High-order perturbation expansion for the spectral analysis of fluid-loaded vibrating structure

International audienceThis paper deals with vibroacoustic under heavy fluid-loading conditions. The aim is to show how the high-order perturbation expansion approach described yields a very simple approximation of the spectrum of a heavy fluid-loaded structure. When the fluid-loading is "light" (e.g. metallic structures in contact with air) perturbation methods have been classically used to compute the spectrum of a fluid-loaded structure. Because of the computational efficiency of the expansions involved, it is now necessary to extend this method to heavy loading problems, such as those involving a metallic structure in contact with water. As we will see, although direct high order expansion methods yields unrealistic results, a judicious re-ordering of the various terms leads to surprisingly simple and efficient analytical results. Numerical examples are given in the simple case of a clamped rectangular plate under various fluid-loading conditions

Multiple Resonances in Fluid-Loaded Vibrating Structures

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

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

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.Comment: Proceedings of Noise and Vibration: Emerging Methods - NOVEM 200

Complex resonance frequencies of a finite, circular radiating duct with an infinite flange

Radiation by solid or fluid bodies can be characterized by resonance modes. They are complex, as well as resonance frequencies, because of the energy loss due to radiation. For ducts, they can be computed from the knowledge of the radiation impedance matrix. For the case of a flanged duct of finite length radiating on one side in an infinite medium, the expression of this matrix was given by Zorumski, using a decomposition in duct modes. In order to calculate the resonance frequencies, the formulation used in Zorumski's theory must be modified as it is not valid for complex frequencies. The analytical development of the Green's function in free space used by Zorumski depends on the integrals of Bessel functions which become divergent for complex frequencies. This paper proposes first a development of the Green's function which is valid for all frequencies. Results are applied to the calculation of the complex resonance frequencies of a flanged duct, by using a formulation of the internal pressure based upon cascade impedance matrices. Several series of resonance modes are found, each series being shown to be related to a dominant duct mode. Influence of higher order duct modes and the results for several fluid densities is presented and discussed

Sound generation by impulse excited plates coupled to acoustics cavities.

International audienceThis paper is concerned with vibroacoustics in the time domain. One of the aims is to compare results given by an semi-analytical technique based on the resonance modes with a finite difference technique. An other goal is to describe the response of a fluid-loaded plate (displacement of the structure and sound pressure in the fluid) coupled to a rigid cavity when it is excited by a Ricker wavelet and to see the influence of the excitation on the response of system

Damping analysis of a free aluminum plate

International audienceAn analysis of the energy dissipation sources acting in a vibrating aluminum plate is pre10 sented in this paper. In a first step, the contact-free modal analysis of a suspended plate 11 is conducted using a laser vibrometer and an acoustic excitation to obtain reference data. 12 The thin nylon suspension set-up guarantees a low boundary damping, which is assumed 13 to be negligible. In a second step, a number of damping sources are modeled. Acoustic 14 damping due to the noise radiation of the non-baffled plate is computed using the boundary 15 integral method and a light fluid approximation to express the vibroacoustic coupling in 16 analytical terms. The damping due to the sheared air flow along the free plate borders is 17 determined on the basis of a simple two-dimensional boundary layer model. Thermoelastic 18 damping is assessed using a Fourier series expression for the temperature field along with a 19 perturbation technique to take thermoelastic coupling into account. Since no robust model 20 is available so far to quantify viscoelastic material damping in aluminum, it is determined 21 in a last step by subtracting measured values of damping to the one that have previously 22 been computed. Aluminum viscoelastic damping turns out to be very small and almost 23 independent of frequency

Sound transmission through a rib-stiffened plate : comparisons of a light fluid approximation with experimental results

International audienceInterest in stiffened plate constructions has been widespread recently in aerospace, marine and engineering structures : their vibratory response can be greatly modified by small weight added to the hull. Semi-analytical and finite element modellings are mostly based on a weak (energetic) formulation of the in vacuo problem. First, the analysis has been simplified by applying the so-called orthotropic equivalent plate theory only valid when the mechanical wavelengths are greater than the stiffeners spacing~; a more accurate and robust method is the discrete model in which the system is divided into subelements~: the stiffeners are therefore considered as beams exerting efforts on the plate. Moreover, the vibro-acoustic response of the system fluid/structure is approximated under the assumption that the fluid-loading is a small perturbation with respect to the in vacuo problem since the surrounding fluid is a gas. This paper applies this approximation to the case of a baffled plate stiffened by ribs

Tuning of a Nonlinear Energy Sink using multi-stability

International audienceThis work addresses the development of a nonlinear absorber based on the concept of a Nonlinear Energy Sink(NES) under different multi-stable configurations. The potential energy of the system can be written under a potential thatpossesses two or more stable equilibrium positions separated by saddle points. The study of the dynamics at different timescales leads to the computation of the Slow Invariant Manifold (SIM) where singular points indicate the possible occurrenceof Strongly Modulated Responses (SMR). It is shown that, compared to a bi-stable NES, the threshold activation of amultistable NES can be significantly lowered with same dissipation ability

Acoustique, Aéroacoustique et Vibrations

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