Statistical Energy Analysis (SEA) is one of the methods in literature to estimate high frequency vibrations. The inputs required for the SEA power balance equations are damping and coupling loss factors, input powers to the subsystems. In this study, the coupling loss factors are derived for two and three plates joined with a stiffener system. Simple formulas given in the literature for coupling loss factors of basic junctions are not used and the factors are calculated from the expressions derived in this study. The stiffener is modelled as line mass, Euler beam, and open section channel having double and triple coupling. Plate is modelled as Kirchoff plate. In the classical SEA approach the joint beam is modelled as another subsystem. In this study, the beam is not a separate subsystem but is used as the characteristics of the joint and to calculate the coupling loss factor between coupled plates. Sensitivity of coupling loss factors to system parameters is studied for different beam approaches. The derived coupling loss factors and input powers are used to calculate the subsystem energies by SEA. The last plate is joined to the first one to simulate the fuselage structure. A plate representing floor structure and acoustic volume are also added. The different modelling types are assessed by applying pressure wave excitation. It is shown that deriving the parameters as given in this study increases the efficiency of the SEA method.

With the advent of power electronics, inverter-driven induction motor are finding increased use in industries because of applications that demand variable speed operations and because of the potential savings in energy usage. However, these drives sometimes produce unacceptably high levels in vibration and acoustic noise. A literature survey has revealed that while there has been intensive research on the design of inverters to minimize acoustic noise radiation from these drives, the vibro-acoustic behaviour of an induction motor structure has received relatively little attention. The primary objective of this research project, therefore, is to develop a general strategy/algorithm for estimating the acoustic noise radiated from inverter-driven induction motors. By using a three-phase, 2.2 kW induction motor, the vibration modes due to various structural components (such as the rotor, the stator/casing, the endshields and the base plate) of the motor structure were analysed by experimental modal testing. Results indicate that the vibration modes due to the rotor are only important at low frequencies. It has been found that the power injection method gives more accurate measurement of the damping of a motor structure than the modal testing and the time decay methods. If a point force excitation is used, then it is more accurate to measure the sound radiation efficiency than the power conversion efficiency for motor structures. The effect of three different inverter designs (an ideal ???almost sinusoidal??? controller and two commercially available PWM inverters) on the radiated acoustic power were assessed for both no-load and load conditions using sound intensity measurements conducted in an anechoic room. The results indicate that although the sound power level due to aerodynamic and mechanical noise increases at a rate of 12 dB per doubling of the motor speed, the electromagnetic noise dominates at low motor speeds and is still a significant noise source even at high motor speeds. For inverters with low switching frequencies, the radiated sound power level is almost 15 dB higher than the ideal case at low speeds and is relatively insensitive to the motor speed. For inverters that implement the random modulation technique, the change in the total sound power level with the level of the random modulation is very small but the tonal nature of the noise is greatly reduced. The vibration behaviour of a motor structure was modeled using the finite element method (FEM) and validated using the experimental modal testing results. It has been found that it is essential to model the laminated stator as an orthotropic structure. While the details of other structural components (such as the endshields, the teeth in the stator and the windings) are not so important, it is essential that they are incorporated into the structural model as simplified structures to account for their mass, stiffness and boundary conditions imposed on the motor structure. Based on this structural model, the radiated acoustic power for various operating conditions has been predicated using the boundary element (BEM) and the electromagnetic force calculated from an electromagnetic finite element model. The predicted results agree reasonably well with experimental measurements. Despite the success of the FEM/BEM approaches, they can be prohibitively expensive (in terms of computer resources required) to apply to large motors and high frequencies. Thus the feasibility of using a statistical method, namely, the statistical energy analysis (SEA), to estimate the radiated acoustic sound power from an inverter-driven induction motor has been examined. In order to carry out this analysis, analytical expressions for calculating the natural frequencies and radiation efficiency of finite length circular cylindrical shells (which are simplified models of the stator and casing of a motor structure) were firstly derived. The internal loss factors and coupling loss factors of the motor structure were determined experimentally using the power injection method. Then by introducing an equivalent surface mobility of circular cylindrical shells for the electromagnetic force, the vibration response and the acoustic noise radiated from each part of the motor structure were estimated. Results indicate that SEA method is potentially an efficient and effective tool in estimating the noise radiated from inverter-driven induction motors.

During its mission, a launch vehicle is subject to broadband, severe, aeroacoustic and structure-borne excitations of various provenances, which can endanger the survivability of the payload and the vehicles electronic equipment, and consequently the success of the mission. Aerospace structures are generally characterized by the use of exotic composite materials of various configurations and thicknesses, as well as by their extensively complex geometries and connections between different subsystems. It is therefore of crucial importance for the modern aerospace industry, the development of analytical and numerical tools that can accurately predict the vibroacoustic response of large, composite structures of various geometries and subject to a combination of aeroacoustic excitations. Recently, a lot of research has been conducted on the modelling of wave propagation characteristics within composite structures. In this study, the Wave Finite Element Method (WFEM) is used in order to predict the wave dispersion characteristics within orthotropic composite structures of various geometries, namely flat panels, singly curved panels, doubly curved panels and cylindrical shells. These characteristics are initially used for predicting the modal density and the coupling loss factor of the structures connected to the acoustic medium. Subsequently the broad-band Transmission Loss (TL) of the modelled structures within a Statistical Energy Analysis (SEA) wave-context approach is calculated. Mainly due to the extensive geometric complexity of structures, the use of Finite Element(FE) modelling within the aerospace industry is frequently inevitable. The use of such models is limited mainly because of the large computation time demanded even for calculations in the low frequency range. During the last years, a lot of researchers focus on the model reduction of large FE models, in order to make their application feasible. In this study, the Second Order ARnoldi (SOAR) reduction approach is adopted, in order to minimize the computation time for a fully coupled composite structural-acoustic system, while at the same time retaining a satisfactory accuracy of the prediction in a broadband sense. The system is modelled under various aeroacoustic excitations, namely a diffused acoustic field and a Turbulent Boundary Layer (TBL) excitation. Experimental validation of the developed tools is conducted on a set of orthotropic sandwich composite structures. Initially, the wave propagation characteristics of a flat panel are measured and the experimental results are compared to the WFEM predictions. The later are used in order to formulate an Equivalent Single Layer (ESL) approach for the modelling of the spatial response of the panel within a dynamic stiffness matrix approach. The effect of the temperature of the structure as well as of the acoustic medium on the vibroacoustic response of the system is examined and analyzed. Subsequently, a model of the SYLDA structure, also made of an orthotropic sandwich material, is tested mainly in order to investigate the coupling nature between its various subsystems. The developed ESL modelling is used for an efficient calculation of the response of the structure in the lower frequency range, while for higher frequencies a hybrid WFEM/FEM formulation for modelling discontinuous structures is used.

With the advent of power electronics, inverter-driven induction motor are finding increased use in industries because of applications that demand variable speed operations and because of the potential savings in energy usage. However, these drives sometimes produce unacceptably high levels in vibration and acoustic noise. A literature survey has revealed that while there has been intensive research on the design of inverters to minimize acoustic noise radiation from these drives, the vibro-acoustic behaviour of an induction motor structure has received relatively little attention. The primary objective of this research project, therefore, is to develop a general strategy/algorithm for estimating the acoustic noise radiated from inverter-driven induction motors. By using a three-phase, 2.2 kW induction motor, the vibration modes due to various structural components (such as the rotor, the stator/casing, the endshields and the base plate) of the motor structure were analysed by experimental modal testing. Results indicate that the vibration modes due to the rotor are only important at low frequencies. It has been found that the power injection method gives more accurate measurement of the damping of a motor structure than the modal testing and the time decay methods. If a point force excitation is used, then it is more accurate to measure the sound radiation efficiency than the power conversion efficiency for motor structures. The effect of three different inverter designs (an ideal ???almost sinusoidal??? controller and two commercially available PWM inverters) on the radiated acoustic power were assessed for both no-load and load conditions using sound intensity measurements conducted in an anechoic room. The results indicate that although the sound power level due to aerodynamic and mechanical noise increases at a rate of 12 dB per doubling of the motor speed, the electromagnetic noise dominates at low motor speeds and is still a significant noise source even at high motor speeds. For inverters with low switching frequencies, the radiated sound power level is almost 15 dB higher than the ideal case at low speeds and is relatively insensitive to the motor speed. For inverters that implement the random modulation technique, the change in the total sound power level with the level of the random modulation is very small but the tonal nature of the noise is greatly reduced. The vibration behaviour of a motor structure was modeled using the finite element method (FEM) and validated using the experimental modal testing results. It has been found that it is essential to model the laminated stator as an orthotropic structure. While the details of other structural components (such as the endshields, the teeth in the stator and the windings) are not so important, it is essential that they are incorporated into the structural model as simplified structures to account for their mass, stiffness and boundary conditions imposed on the motor structure. Based on this structural model, the radiated acoustic power for various operating conditions has been predicated using the boundary element (BEM) and the electromagnetic force calculated from an electromagnetic finite element model. The predicted results agree reasonably well with experimental measurements. Despite the success of the FEM/BEM approaches, they can be prohibitively expensive (in terms of computer resources required) to apply to large motors and high frequencies. Thus the feasibility of using a statistical method, namely, the statistical energy analysis (SEA), to estimate the radiated acoustic sound power from an inverter-driven induction motor has been examined. In order to carry out this analysis, analytical expressions for calculating the natural frequencies and radiation efficiency of finite length circular cylindrical shells (which are simplified models of the stator and casing of a motor structure) were firstly derived. The internal loss factors and coupling loss factors of the motor structure were determined experimentally using the power injection method. Then by introducing an equivalent surface mobility of circular cylindrical shells for the electromagnetic force, the vibration response and the acoustic noise radiated from each part of the motor structure were estimated. Results indicate that SEA method is potentially an efficient and effective tool in estimating the noise radiated from inverter-driven induction motors.

Este trabalho baseia-se no estudo e aplicação da Análise Estatística de Energia (SEA). Tal técnica é amplamente empregada nos estudos de vibrações em altas freqüências, dominadas por altas densidades modais e oferecendo toda a solução para o modelo em termos de parâmetros estatísticos. Aplica-se SEA tanto a modelos teóricos e numéricos quanto a modelos experimentais. Qualquer uma das duas abordagens descrita anteriormente tem como objetivo a obtenção dos parâmetros SEA, conhecidos por fator de perda por dissipação interna, fator de perda por acoplamento e densidade modal. Para o estudo e aplicação experimental da técnica SEA utiliza-se o Método de Injeção de Potência, sendo este aplicado a estruturas acopladas do tipo viga, numa configuração em T e estruturas acopladas do tipo placa que formam uma caixa. O estudo numérico e analítico também faz parte deste trabalho, tendo como base o desenvolvimento de uma formulação para vigas relativamente espessas, mostrando a influência geométrica na transmissão da vibração entre subsistemas. Comparações também são feitas entre os resultados obtidos experimentalmente na caixa e na viga T com os obtidos analiticamente e computacionalmente e em ambos os casos estes apresentaram uma boa correlação. Por fim, uma estrutura composta por uma cavidade acústica é estudada e um aparato o para injeção de potência é construído com base no estudo em altas freqüências. / This work is based in the study and application of the Statistical Energy Analysis (SEA), which is applied to high frequencies vibrations characterized by high modal densities and the solution, is given in statistical terms. This analysis is used in numerical, analytical and experimental models and the principal objective is the estimative of the SEA parameters, known by damping loss factors, coupling loss factors and modal densities. The experimental model is based on the Power Injection Method (PIM), and this was applied in coupled structures, like beam type, that was coupled in a T-beam configuration and the other type of coupling was studied in a box type structure. An analytical model was developed in this thesis, it was based on the Timoshenko beam formulation and the possible geometrical effects were studied. The results obtained as experimentally as numerically or analytically were compared and showed a good agreement. Finally, an acoustic cavity was studied and a new display was constructed to inject power in the cavity and a high frequency study was performed.

The standard, EN12354-1 describes a simplified statistical energy analysis (SEA) model to predict the apparent sound reduction index between two rooms inclusive of the contributions of the flanking paths. There is interest worldwide in applying the EN12354 model to lightweight building elements. However, lightweight elements typically do not meet the requirements of an SEA subsystem and therefore applying the EN12354 model to these elements may result in inaccurate predictions. The purpose of this investigation was to systematically evaluate the application of the EN12354 model to lightweight building constructions. The evaluation included the determination of the probability density functions and the propagated uncertainty of the calculations. Knowledge of the probability density functions resulted in alternative calculations of the structure-borne sound transmitted through the constructions. The uncertainty analysis revealed that the uncertainty of the predictions is directly affected by the variance of the vibratory field measured on the elements. The vibratory fields of lightweight elements typically show large variances and therefore the propagated uncertainty of the EN12354 predictions for these elements can be significant. The investigation included measurements both in the laboratory and in the field. The results of the laboratory measurements were compared to both predictions using the EN12354 methods and ESEA models which included higher order flanking paths and non-resonant transmission paths. The field measurements included in this investigation were unique because the flanking intensity sound reduction indices of the elements in the source room were measured. The measurements allowed for the EN12354 predictions for each flanking element to be assessed instead of just the apparent sound reduction index between the rooms. The study resulted in proposed correction factors for when reciprocity does not hold and proposed changes to ISO10848 to improve the accuracy of the predictions when the EN12354 method was applied to lightweight building elements. However, neither the proposed correction factors nor the proposed changed to ISO10848-1 could correct for the potentially large differences between the predicted and the measured results. Based on the findings of this study, the use of the EN12354 model for the calculation of the apparent sound reduction index of lightweight elements is not endorsed. Lightweight constructions may not be categorized as ideal SEA subsystems due to the lack of diffuseness of the vibratory field. Furthermore, in order for EN12354 to be applied to lightweight constructions, a reliable method of calculating the resonant component of the sound reduction index of double-leaf elements is required. Therefore, statistical methods including the EN12354 method may be unsuitable for use for the prediction of flanking noise for lightweight building constructions.

Este trabalho baseia-se no estudo e aplicação da Análise Estatística de Energia (SEA). Tal técnica é amplamente empregada nos estudos de vibrações em altas freqüências, dominadas por altas densidades modais e oferecendo toda a solução para o modelo em termos de parâmetros estatísticos. Aplica-se SEA tanto a modelos teóricos e numéricos quanto a modelos experimentais. Qualquer uma das duas abordagens descrita anteriormente tem como objetivo a obtenção dos parâmetros SEA, conhecidos por fator de perda por dissipação interna, fator de perda por acoplamento e densidade modal. Para o estudo e aplicação experimental da técnica SEA utiliza-se o Método de Injeção de Potência, sendo este aplicado a estruturas acopladas do tipo viga, numa configuração em T e estruturas acopladas do tipo placa que formam uma caixa. O estudo numérico e analítico também faz parte deste trabalho, tendo como base o desenvolvimento de uma formulação para vigas relativamente espessas, mostrando a influência geométrica na transmissão da vibração entre subsistemas. Comparações também são feitas entre os resultados obtidos experimentalmente na caixa e na viga T com os obtidos analiticamente e computacionalmente e em ambos os casos estes apresentaram uma boa correlação. Por fim, uma estrutura composta por uma cavidade acústica é estudada e um aparato o para injeção de potência é construído com base no estudo em altas freqüências. / This work is based in the study and application of the Statistical Energy Analysis (SEA), which is applied to high frequencies vibrations characterized by high modal densities and the solution, is given in statistical terms. This analysis is used in numerical, analytical and experimental models and the principal objective is the estimative of the SEA parameters, known by damping loss factors, coupling loss factors and modal densities. The experimental model is based on the Power Injection Method (PIM), and this was applied in coupled structures, like beam type, that was coupled in a T-beam configuration and the other type of coupling was studied in a box type structure. An analytical model was developed in this thesis, it was based on the Timoshenko beam formulation and the possible geometrical effects were studied. The results obtained as experimentally as numerically or analytically were compared and showed a good agreement. Finally, an acoustic cavity was studied and a new display was constructed to inject power in the cavity and a high frequency study was performed.

Pendant sa mission, un lanceur est soumis à des excitations large bande, sévères, aérodynamiques, de provenances diverses, qui peuvent mettre en danger la survivabilité de la charge utile et de l’équipement électronique du véhicule, et par conséquent le succès de la mission. Les structures aérospatiales sont généralement caractérisées par l’utilisation de matériaux composites exotiques des configurations et des épaisseurs variantes, ainsi que par leurs géométries largement complexes. Il est donc d’une importance cruciale pour l’industrie aérospatiale moderne, le développement d’outils analytiques et numériques qui peuvent prédire avec précision la réponse vibroacoustique des structures larges, composites de différentes géométries et soumis à une combinaison des excitations aéroacoustiques. Récemment, un grand nombre de recherches ont été menées sur la modélisation des caractéristiques de propagation des ondes au sein des structures composites. Dans cette étude, la méthode des éléments finis ondulatoires (WFEM) est utilisée afin de prédire les caractéristiques de dispersion des ondes dans des structures composites orthotropes de géométries variables, nommément des plaques plates, des panneaux simplement courbés, des panneaux doublement courbés et des coques cylindriques. Ces caractéristiques sont initialement utilisées pour prédire la densité modale et le facteur de perte par couplage des structures connectées au milieu acoustique. Par la suite, la perte de transmission (TL) à large bande des structures modélisées dans le cadre d’une analyse statistique énergétique (SEA) dans un contexte ondulatoire est calculée. Principalement en raison de la complexité géométrique importante de structures, l’utilisation des éléments finis (FE) au sein de l’industrie aérospatiale est souvent inévitable. L’utilisation de ces modèles est limitée principalement à cause du temps de calcul exigé, même pour les calculs dans la bande basses fréquences. Au cours des dernières années, beaucoup de chercheurs travaillent sur la réduction de modèles FE, afin de rendre leur application possible pour des systèmes larges. Dans cette étude, l’approche de SOAR est adoptée, afin de minimiser le temps de calcul pour un système couplé de type structurel-acoustique, tout en conservant une précision satisfaisante de la prédiction dans un sens large bande. Le système est modélisé sous diverses excitations aéroacoustiques, nommément un champ acoustique diffus et une couche limite turbulente (TBL).La validation expérimentale des outils développés est réalisée sur un ensemble de structures sandwich composites orthotropes. Ces derniers sont utilisés afin de formuler une approche couche équivalente unique (ESL) pour la modélisation de la réponse spatiale du panneau dans le contexte d’une approche de matrice de raideur dynamique. L’effet de la température de la structure ainsi que du milieu acoustique sur la réponse du système vibroacoustique est examiné et analysé. Par la suite, un modèle de la structure SYLDA, également fait d’un matériau sandwich orthotrope, est testé principalement dans le but d’enquêter sur la nature de couplage entre ses divers sous-systèmes. La modélisation ESL précédemment développée est utilisé pour un calcul efficace de la réponse de la structure dans la gamme des basses et moyennes fréquences, tandis que pour des fréquences plus élevées, une hybridisation WFEM / FEM pour la modélisation des structures discontinues est utilisé. / During its mission, a launch vehicle is subject to broadband, severe, aeroacoustic and structure-borne excitations of various provenances, which can endanger the survivability of the payload and the vehicles electronic equipment, and consequently the success of the mission. Aerospace structures are generally characterized by the use of exotic composite materials of various configurations and thicknesses, as well as by their extensively complex geometries and connections between different subsystems. It is therefore of crucial importance for the modern aerospace industry, the development of analytical and numerical tools that can accurately predict the vibroacoustic response of large, composite structures of various geometries and subject to a combination of aeroacoustic excitations. Recently, a lot of research has been conducted on the modelling of wave propagation characteristics within composite structures. In this study, the Wave Finite Element Method (WFEM) is used in order to predict the wave dispersion characteristics within orthotropic composite structures of various geometries, namely flat panels, singly curved panels, doubly curved panels and cylindrical shells. These characteristics are initially used for predicting the modal density and the coupling loss factor of the structures connected to the acoustic medium. Subsequently the broad-band Transmission Loss (TL) of the modelled structures within a Statistical Energy Analysis (SEA) wave-context approach is calculated. Mainly due to the extensive geometric complexity of structures, the use of Finite Element(FE) modelling within the aerospace industry is frequently inevitable. The use of such models is limited mainly because of the large computation time demanded even for calculations in the low frequency range. During the last years, a lot of researchers focus on the model reduction of large FE models, in order to make their application feasible. In this study, the Second Order ARnoldi (SOAR) reduction approach is adopted, in order to minimize the computation time for a fully coupled composite structural-acoustic system, while at the same time retaining a satisfactory accuracy of the prediction in a broadband sense. The system is modelled under various aeroacoustic excitations, namely a diffused acoustic field and a Turbulent Boundary Layer (TBL) excitation. Experimental validation of the developed tools is conducted on a set of orthotropic sandwich composite structures. Initially, the wave propagation characteristics of a flat panel are measured and the experimental results are compared to the WFEM predictions. The later are used in order to formulate an Equivalent Single Layer (ESL) approach for the modelling of the spatial response of the panel within a dynamic stiffness matrix approach. The effect of the temperature of the structure as well as of the acoustic medium on the vibroacoustic response of the system is examined and analyzed. Subsequently, a model of the SYLDA structure, also made of an orthotropic sandwich material, is tested mainly in order to investigate the coupling nature between its various subsystems. The developed ESL modelling is used for an efficient calculation of the response of the structure in the lower frequency range, while for higher frequencies a hybrid WFEM/FEM formulation for modelling discontinuous structures is used.

This thesis describes methods of high frequency noise and vibrations computation of cabin part of EV–55M (aircraft developed by Evektor Kunovice). There is a brief summary of methods used for determining high frequency noise and vibrations in the first part of the thesis. Detailed explanation is given for Statistical Energy Analysis (SEA) which is nowadays the most dominant method in this area. The energy balance equation is derived in this chapter and SEA parameters such as modal density, damping loss factor, coupling loss factor and power input are introduced here. Next part deals with main noise sources of propeller driven and jet aircraft and passive and active noise controls are discussed. Practical part of this thesis deals with modeling aircraft EV–55M fuselage using VA One SEA module. Two models were created. First of them is only an outside fuselage with aircraft flooring and the second one is extended by interior trim panels and is applicable for simulation of noise control treatments. Computational modeling is accompanied by experimental measurement of passive noise control material characteristics. Postprocessing of information obtained from impedance tube measurement was performed in FOAM – X. Determined characteristics of porous material were used as inputs to VA One and reduction of sound pressure level in fuselage cavities by using noise control treatment was found. In conclusion there is a summary of noise transmission paths from sources to interior cavity and some treatments of them are simulated