A condensed transfer function method as a tool for solving vibroacoustic problems

Journal of Sound and Vibration

Guyader

et al. 2016

International audienceThe vibroacoustic behavior of axisymmetric stiffened shells immersed in water has been intensively studied in the past. On the contrary, little attention has been paid to the modeling of these shells coupled to non-axisymmetric internal frames. Indeed, breaking the axisymmetry couples the circumferential orders of the Fourier series and considerably increases the computational costs. In order to tackle this issue, we propose a sub-structuring approach called the Condensed Transfer Function (CTF) method that will allow assembling a model of axisym-metric stiffened shell with models of non-axisymmetric internal frames. The CTF method is developed in the general case of mechanical subsystems coupled along curves. A set of orthonormal functions called condensation functions, which depend on the curvilinear abscissa along the coupling line, is considered. This set is then used as a basis for approximating and decomposing the displacements and the applied forces at the line junctions. Thanks to the definition and calculation of condensed transfer functions for each uncoupled subsystem and by using the superposition principle for passive linear systems, the behavior of the coupled subsystems can be deduced. A plane plate is considered as a test case to study the convergence of the method with respect to the type and the number of condensation functions taken into account. The CTF method is then applied to couple a submerged non-periodically stiffened shell described using the Circumferential Admittance Approach (CAA) with internal substructures described by Finite Element Method (FEM). The influence of non-axisymmetric internal substructures can finally be studied and it is shown that it tends to increase the radiation efficiency of the shell and can modify the vibrational and acoustic energy distribution

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Section: Introductionmentioning

confidence: 92%

“…At this stage of the study, it cannot be said if one of the three condensation functions perform best. The gate functions however present the advantages of being easy to implement and of having a lower condition number, being thus less sensitive to numerical 280 errors [30]. In Fig.…”

Section: Convergence Criteriamentioning

confidence: 99%

Prediction of the vibroacoustic behavior of a submerged shell with non-axisymmetric internal substructures by a condensed transfer function method

Journal of Sound and Vibration

Guyader

et al. 2016

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“…They are defined on the junction Γ and are functions of the curvilinear abscissa s. Examples of sets of condensation functions and the validation on the case of the vibrational behavior of a thin plate excited by a harmonic point load have been presented in an earlier study. 26 An example of condensation functions which have shown good results and are easy to implement are the gate functions, defined according to their length L s as follows:…”

Section: Coupling Of a Stiffened Submerged Shell With Non-axisymmementioning

confidence: 99%

“…Results show that L s should be smaller than half the smallest structural wavelength at the considered frequency to ensure good convergence. 23,26 In the present case of a circular shell, the displacement at a point s is written as a 4 components vector…”

Section: Coupling Of a Stiffened Submerged Shell With Non-axisymmementioning

confidence: 99%

See 1 more Smart Citation

A substructuring approach for modeling the acoustic scattering from stiffened submerged shells coupled to non-axisymmetric internal structures

The Journal of the Acoustical Society of America

Audoly³

2016

Self Cite

The scattered pressure from a stiffened axisymmetric submerged shell impinged by acoustic plane waves has been investigated experimentally, analytically and through numerical models. In the case where the shell is periodically stiffened, it is shown that helical, Bragg, and Bloch-Floquet waves can propagate. The influence of non-axisymmetric internal frames on these scattering phenomena is nevertheless not well known, as it can considerably increase the computational cost. To overcome this issue, the condensed transfer function (CTF) method, which has been developed to couple subsystems along linear junctions in the case of a mechanical excitation, is extended to acoustical excitations. It consists in approximating transfer functions on the junctions and deducing the behavior of the coupled system using the superposition principle and the continuity equations at the junctions. In particular, the CTF method can be used to couple a dedicated model of an axisymmetric stiffened submerged shell with non-axisymmetric internal structures modeled by the finite element method. Incident plane waves are introduced in the formulation and far-field reradiated pressure is estimated. An application consisting of a stiffened shell with curved plates connecting the ribs is considered. Supplementary Bloch-Floquet trajectories are observed in the frequency-angle spectrum and are explained using a simplified interference model.

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Hybrid Methods for the Vibro‐acoustic Response of Submerged Structures

Fluid–Structure Interaction

2022