Multiple Resonances in Fluid-Loaded Vibrating Structures

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 classical frequency shift of in vacuo single resonance (in both real part because of fluid added mass and imaginary part because of energy lost by radiation into fluid), but also in an increase in number of resonance frequencies : as a result of loading, a single in vacuo resonance frequency of structure is transformed into a multiple resonance frequency. Here we show that this phenomenon is said to be a refinement of 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 case of a light loading conditions the scattering frequencies of a fluid loaded elastic structure (ie resonance frequencies) are nearly real eigenfrequencies of elastic body alone and complex scattering frequencies of fluid with a rigid solid. A theoretical explanation of observed phenomenon of multiple resonance is given using classical results of 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 fluid-loading is accounted for.