SmEdA vibro-acoustic modelling in the mid-frequency range including the effect of dissipative treatments

Abstract

Vibro-acoustic simulation in the mid-frequency range is of interest for automotive and truck constructors. The dissipative treatments used for noise and vibration control such as viscoelastic patches and acoustic absorbing materials must be taken into account in the problem. The Statistical modal Energy distribution Analysis (SmEdA) model consists in extending Statistical Energy Analysis (SEA) to the mid-frequency range by establishing power balance equations between the modes of the different subsystems. The modal basis of uncoupled-subsystems that can be estimated by the finite element method in the midfrequency range is used as input data. SmEdA was originally developed by considering constant modal damping factors for each subsystem. However, this means that it cannot describe the local distribution of dissipative materials. To overcome this issue, a methodology is proposed here to take into account the effect of these materials. This methodology is based on the finite element models of the subsystems that include well-known homogenized material models of dissipative treatments. The Galerkin method with subsystem normal modes is used to estimate the modal damping loss factors. Cross-modal coupling terms which appear in the formulation due to the dissipative materials are assumed to be negligible. An approximation of the energy sharing between the subsystems damped by

Research Progress on High‐Intermediate Frequency Extension Methods of SEA

“…is method was originally developed by considering the constant mode damping factor of each subsystem, which could not describe the local distribution of dissipated materials. To overcome this problem, Maxit and Guyader [6,102] proposed a statistical method of mode energy including dissipated materials. is method is based on the subsystem FEM and the homogenous material model of dissipation processing to process the structural plate cavity system.…”

Assessment of the apparent bending stiffness and damping of multilayer plates; modelling and experiment

“…dated on measured and synthesized signals for frequency domain where the Fourier transform meets its limits (due to high modal overlap or poor signal-to-noise ratio). Recently, the method has been also successfully applied on an orthotropic ribbed plate [30], bilayer plates [31], or plate-cavity system [ [32], [33]].…”

SmEdA Vibro-Acoustic Modeling of a Trimmed Truck Cab in the Mid-Frequency Range

“…For an acoustic subsystem, the well-known equivalent fluid model can be used to represent the acoustic behavior of the poroelastic materiel. The complex equivalent fluid density and the complex equivalent fluid compressibility can be estimated from acoustic tube measurements with the Utsuno two cavities method [7]. This type of modelling has two main advantages: (a) it permits increasing the upper frequency bound of the FEM calculation compared to a full detailed model; (b) it is well adapted for 10/19/2016 optimizing dissipative materials.…”

“…Analytical expressions of the modal damping loss factors are obtained in function of the subsystem modeshapes and the complex matrices of the finite element model of the dissipative subsystem. These theoretical developments are described in details in [7]. These calculations may be achieved in post-processing of the modal extraction calculation and they are few time-consuming; -The final step consists in resolving the SmEdA equations (1) depending on the subsystem modal information estimated numerically in the two previous steps.…”

“…It may be the visco-elastic layers used for damped the structural vibration or the porous elastic materials used for their sound absorbing ability. An approach based on SmEdA for taking into account these dissipative treatments has been recently developed during the PhD thesis of Ha Dong Hwang [7]. Basically, this method consists to develop an equivalent model of the dissipative materiel in order to be easily implemented in the subsystem FE model, to extract the subsystem modes of the dissipative subsystem and then to estimate the modal damping loss factors using a projection of the complex finite element matrices.…”