Fluid-Loaded Vibrating Structures

TL;DR

This paper investigates the phenomenon where fluid loading causes a single resonance frequency of a vibrating structure to split into multiple resonances, providing a theoretical explanation based on entire function zeros.

Contribution

It refines classical results by showing that fluid loading transforms each in vacuo resonance into infinitely many resonances, supported by a theoretical analysis.

Findings

Single in vacuo resonance becomes multiple resonances under fluid loading

Theoretical explanation uses zeros of entire functions

Each resonance frequency transforms into infinitely many resonances

Abstract

This study deals with spectral analysis of fluid-loaded vibrating structure. 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 into the fluid), but also in an increase in the number of the resonance frequencies : as a result of the loading, a 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 a refinement of the Sanchez's classical result in their book (Vibration and coupling of continuous systems, Springer-Verlag -1989-, paragraph 9.3) 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 observed phenomenon of multiple resonance is given using classical results of the distribution of zeros of entire functions. It is established that every single in vacuo resonance frequency of a rectangular plate is transformed into an infinite number of resonances when the fluid-loading is accounted for.