Extension of SEA model to subsystems with non-uniform modal energy distribution

International audienceIn order to enlarge the application field of Statistical Energy Analysis (SEA), a reformulation is proposed. The model described here, Statistical modal Energy distribution Analysis (SmEdA), does not assume equipartition of modal energies contrary to classical SEA. Theoretical derivations are based on dual modal formulation described in [1,2] for the general case of coupled continuous elastic systems. Basic SEA relations describing power flow exchanged by two oscillators are used to obtain modal energy equations. They permit to determine modal energies of coupled subsystems from the knowledge of modes of uncoupled subsystems. The link between SEA and SmEdA is established and render possible to mix the two approaches: SmEdA for subsystems where equipartition is not verified and SEA for other subsystems. Three typical configurations of structural couplings are described for which SmEdA improves energy prediction compared to SEA: (a) coupling of subsystems with low modal overlap. (b) coupling of heterogeneous subsystems. (c) case of localised excitations. The application of the proposed method is not limited to academic structures, but could easily be applied to complex structures by using finite element method (FEM). In this case, FEM are used to calculate the modes of each uncoupled subsystems; these data are then used in a second step to determine modal coupling factors necessary to SmEdA to modelise the coupling

Noise radiated from a periodically stiffened cylindrical shell excited by a turbulent boundary layer

© 2019 Elsevier Ltd This work proposes a semi-analytical method to model the vibroacoustic behavior of submerged cylindrical shells periodically stiffened by axisymmetric frames and excited by a homogeneous and fully developed turbulent boundary layer (TBL). The process requires the computation of the TBL wall-pressure cross spectral density function and the sensitivity functions for stiffened cylindrical shells. The former is deduced from an existent TBL model and the latter are derived from a wavenumber-point reciprocity principle and a spectral formulation of the problem. The stiffeners' dynamic behavior is introduced in the formulation through circumferential admittances that are computed by a standard finite element code using shell elements. Four degrees of freedom are taken into account for the coupling between the shell and the stiffeners: three translation directions and one tangential rotation. To investigate the effect of the stiffeners on the radiated noise, two case studies are considered. The first one examines a fluid-loaded cylindrical shell with regularly spaced simple supports. The influence of Bloch-Floquet waves and the support spacing on the noise radiation are highlighted. The second case study inspects the fluid-loaded cylindrical shell with two different periodic ring stiffeners, namely stiffeners with T-shaped and I-shaped cross-sections. Their influence on the vibroacoustics of the shell is thoroughly analyzed

Ergodic billiard and statistical energy analysis

International audienceThis paper highlights the importance of ergodicity of billiards in Statistical energy analysis (SEA), a statistical theory of sound and vibration. We show that the main relationship of statistical energy analysis, the so-called coupling power proportionality, is intimately linked with the establishment of a diffuse vibration field in subsystems. In particular, we show that when subsystems have ergodic geometries or when the nature of excitation enforces a diffuse field, the energy exchange between two weakly coupled subsystems is proportional to the difference of vibrational energies. But when the field is not diffuse (either non isotropic or non homogeneous), the exchange of energy does not generally follow this proportionality. Numerical simulations are provided to support the discussion

Identification of low-wavenumber wall pressure field beneath a turbulent boundary layer using vibration data

Although the most energetic part of the wall pressure field (WPF) beneath a turbulent boundary layer (TBL) is within the convective region, this region is mostly filtered out by the structure when excited by a low Mach number turbulent flow. Therefore, structural vibration is primarily induced by the low-wavenumber components of the WPF. This highlights the importance of an accurate estimation of the low-wavenumber WPF for predicting flow-induced vibration of structures. Existing semi-empirical TBL models for the WPF agree well in the convective region but significantly differ from one another in estimating the low-wavenumber levels. In this study, we aim to investigate the feasibility of estimating the low-wavenumber WPF by analyzing vibration data from a structure excited by a TBL. The proposed approach is based on the relationship between the TBL forcing function and structural vibrations in the wavenumber domain. By utilizing vibration data obtained from a structure excited by a TBL and incorporating the sensitivity functions of the respective structure, it is possible to estimate the cross-spectrum density of the pressure fluctuations in the wavenumber domain. To demonstrate the effectiveness of the proposed method, an analytical model of a simply-supported panel excited by a reference TBL model is employed. The vibration data of the panel is then used in an inverse method to identify the low-wavenumber levels of the pressure fluctuations, which are then compared to those of the reference TBL model. The performance of the proposed method is examined through a parametric study and virtual experiments

Experimental vibration analysis of a beam with ABH stiffeners

In recent years, acoustic black holes (ABHs) have gained attention as a promising method for passive vibration control in engineering applications. This work experimentally investigates the use of ABHs in a stiffened beam to mitigate its vibrational response. The ABHs are embedded in the stiffeners rather than in the beam. Therefore, the structural integrity of the system is maintained. The study presents measured vibration responses of two stiffened beams excited by an impact force. The first case is a stiffened beam with traditional rectangular stiffeners, while the second case has ABH stiffeners. The ABH stiffeners are designed to match the surface area and moment of inertia of the rectangular stiffeners at the contact point with the beam, ensuring that both cases have similar weight and static stiffness. The experimental investigation explores two configurations: stiffeners without damping layers, and with constrained viscoelastic damping layers. The effect of the damping layers on the vibrational responses of both stiffened beams is examined. Results demonstrate the effectiveness of replacing traditional rectangular stiffeners with ABH stiffeners for vibration mitigation, highlighting the potential advantages of ABH technology in vibration reduction of stiffened structures

Semi-analytical formulation to predict the vibroacoustic response of a fluid-loaded plate with ABH stiffeners

Stiffened structures are widely used in aeronautics, marine and rail industries. When stiffeners are integrated into host structures, so-called Bloch–Floquet waves are generated due to interactions between the host's flexural waves and the stiffeners’ flexural and torsional waves. It is reported in the literature that these waves are often the source of undesirable noise and vibrations when the stiffened structure is excited by a force. To mitigate unwanted noise and vibrations from the stiffened structures, this study proposes to replace common rectangular stiffeners with acoustic black hole (ABH) stiffeners. To do this, a semi-analytical model is initially developed in the wavenumber domain to predict the forced vibroacoustic response of a 2D fluid-loaded infinite plate with stiffeners on one side. In the proposed model, the stiffeners are characterised by their translational and rotational dynamic stiffnesses which can be estimated by a finite element method (FEM). These dynamic stiffnesses are then coupled with the analytical formulation of the fluid-loaded plate to obtain the expressions of the spectral displacement and radiated pressure. Comparisons of the results in terms of the plate's mean quadratic velocity and radiated sound power for the rectangular and ABH stiffeners show that by using the ABH stiffeners instead of the conventional stiffeners, one can significantly reduce the vibroacoustic response of light/heavy fluid-loaded plates

Vibroacoustic response of a heavy fluid loaded plate with ABH stiffeners

Abstract Stiffened structures are essential for a wide range of engineering applications including aeronautics, marine and rail systems. Adding stiffeners to a host structure leads to generation of Bloch-Floquet waves, which are induced by the interaction between the flexural waves in the host structure and the flexural/torsional waves in the stiffeners. These waves could generate unwanted noise and vibrations which should be mitigated. Acoustic black holes (ABHs) are widely used as a passive-control approach to mitigate vibrations of elastic structures. This study aims to use ABHs integrated as stiffeners for a fluid-loaded plate. Hence, the host structure is not modified, and its structural integrity is maintained. A heavy fluid-loaded infinite plate with periodic ABH stiffeners under a line force excitation is considered (i.e., a two-dimensional model). To obtain the vibrocoustic response, the system is modelled using the COMSOL Multiphysics®. The effectiveness of the ABH stiffeners in mitigating the vibration and noise from the fluid loaded plate is examined.</jats:p

Spatial coherence of pipe vibrations induced by an internal turbulent flow

Whereas the spatial coherence of wall pressure and vibratory fields induced by turbulent boundary layers (TBLs) on flat plates have been studied at extent, their equivalents for cylindrical structures still need further investigation. To that end, this work develops a semi-analytical model which is valid for infinite cylindrical shells filled with a heavy fluid and excited by an internal TBL. The cylindrical shell can be also coupled to two ring stiffeners that account for the flanges generally used to connect a pipe to other portions of a circuit. The cross-spectrum density (CSD) function of the shell radial accelerations is estimated from the system circumferential sensitivity functions and the CSD of the wall pressure field induced by the TBL. The spatial coherence of the pipe vibration field is therefore analysed for a pipe with and without flanges. This is of critical importance for applications such as non-intrusive techniques for detecting acoustic sources inside pipes, like beamforming using arrays of accelerometers. If the pipe conveys a flow, the beamforming efficiency can strongly deteriorate because of the background noise induced by the TBL, which pollutes the coherence signal between sensors. The effects that the spatial coherence could have on the beamforming results of a line of point sensors (accelerometers) and a ring of wire sensors (piezoelectric coiled wires) are also investigated in this paper

Modeling of micro-perforated panels in a complex vibro-acoustic environment using patch transfer function approach

2011-2012 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Sound radiation from a plate immersed in water near the free surface

The results on the acoustic response of a heavy fluid-loaded baffled plate excited by a harmonic point force are presented. The displacements of the fluid-loaded plate are decomposed on the basis of the in-vacuo plate modes and the radiated acousic waves are determined solving the Helmholtz equation in a fluid. The Green's function for the acoustic waveguide domain formed by the baffled plate and the free surface is modelled by the source-image method. Predictions for the radiated sound power from the plate and pressure spectra are calculated for varying depths of the free surface and compared against results from an unbounded domain to infer the effect of the free surface on the acoustic response of the plate. The proposed analytical model is verified by comparison with finite element simulations