Statistical Energy Analysis

Cette étude porte sur l'utilisation de la Transformée en Ondelettes Continue (TOC) pour caractériser les systèmes mécaniques faiblement non-linéaires et faiblement amortis, soumis à une excitation ambiante modélisée sous forme de bruit blanc gaussien. Après une analyse théorique de ces systèmes, dont la réponse est étudiée dans le plan temps-fréquence, une méthode de caractérisation de leurs non-linéarités basée sur la TOC est proposée. Enfin, des simulations numériques basées sur un cas d'étude simple permettent d'étayer les résultats théoriques avancés. Mots clés -Transformée en ondelettes continue, Système faiblement non-linéaire, Excitation ambiante.

The present paper reviews the vibro-acoustic modelling of extruded aluminium train floor structures including the state-of-the-art of its industrial applications, as well as the most recent developments on mid-frequency modelling techniques in general. With the common purpose to predict mid-frequency vibro-acoustic responses of stiffened panel structures to an acceptable accuracy at a reasonable computational cost, relevant techniques are mainly based on one of the following three types of mid-frequency vibroacoustic modelling principles: (1) enhanced deterministic methods, (2) enhanced statistical methods, and (3) hybrid deterministic/statistical methods. It is shown that, although recent developments have led to a significant step forward in industrial applicability, mature and adequate prediction techniques, however, are still very much required for solving sound transmission through, and radiation from, extruded aluminium panels used on high-speed trains. Due to their great potentials for predicting mid-frequency vibro-acoustics of stiffened panel structures, two of recently developed mid-frequency modelling approaches, i.e. the so-called hybrid finite element-statistical energy analysis (FE-SEA) and hybrid wave-based methodstatistical energy analysis (WBM-SEA), are then recapitulated.

The noise inside railway vehicles plays an important role for the comfort of passengers and train crew. In determining the interior noise, the noise transmission through the train floor and sidewalls is particularly important. Modern train body structures are often made of extruded aluminium panels and the current work focuses on modelling the noise radiation from, and transmission through such structures. Use is made of a statistical energy analysis (SEA) approach which is established with the support of a waveguide finite element (2.5D FE) model. The latter is used to study the vibration properties of the extruded panel that are then utilized to calibrate simple equivalent analytical models for the various components of the extrusion. These in turn are used to define the input parameters for the SEA model, e.g. the modal densities and the coupling loss factors between subsystems. With the aid of such a calibration, the predictions from the SEA model of the sound transmission loss and of the radiation efficiency of the extruded panel agree well with measurements and numerical models using the 2.5D FE/BE approach and the VA One software. By following the procedures outlined in this paper, SEA models can be established by using a simple analytical representation of different parts of the extruded panel and hence without the need to develop ad-hoc and computationally expensive numerical models.

After a brief introduction to the theory and physical interpretation of Lagrangian force density in general sound fields, this article focuses on its stationary average property providing the general expression of the actionreaction law for acoustic fields. This fundamental property allows to define the tension field of sound, which turns out to be easily measured as the gradient of the average potential energy density. The acoustic tension field has been then analytically calculated and visualized for quasi-stationary wave fields and divergent spherical waves. Moreover 2-D graphics comparing the behaviors of sound energy trajectories and tension fields are here reported.

The Energy Flow Method (EFM) is a computationally efficient method, by which the results of a Finite Element Analysis (FEA) may be post-processed to form energy flow models. It can be used to study structure borne transmission in structures, based on modal descriptions of the structure and the internal cavity. The EFM allows to form a Energy Influence Coefficient model (EIC) or an inverse SEA model. A first issue consists in partitioning the FE model into SEA sub-systems, with respect to the SEA assumptions (particularly the weak coupling assumptions). An automatic technique based on cluster analysis, can be used to determine an appropriate SEA sub-structuring, before calculating the Coupling Loss Factors (CLF) between mechanical subsystem. A second issue is to calculate the CLF between structural and acoustic subsystems. This paper presents an industrial application of these techniques, for the analysis of structure borne transmission inside a tramway vehicle. The EFM technique is used to calculate the vibro-acoustic transfer of the car body of the tramway, and comparison with measurements on a vehicle are presented.

The coupling loss factors are of critical importance when building and solving Statistical Energy Analysis (SEA) models. This paper proposes a methodology to numerically estimate these factors for frame-type structures. The estimated factors are compared with those obtained through analytical expressions for frame structures, where members are joined at right angles. The example used to verify the proposed technique consists of two infinite beams connected at a right angle modeled via the Spectral Element Method (SEM) using throw-off elements. It is shown that the obtained coupling loss factors compare very well with the analytical expressions that may be derived for this simple right-angle connection case. By using the SEM approach, the coupling loss factors can be obtained for arbitrary frame structure connections, thus facilitating the analysis via SEA.

est l'aboutissement d'un long cheminement scientifique et humain. Si, dans les pages qui suivent, la partie scientifique est largement mise en valeur, je souhaiterais profiter de ce petit espace qui m'est laissé pour adresser d'immenses remerciements à toutes les personnes qui m'ont accompagné durant ces années de thèse. Tout d'abord, je tiens à remercier à Louis Jézéquel et Mohammed Ichchou pour m'avoir fait confiance et m'avoir permis d'apprendre beaucoup à leurs côtés. Merci ensuite à messieurs Lallement et Sarhaoui pour avoir accepté de rapporter mes travaux. Merci à Fabrice Thouverez de m'avoir fait l'amitié de participer au jury. Merci surtout à Agnès pour son soutien indéfectible dans les moments de doute, et pour sa patience... La liste est encore longue et je crains d'en oublier certains. Je citerai néanmoins les personnes qui, au quotidien, font qu'il m'est toujours agréable de venir au laboratoire : Isabelle, Lionel, Bernard, Patrick et Stéphane pour la partie technique, mais aussi les anciens et futur anciens,

Statistical energy analysis (SEA) is a well-known method, which can be also used for prediction of transmission loss. The difficulty in this method is to estimate the coupling loss factors, which are needed to calculate the energy transfer between the subsystems. It has been shown in previous articles on examples for structure-to-structure and structure-to-cavity coupling, that the statistical modal energy distribution analysis (SmEdA) is a convenient method for calculating this coupling loss factors. This approach relies on a dual modal formulation to describe vibrations of coupled subsystems. However, the original SmEdA formulation takes into account only the resonant modes related to a frequency band. That is the reason for developing an improved approach on the basis of SmEdA in the framework of the Marie Curie project "MID-FREQUENCY". This improved method integrates the non resonant modes in the calculation. The application possibilities and the advantages of the new extended version of SmEdA are demonstrated on the example of transmission loss of a plate between two finite cavities. The principal advantages are that transmission loss can be predicted for non-diffuse sound fields and for different boundary conditions.

Statistical energy analysis (SEA) is applied to study the transmission of random incidence sound waves through two finite independent panels separated by a gap filled with helium. The study was made for the following two cases: (1) glass panes with a cavity, and (2) vinyl panes with a cavity. The analytical SEA model chosen is similar to the one developed earlier by one of the authors [A. J. Price and M. J. Crocker, J. Acoust. Soc. Am. 47, 683–693 (1970)]. The analytical model consists of five linearly coupled oscillator systems, room-panel-cavity-panel-room. Both resonant and nonresonant transmissions have been considered for each wall of the double panel system. Allowance has also been made in the analytical model to include the effects of the absorption in the cavity. The results show that the use of helium instead of air in the gap of the double panel systems shifts the coincidence frequency region to a higher frequency and also increases the transmission loss values.

For the vibro-acoustic simulations of interior noise, it is necessary to take the damping behavior of relevant acoustic materials into account. On the one hand, deterministic methods like the well known Finite Element Method or the recently developed Wave Base Technique, consider this as a normal impedance boundary condition. On the other hand, statistical methods like the Statistical Energy Analysis are using absorption coefficients, which can be determined for example out of the normal impedance. This paper discusses a methodology to identify the normal impedance out of measured pressure data. For this, a suitable mathematical optimization problem will be introduced by using deterministic simulations methods and optimization processes. First validation results will illustrate the potential of the proposed methodology to identify the impedance out of measured pressure data.

Engineering systems such as aircraft, ships and automotive are considered built-up structures. Dynamically they are taught of as being fabricated from many components that are classified as 'deterministic subsystems' (DS) and 'nondeterministic subsystems' (Non-DS). Structures' response of the DS is deterministic in nature and analysed using deterministic modelling methods such as finite element (FE) method. The response of Non-DS is statistical in nature

An unstructured zero-order energy finite element method (uEFEM 0 ) formulation is presented to simulate the high-frequency behavior of plate structures in contact with acoustic enclosures, which is can be seen as a typical simplification of cars. In this formulation, the vibration energy of all the bending, longitudinal and shear wave fields in the plates and sound press level in the acoustic enclosure can be obtained. This uEFEM 0 formulation is validated by comparing the results with those from Statistical Energy Analysis (SEA). Good correlations are observed and the potential effort of the uEFEM 0 as a NVH tool in car industry is identified.

Il y a deux grandes familles d'opérateurs de fusion : les opérateurs majoritaires et les opérateurs d'arbitrage. Alors qu'il existe de nombreux opérateurs majoritaires, très peu d'opérateurs d'arbitrage ont été définis jusqu'à présent. Dans cet article, nous étudions une notion plus générale que la fusion avec arbitrage : la notion de fusion égalitaire. Nous traduisons dans le cadre de la fusion de croyances deux conditions existantes en théorie du choix social, la condition de Sen-Hammond et la propriété de Pigou-Dalton. Nous montrons que les opérateurs de fusion satisfaisant la condition de Sen-Hammond sont essentiellement ceux qui utilisent le leximax comme fonction d'agrégation. Nous introduisons également deux nouvelles familles d'opérateurs de fusion de croyances, basées respectivement sur la médiane et sur les sommes cumulées (courbes de Lorenz). Nous identifions leurs propriétés de rationalité, en particulier nous étudions leur comportement égalitaire.

One of the most important things when we want to solve a mechanical or vibroacoustic problem falls on subdivision of the study domain, which directly affects the process. Thus, in this thesis we present a detailed study of the subsystem identification technique, that in the case of SEA (Statistical Energy Analysis) method is based on the classification of the domain according to transfer energy between subsystems. A subsystem is a set of nodes with a similar behaviour, which allows us to subdivide a domain into different groups. This subdivision is achieved by performing a cluster analysis of the transfer matrix powers. The Transfer matrix, which we obtain from the mechanical properties of our engineering structure, allows us to describe and quantify the direct transmission of signals between nodes. The identification of subsystems in complex or large geometries is very useful in the SEA method applied to vibroacoustic problems, but also to the reduction of the operational cost in a finite element problems, such as it has been done in this thesis, optimising the Newmark method. All these concepts are implemented, a posteriori, in the analysis of vibroacoustics problems through different representative geometries, in order to analyse the accuracy and applicability of the method.

It is a common practice in aerospace and automobile industries to use double wall panels as fuselage skins or in window panels to improve acoustic insulation. However, the scientific community is yet to develop a reliable prediction method for a suitable vibro-acoustic model for sound transmission through a curved double-wall panel. In this quest, the present work tries to delve into the modeling of energy transmission through a double-wall curved panel and the subsequent radiation of sound power in low to mid frequency range into the free field from the exterior curved panel. A modal expansion theory based on Green's theorem is implemented to model the energy transmission through an acoustically coupled double-wall curved panel. A method based on the boundary element (BE) technique is then employed to calculate the radiated sound into the free field from the curved panel. The main advantage derived from BEM is that it is sufficient to discretise the radiated surface alone and there is no need to mesh the infinitely extended acoustic domain surrounding the vibrating surface as the non-reflecting boundary condition has been already implemented while developing the governing BEM equation. The developed BEM program is first validated experimentally for a flat panel where it is found to work with reasonable accuracy. The BEM program is also compared for a curved panel numerically with the elemental radiator approach. It has been observed in the present study that the radius of curvature of the surface has a prominent effect on the characteristics of radiated sound power into the free field. Effect of thickness of the air gap between the two curved surfaces on sound power radiation has also been noted. Mass and Stiffness matrix of the panel Displacement of the panel 'a' and 'b' Modal coordinate of the panel 21st International Congress on Sound and Vibration (ICSV21),

Sandwich panels are usually modeled by considering only asymmetric motion which assumes the core deforms by transversal shearing without any compressive deformation over the thickness. This assumption is acceptable for panels with relatively stiff and thin cores. However, symmetric motion becomes important when the core is thick or soft. Under such conditions, the compressive deformation over the core thickness becomes significant. This paper addresses the prediction of the Sound Transmission Loss (STL) and composite Damping Loss Factor (DLF) of sandwich panels with either thin or thick cores as well as stiff or soft (viscoelastic) cores. Both the skin and the core are assumed to be orthotropic. A spectral finite element based approach is developed wherein the stress and strain components in each layer are described using the properties in that layer for a forced trace wave number and heading direction. The proposed approach provides a reliable and numerically efficient tool to account for the compressive deformation effect of thick orthotropic sandwich layers. Moreover, the proposed model is also able to consider panels with multiple of layers with varying properties.

Statistical modal Energy distribution Analysis (SmEdA) can be used as an alternative to Statistical Energy Analysis for describing subsystems with low modal overlap. In its original form, SmEdA predicts the power flow exchanged between the resonant modes of different subsystems. In the case of sound transmission through a thin structure, it is well-known that the non resonant response of the structure plays a significant role in transmission below the critical frequency. In this paper, we present an extension of SmEdA that takes into account the contributions of the non resonant modes of a thin structure. The dual modal formulation (DMF) is used to describe the behaviour of two acoustic cavities separated by a thin structure, with prior knowledge of the modal basis of each subsystem. Condensation in the DMF equations is achieved on the amplitudes of the non resonant modes and a new coupling scheme between the resonant modes of the three subsystems is obtained after several simplifications. We show that the contribution of the non resonant panel mode results in coupling the cavity modes of stiffness type, characterised by the mode shapes of both the cavities and the structure. Comparisons with reference results demonstrate that the present approach can take into account the non resonant contributions of the structure in the evaluation of the transmission loss.

Les structures à double paroi sont largement utilisées dans la lutte contre les nuisances sonores et vibratoires en raison de leur supériorité en terme d'isolation acoustique sur les parois simples. Parmi les exemples typiques on peut citer les doubles vitrages, le fuselage des avions, les véhicules, etc. Dans ce contexte, nous nous sommes intéressés à l'étude expérimentale et numérique du comportement vibroacoustique des doubles parois feuilletées. Le système étudié est composé de deux plaques sandwichs à cœur viscoélastique séparées par une cavité remplie d'air. Nous avons développé un modèle éléments finis basé sur une formulation variationnelle impliquant le déplacement en tout point de la structure et la pression acoustique dans la cavité d'air. Due aux propriétés mécaniques complexes du matériau viscoélastique utilisé dans le cœur des panneaux, cette formulation est complexe et dépend de la fréquence. La résolution de ce modèle par les méthodes directes a un co...

Although applications for Statistical Energy Analysis (SEA) techniques are more widely used in the aerospace industry today, opportunities to anchor the response predictions using measured data from a flight-like launch vehicle structure are still quite valuable. Response and excitation data from a ground acoustic test at the Marshall Space Flight Center permitted the authors to compare and evaluate several modeling techniques available in the SEA module of the commercial code VA One. This paper provides an example of vibration response estimates developed using different modeling approaches to both approximate and bound the response of a flight-like vehicle panel. Since both vibration response and acoustic levels near the panel were available from the ground test, the evaluation provided an opportunity to learn how well the different modeling options can match band-averaged spectra developed from the test data. Additional work was performed to understand the spatial averaging of the measurements across the panel from measured data. Finally an evaluation/comparison of two conversion approaches from the statistical average response results that are output from an SEA analysis to a more useful envelope of response spectra appropriate to specify design and test vibration levels for a new vehicle.

Although applications for Statistical Energy Analysis (SEA) techniques are more widely used in the aerospace industry today, opportunities to anchor the response predictions using measured data from a flight-like launch vehicle structure are still quite valuable. Response and ...

Orthotropic multi-layered panels are well-spread in transport industry. Specific methods of prediction need to be addressed depending on construction. Laminate models based on zigzag theory are useful for aircraft fuselage prediction and more generally for composite panels. As soon as a very soft layer is inserted between stiff layers, breathing modes are occurring in mid and high frequencies and assumed zigzag displacement field is no more representative of the actual behavior. It has to be replaced by 3D FEM modeling increasing cost of calculation. In Statistical Energy Analysis (SEA) models, because of the extended calculation range, the 'classical' laminate equations are limiting the class of simulated systems and zigzag theory is most often pushed outside its natural limits. A new multi-scaled dynamic laminate model has thus been developed to take into account transverse decoupling of layers while converging correctly to equivalent static plate at low frequency. This laminate model accepts any kind of mechanical orthotropic layers as well as thin 2D acoustic layers. They may be ribbed or not to increase stiffness. Damping loss factor of the assembly is predicted from internal damping of the various layers. Basic equations will be presented as well as some early validation work.

Orthotropic multi-layered panels are well-spread in transport industry. Specific methods of prediction need to be addressed depending on construction. Laminate models based on zig-zag theory are useful for aircraft fuselage prediction and more generally for composite panels. As soon as a very soft layer is inserted between stiff layers, breathing modes are occurring in mid and high frequencies and assumed zig-zag displacement field is no more representative of the actual behavior. It has to be replaced by 3D FEM modeling increasing cost of calculation. In Statistical Energy Analysis (SEA) models, because of the extended calculation range, the ‘classical’ laminate equations are limiting the class of simulated systems and zig-zag theory is most often pushed outside its natural limits. A new multi-scaled dynamic laminate model has thus been developed to take into account transverse decoupling of layers while converging correctly to equivalent static plate at low frequency. This laminat...

The project "Silent Timber Build" will develop new prediction tools for timber structures. There are several challenges that have to be overcome to provide a full prediction tool. The differences in weight, stiffness and density for wooden structures compared to traditional, heavy and more homogeneous structural material have repercussions on how the sound propagates throughout the structures, affecting the sound and vibration insulation performance and also theories to be used in prediction models. Finite element simulations have proved to be useful in the design phase in a certain low and very low frequency range. By further developing reliable finite element tools for low frequencies, the performance of future wooden constructions can be predicted in a full frequency range, saving both time and money as all calculations, and modifications can be done during the design phase. However the upper limit for using FEM has to be further investigated and then be merged with sta...

Due to a new pass-by noise regulation, Vehicle exterior noise will have to be reduced in the coming years. This may be achieved by optimizing underbody and underhood absorption and screening apertures. There is then a need for numerical techniques able to predict sound reduction related to acoustic absorption and transmission loss changes. Through a work supported by ADEME and headed by PSA, energy-based predictive techniques such as Analytical Statistical Energy Analysis (ASEA) and discretized Energy Flow Analysis (DEFA) were tested against the actual physical problem to be solved through a series of benchmarks. Both theories are compared across several simple acoustic problems. It is concluded that both methods do not fit to the initial acoustic optimization requirement due to their intrinsic assumptions that restrict their applicative range. More fitted numerical techniques are now investigated: among new candidates, the Virtual SEA (VSEA) technique that allows the creation of a ...

In the mid-frequency range (200-2000 Hz), difficulty is encountered when modeling car body vibroacoustic interactions, mainly due to the complexity of automotive design. Analytical Statistical Energy Analysis (ASEA) is efficient to bring to the fore regions of interest regarding NVH design but was proven to be accurate only above 2000 Hz. To overcome ASEA limitations at lower frequencies, Virtual SEA (VSEA) technique was introduced to translate the dynamic information contained in a finite element (FE) model into an SEA model. Any FE model, whatever its complexity, can thus be processed thanks to an automatic sub-structuring algorithm and a built-in VSEA modal synthesis solver, fast leading to robust numerical SEA model. VSEA also addresses structure-borne noise problems by coupling structural VSEA subsystems to analytical acoustic subsystems through a virtual wave number. Investigation of damping and trim treatment effects on mixed acoustic and structural subsystems are thus possib...

The vibro-acoustic response of the fairing of the Vehicle Satellite Launcher (VLS) is obtained, using the Statistical Energy Analysis Technique (SEA). The SEA virtual prototype of the refered fairing is built up, applying the estimated acoustic loading (160 OSPL), during the lift off. The structural and acoustic subsystems are connected and the approaches of this high frequency analysis technique are described. 1/3 octave band analysis is run and the results, as well as some comments about the uncertainties of this technique in low frequency band analysis are described.

Finite element method (FEM) and boundary element method (BEM) are methods usually applied on lowfrequency coupled fluid-structure analysis. On the other hand, statistical energy analysis (SEA) is a technique applied on small wavelength bandwidth predictions. However, in the midfrequency, where deterministic calculations are costly and confidence intervals of SEA are not satisfied, hybrid FEM/ SEA models can be used. This work presents a coupled vibro-acoustic analysis methodology of the Brazilian Satellite Launcher Vehicle payload fairing. FEM/FEM model accounts for the low-frequency internal responses. The high-frequency responses are computed by a SEA coupled elasto-acoustic model, and a hybrid FEM/SEA model calculates the payload fairing mid-frequency behavior.

In the recent years the composite materials aggrandize attention of researchers since metals have been replaced with these composites. The properties such as high strength to weight ratio, high modulus, excellent resistance to fatigue, creep, corrosion and wear as well as economical. Most of the studies done so for related to composite materials analytical, numerical or experimental focused on the strength evaluation. In the present study the vibro-acoustic analysis of the composite specimen has been carried out, since in case of structural application it plays a significant role. The vibro- acoustic analysis of the fabricated composite specimens is carried out numerically employing different boundary conditions.

Cette thèse compte 161 pages mais celle-ci est peut-être la plus difficile à écrire. Comment remercier en quelques mots tous ceux qui ont participé de près ou de loin à ce travail et surtout comment faire pour ne pas en oublier ? Cela demanderait quasiment une autre thèse... Je vais donc essayer de faire au mieux. Honneur à mon directeur de thèse, Monsieur Cilles ROBERT, pour lequel peu de mots suffiront car nous savons tous les deux ce que je lui dois. Je tiens à remercier Monsieur le professeur D. JUVÉ, Directeur du Département de Mécanique des Fluides, Acoustique et Energétique de 1 'Ecole Centrale de Lyon, pour m 'avoir accueilli dans son équipe pendant ces trois années.

Sandwich-rakenteella tarkoitetaan tässä kolmikerroksista levyä. Käyttämällä kahta ohutta, jäykkää kuorta ja niiden väliin liimattua paksua ydintä saadaan rakenteesta kevyt ja jäykkä. Tämä on hyvä toiminnallinen ominaisuus, mutta äänenhallinnan kannalta epäedullinen. Sandwich-rakenteiden käyttö koneiden ja kuljetusvälineiden äänikriittisissä osissa kasvaa. Siksi VTT:llä on tutkittu tilastollisen energia-analyysin (SEA) käyttöä kyseisen tyyppisten rakenteiden mallinnuksessa. Aihe on laaja. Tässä esityksessä rajoitutaan yksittäiseen levyyn ääneneristävyys-ja äänensäteilynäkökulmasta. 2 YLEISTÄ SANDWICH-LEVYN VIBROAKUSTIIKASTA Kuorilaminaattia voidaan dynamiikan kannalta pitää ohuena laattana. Vastaavasti ydinkerrosta voidaan pitää esim. paksuna laattana, jolla yksinään on pieni taivutusjäykkyys (kennoydin) tai ns. solidina (vaahtoydin). Kytkemällä yhteen eri kerrosten dynamiikkaa hallitsevat yhtälöt voidaan johtaa koko rakennetta kuvaavat osittaisdifferentiaaliyhtälöt. Nämä ovat, tehdyistä oletuksista riippuen, 6...12 kertalukua, ks. [1-6]. Aikaharmonisen ratkaisuyritteen kautta saadaan ns. dispersioyhtälö(t). Dispersioyhtälön juurina saadaan joukko aaltolukuja, jotka identifioivat eri suuntiin eteneviä ja etenemättömiä aaltoja.

Dynamical Energy Analysis (DEA) has been introduced as a mesh-based high frequency method modelling structure borne sound for complex built-up structures. This has proven to enhance vibro-acoustic simulations by making it possible to work directly on existing finite element meshes circumventing time-consuming and costly remodeling strategies. In addition, DEA provides detailed spatial information about the vibrational energy distribution within a complex structure in the mid-to-high frequency range. DEA has been used to calculate the structure borne sound of an assembled agricultural tractor and good agreement between measurements and DEA calculations has been shown. In particular, it has been demonstrated that DEA can model shell structures accurately. However, it is still difficult to model a solid structure because currently DEA is based on wave transmission calculations through plate/plate junctions. Additionally, accurate FE meshes of assembled complex structures are often not available due to the uncertainties of modelling welds, bolts and rubber bushes between components. We propose here to integrate measurement data into DEA to improve the effectiveness of DEA modelling. Advanced Transfer Path Analysis (ATPA) is employed to extract energy transmission characteristics of a structure. The direct transfer functions between interface points are calculated using ATPA based on measured frequency response functions. DEA elements connecting interface points and representing energy transmission characteristics of the structure are created based on the ATPA result. The proposed method is verified with a finite element model of a simple structure.

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence 1 in expectation to the solution within a specified tolerance. This generalized framework is specialized to the problems of sparse signal recovery in compressed sensing and low-rank matrix recovery, giving methods with provable convergence guarantees that often outperform their deterministic counterparts. We also analyze the settings where gradients and projections can only be computed approximately, and prove the methods are robust to these approximations. We include many numerical experiments which align with the theoretical analysis and demonstrate these improvements in several different settings.

One of the major objectives of the Automotive Research Center (a US Army TACOM Center of Excellence for the modelling and simulation of ground vehicles at the University of Michigan) is to develop new methodologies for advanced structures and materials for next-generation ground vehicles. Several major developments in this area are detailed in this paper. First, an advanced topology optimisation technique is presented, which provides a tool for laying out new, conceptually advanced designs for vehicle structures, or substructures, to achieve the lower weight and higher performance requirements for next-generation ground vehicles. Second, a 'sizing' design optimisation process is presented for detailed design changes in order to improve the vibrant-acoustic response of a complex vehicle structure. This process incorporates efficient analysis and sensitivity analysis capabilities for vibro-acoustic systems. In addition, a component-based technique is presented for generating reduced-order models of a vehicle structure in order to lower the computational costs of vibration analysis. This technique is also extended to analysing vibration transmission in a complex vehicle structural system to determine the power flow among components and the effect of parameter uncertainties. Finally, an energy boundary element analysis method is presented for efficient and accurate high-frequency noise analysis, which extends the capability for predicting the acoustic field around the vehicle due to various sources.

Vibration of exhaust system due to the engine operation and the condition of the road surface which is transferable to the body through the hanger affects the noise, vibration and harshness performance of the vehicle, and the life time of the hangers. In order to solve this problem of the automobile exhaust system, experimental modal analysis was carried out by utilizing a sample exhaust system of passenger car as a research object within the frequency of interest. LMS Test. Lab was used to perform modal analysis. This study estimated the dynamic characteristics of the exhaust system such as natural frequencies and mode shapes. Using frequency response function at every measuring point, root mean square value (RMS) of vibrating energy was calculated to select hanger location of exhaust system where the RMS value is comparatively small. Experimental modal analysis is an efficient tool to study and estimate the dynamic properties of the exhaust system, and calculating RMS value is als...

In the field of stochastic structural dynamics, perturbation methods are widely used to estimate the response statistics of uncertain systems. When large built up systems are to be modelled in the mid-frequency range, perturbation methods are often combined with finite element model reduction techniques in order to considerably reduce the computation time of the response. Existing methods based on Component Mode Synthesis (CMS) allow the uncertainties in the system parameters to be treated independently in each of the substructures and the perturbation in the local parameters to be propagated to the full system global parameters. However, local treatment of damping uncertainty is usually avoided by assuming proportional damping. Here, a perturbation method that includes local modal damping uncertainty and its propagation to the global response is proposed. Local damping is accounted for in the CMS model by use of complex modes. A perturbation relationship between local and global mo...

The identification of the acoustical properties of materials plays a key role in the numerical prediction of the acoustic performance and the structural behavior of any mechanical system. Therefore, to obtain an accurate frequency-dependent response, it is essential a suitable choice of the parametric models for each material. However, such models could be inadequate by the material nature or not valid for a given frequency range. In this work, a novel numerical optimization strategy for the characterization of material acoustic properties is introduced, which only uses a reduced number of experimental measurements with the advantage of avoiding parametric model choices.

An extension of the modal overlap factor is introduced that includes ensemble variations and frequency averaging of plates and acoustic spaces. Uniformly and normally distributed variations of geometric and material parameters are considered. Using this modal overlap factor, approximate formulas are derived to identify the limit of predictability for the combined case of damping, ensemble variation, and frequency averaging. The extended modal overlap factor is used to define a high-frequency threshold for plates and acoustical spaces that depends on system parameters and their variations as well as on damping, and the bandwidth of frequency averaging. Monte-Carlo simulations are shown to illustrate and validate the results.

A new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures-also referred to as Dynamical Energy Analysis (DEA)-has been proposed recently (G Tanner, JSV 320, 1023 (2009)). The technique interpolates between "Statistical Energy Analysis" (SEA) and "ray tracing" containing both these methods as limiting cases. Within the new theory SEA is identified as a low resolution ray tracing algorithm and typical SEA assumptions can be quantified in terms of the properties of the ray dynamics. We have developed an efficient DEA code and have tested it for a range of multi-component model systems. For reference purposes, we have undertaken numerically exact calculations for solving the underlying wave equations using both finite element (FEM) and boundary element (BEM) methods. The FEM calculations use sophisticated hp-adaptive discontinuous Galerkin methods. For the BEM calculations, we have developed a multi-component BEM solver for wave problems with variable wave speed and damping parameters across subsystems .

An advanced version of statistical energy analysis (SEA), called AutoSEA2, is described. The three-dimensional subsystem was responsible for intuitiveness of SEA modeling and minimized cumulative guestimation errors. The auto-connect function reduced the modeling time and avoided manual data input errors. The implementation of full wave transmission theory improved the accuracy and minimized the need for user expertise in modeling junctions. AutoSEA2 delivered a `design evaluation' solution for addressing noise and vibration performance issues.