Statistical Energy Analysis Method Research Articles

Experimental Studies of the Elastic-Dissipative Properties of Structural Materials and the Calculation of Sound Insulation of Building Partitions Based on Refined Characteristics by the SEA Method

An analytical solution to the problem of sound and vibration transmission through structures, taking into account the energy exchange with adjacent structures, requires determination of the elastic-dissipative properties of structural materials: the elastic modulus and the loss factor. In this work, the parameters of the elastic modulus and the loss factor of three known building materials are investigated and experimentally established in comparison with previously obtained data of other authors. For the automation and accuracy of measuring the internal loss factor, a new measurement technique was transferred using Zetlab software and digital equipment. The calculation of sound insulation of a single-layer enclosing structure is performed based on the method of statistical energy analysis (SEA) using the measured data of the elastic modulus and loss factor. In order to determine the reliability of the data obtained for the elastic modulus and the coefficient of internal loss of structural materials, a comparison was made of the values of sound insulation of a single-layer panel made of gypsum fiber board, obtained by means of experimental research, using the calculated values of sound insulation calculated using the elastic modulus and the coefficient of internal losses from literature sources and using the calculated sound insulation values calculated using the measured values of the modulus of elasticity and the internal loss factor.

A similitude for the middle-frequency vibration response of satellite solar array based on the wave coupling hybrid finite element–statistical energy analysis method

A similitude is proposed for the dynamic response analysis of a satellite solar array. It is defined by invoking the wave coupling hybrid finite element–statistical energy analysis method which is considered as an effective way to solve the wide frequency (especially middle-frequency) vibration response of complex structures. The scaling laws are then derived by looking for equalities in the structural responses. A numerical case involving an assembly of two plates is discussed to verify the proposed scaling laws. Moreover, the new similitude is applied to a simplified satellite solar array model. If the analysis frequency step is selected appropriately, it is shown that a complete similitude can be defined: it allows predicting the vibration response of satellite solar array and provides the possibility for the model test of complex structures.

A review of the different approaches to predict the sound transmission loss of building partitions

The computation of sound transmission through solid structures has been of great interest since the first half of the 20th century. Several prediction methods can be found in the large body of literature, applicable to many kinds of structures, and derived using different approaches. This article presents a review of the most significant approaches to compute sound transmission through a building partition; it aims to provide an extensive update and critical literature review of the different approaches which can be used to compute sound transmission through a building partition. Different approaches, suitable for different kinds of building structures, based on analytical and semi-analytical solutions, wave-propagation, numerical or statistical energy analysis methods are described, highlighting advantages and drawbacks.

Prediction of the acoustic effect of an interior trim porous material inside a rigid-walled car air cavity model

In this paper, a simplified car air cavity model for predicting the influence of an interior trim material on the cabin interior sound pressure level (SPL) was presented. This work studies a rigid-walled car cabin model with one flexible wall. The interior trim material (a porous sound-absorbing material) was mounted in between the enclosed car air cavity and the flexible wall. A single point acoustic source is used to acoustically excite the rigid-walled car air cavity model, where the loudspeaker is positioned at front corner of the car cabin to simulate noise entering via an airborne path. The variation of the car air cavity interior sound pressure level corresponding to the presence of different porous sound-absorbing materials was experimentally investigated for high frequencies. The acoustical effects of the interior trim porous material on the proposed structural and acoustic coupled system were predicted by using the Statistical Energy Analysis (SEA) method for noise in one third octave bands. The comparison of results revealed that the experimentally acquired car cabin interior sound pressure level agrees fairly well with the simplified SEA model, both with and without the porous sound-absorbing materials, for high frequency one third octave band levels.

Calculation Model of Sound and Vibration Propagation in a Building Fragment Based on the Method of Statistical Energy Analysis

The theory sound insulation based on the matching of the wave fields by M. S. Sedov and Statistical energy analysis (SEA) are used to model sound transmission through single and double leaf partitions. A fragment of a building is considered as a set of acoustically connected rooms and structures. On the basis of the method of statistical energy analysis, the equations of energy balance are written, the solution of which allows to determine the energy of sound in the rooms and the energy of sound vibration in the structures. A complete model of the SEA, including bending, longitudinal and shear waves in structures and sound waves in the air volumes of the rooms, is proposed. The coupling loss factors from room to room (non-resonant sound transmission through partitions) are calculated on the theory by M. S. Sedov. It is given the calculation of the coupling loss factors, internal losses and modal densities. The results of vibro-acoustic calculations and measurements on models of the building fragments are presents.

Experimental investigations of different fiber orientations on damping loss factor of fiberglass composite specimens

The composite materials having low weight to strength ratio and easy to manufacture due to which the usage of composites for different applications has aggrandized remarkably. Statistical energy analysis is used to predict the vibrational response of the complexstructuralsystems. In the present work rectangular composite specimens have been used as an idealized subsystem. To analyse theoretically the vibrational response of these fabricated composite specimens employing glass fibers and different epoxy resins, Statistical Energy Analysis (SEA) method is implemented. The SEA response majorly depends on three parameters i.e. damping loss factors, modal densities, and coupling loss factors of the subsystems. In the present study, the damping loss factors of fabricated rectangular composite laminates have been estimated by employing both theoretical and experimental approach. Furthermore an experimental investigation has been employed to observe the effect of different fiber orientations on damping loss factor of the identical composite specimens. From the obtained results it has been observed that the damping loss factor for a composite plate with unidirectional fiber orientation is greater than the plates with quasi isotropic and cross ply orientations.

Optimization of mid-frequency vibration for complex built-up systems using the hybrid finite element–statistical energy analysis method

This article deals with the sensitivity analysis of dynamic response and optimal size design of complex built-up systems in the mid-frequency range. A complex built-up system may be fabricated from many components which often differ greatly in materials and sizes. It may be subjected to many different wavelength structural deformations and may typically exhibit mixed mid-frequency behaviour which is very sensitive to uncertainties at higher frequencies. To perform optimization on the mid-frequency vibration of complex built-up systems, the hybrid finite element (FE)–statistical energy analysis (SEA) method, in which the deterministic and statistical subsystem are respectively modelled using FE and SEA, is implemented in this work. In this context, an efficient direct differentiation method for sensitivity analysis is derived. Two numerical examples illustrate the efficiency and effectiveness of the proposed optimization model.

Review of Hybrid Finite Element – Statistical Energy Analysis methods in vehicle NVH predictions

In the vehicle industry, the noise, vibration and harshness (NVH) characteristics of a car are becoming more and more important. In order to control these, it is necessary to know the sources and contributors to the interior noise level. This paper provide an overview of the state-of-the-art on predicting the NVH characteristics of fully trimmed vehicles in the mid-frequency gap between 400 Hz to 1 kHz. It is shown that for this frequency range, typically a hybrid FE-SEA method is used. This method provides a mixture of the advantages of the deterministic and statistical approaches. The first part of the paper introduces the method, followed by an overview of the different fields of usage in the vehicle industry. At the end of the paper, gaps in the knowledge are identified.

Application of the dynamic condensation approach to the hybrid FE-SEA model of mid-frequency vibration in complex built-up systems

The hybrid Finite Element (FE) – Statistical Energy Analysis (SEA) method developed for mid-frequency vibration of complex built-up systems needs to compute the total dynamic flexibility matrix at every frequency, which is very time consuming. This paper presents an improved hybrid FE-SEA method to overcome this problem. In the present method, first, dynamic condensation is introduced to reduce the order of the deterministic FE component, which results in significant reduction of the total dynamic stiffness matrix. Then, noting that the dynamic stiffness matrix of the deterministic component is established by using the FE method, a fast inverse algorithm is employed to calculate the dynamic flexibility matrix of the slave degrees of freedom of the deterministic component generated in the condensation process. These two steps avoid the direct inverse computation of a large matrix at each frequency point of interest, resulting in significant time saving. A numerical example illustrates the efficiency and convergence of the proposed method.

Structure-borne noise from long-span steel truss cable-stayed bridge under damping pad floating slab: Experimental and numerical analysis

This study investigates the structure-borne noise characteristics and a control measure of the long-span steel truss cable-stayed bridge (LSTCB) which are induced by running trains in urban rail transit. A frequency-domain theoretical model of a vehicle–track coupling interaction system, in which the vibration reduction track structure of damping pad floating slab (DPFS) are taken into account, is firstly established, from which the wheel–rail dynamic force, the force transmission rate, and the force transmitted to the bridge can be obtained. After that, a vibration model of the LSTCB and a noise model of the steel truss girder are established, which are based on the refined finite element method (FEM) and statistical energy analysis (SEA) method respectively, to predict the structure-borne noise of the LSTCB. Next, the near-field noise test of an LSTCB under DPFS at an urban rail transit line, are analyzed and used to validate the prediction model. Then, the structure-borne noise characteristics of the LSTCB and noise reduction effect of DPFS are studied. It is found that the wheel-rail transfer to the track slab and bridge are influenced by the track structure system; the attenuation rate of the near-field sound pressure level (SPL) is relatively slow in the range of 20–100 Hz, fast after 100 Hz, and faster than the far-field SPL; the vibration energies that input to the LSTCB are mainly distributed in the bridge deck, longitudinal web, and transverse web; the sound radiation capability of the bridge deck is stronger than that of other subsystems; compared with the common track structure (embedded sleeper), the track structure of DPFS can reduce the overall sound pressure level of the LSTCB by 10–13 dB(A).

THEORETICAL AND EXPERIMENTAL RESEARCH OF VIBROACOUSTIC SYSTEMS WITH THE SMALL NUMBER OF ELEMENTS

The known methods of acoustical calculation in buildings not fully describe the phenomenon of sound transmission. This paper presents theoretical studies of the sound and vibration in building models, a method of statistical energy analysis (SEА), taking into account nonresonant phenomena and experimental testing of the specified parameters. The SEA-based equations are obtained for the energy balance, the solution of which allows to determine the sound energy in rooms and sound vibration in structures. The energy coupling coefficients, including those allowing for non-resonant sound transmission from adjacent acoustic subsystems, internal losses and the density of mode oscillation are calculated. The results of calculations and measurements of building model fragments, including identical and double partitions, are presented. The proposed method of calculation allows to predict the sound transmission through the partition with regard to adjacent structures.

Reduction of Hybrid FE-SEA Model for the Mid-Frequency Vibration of Vibro-Acoustic Systems Using Dynamic Condensation Approach

In this paper, an improved hybrid finite element (FE)-statistical energy analysis (SEA) method is proposed for the mid-frequency vibration of vibro-acoustic systems. Within the framework of the hybrid FE-SEA method, the present method reduces the size of the total dynamic matrix of a vibro-acoustic system by employing dynamic condensation to reduce the order of the dynamic matrix of the acoustic cavity. A fast algorithm is introduced to obtain the dynamic flexibility matrix of the slave degrees-of-freedom (DOFs) of the acoustic cavity FE model, thereby avoiding the direct inverse computation of a large dynamic stiffness matrix at each frequency point of interest. The first numerical example illustrates the validity and efficiency of the present method, while the convergence and accuracy analysis of the proposed method is investigated numerically by the second example.

A Statistical Energy Analysis (SEA) model of a fuselage section for the prediction of the internal Sound Pressure Level (SPL) at cruise flight conditions

Comfort plays an increasingly important role in the interior design of airplanes. In general, comfort is defined as ‘freedom from pain, well-being’; in scientific literature, indeed, it is defined as a pleasant state of physiological, psychological and physical harmony between a human being and the environment or a sense of subjective well-being. Cabin noise in passenger aircraft is one of the comfort parameter, which creates straightaway discomfort when exceeding personal thresholds. In general the cabin noise varies by the seat position and changes with flight condition. It is driven by several source types, which are transmitted through different transfer paths into the cabin. In the forward area the noise is mainly dominated by the turbulent boundary layer described by pressure vortexes traveling along the fuselage surface.In this paper evaluation of the Sound Pressure level, for the medium-high frequency range, of an aircraft fuselage section at different stations and locations inside the cabin has been performed numerically by using Statistical Energy Analysis (SEA) method. Different configurations have been considered for the analysis: from the “naked” cabin (only primary structure) up to “fully furnished” (primary structure with interiors and noise control treatments) one. These results are essential to understand which are the main parameters affecting the noise insulation. Furthermore the Power Inputs evaluation has been determined to see the contribution of each considered aeronautic component on the acoustic insulation. Finally, the effect of a viscoelastic damping layer embedded in the glass window has been evaluated.

Stochastic hybrid perturbation technique-based smoothed finite element-statistical energy method for mid-frequency analysis of structure–acoustic systems with parametric and nonparametric uncertainties

At present, the most widely used mid-frequency method, i.e., the hybrid finite element-statistical energy analysis method (FE/SEA), still holds potential flaws, e.g., low accuracy and ignoring uncertain factors. In order to eliminate these problems, a generalized smoothing finite element statistical energy analysis method (SFE/SEA) is first proposed in this work, which is constructed based on the edge-based gradient smoothing technique, thus reducing the dispersion error in the deterministic calculations. Second, on the basis of the proposed SFE/SEA, the parametric uncertainty models will be introduced, combining the second-order random interval perturbation method and the random interval moment method, etc.; thus, a mid-frequency analysis method (SHPSFEM/SEA) considering both parametric uncertainties (both the random and interval variables) and nonparametric uncertainties is proposed, to effectively analyze the probability and interval characteristics of the random structural–acoustic coupled systems. Moreover, for the interval parameters with wide variation range, the subinterval perturbation method (S-SHPSFEM/SEA) is introduced by dividing the large interval parameters into small interval parameters. The proposed methods are compared with the Monte Carlo simulations of the hybrid FE/SEA model. The high accuracy and efficiency of the proposed methods are verified by two numerical examples.

Acoustical system modelling of the heavy truck air intake system

In this paper, a statistical energy analysis method is applied to the heavy truck air intake system to predict the intake orifice noise, as well as the radiated noise. Because very few modes exist below 500 Hz for the intake system subjected to the analysis, the noise contribution of the system below 500 Hz has been considered. Below that frequency band, results have lower confidence levels because of the method's statistical characteristics. Radiated noise analysis has been performed to predict the noise radiation from the air intake system part surfaces. With this method, radiated noise directivity from the air intake system part surfaces can also be predicted. This information provides an idea of noise reduction. The effect of the material on the radiated noise has been studied. At higher frequencies, the confidence level regarding the dynamical response becomes higher, such that it leads us to predict high frequency problems.

Acoustical system modelling of the heavy truck air intake system

In this paper, a statistical energy analysis method is applied to the heavy truck air intake system to predict the intake orifice noise, as well as the radiated noise. Because very few modes exist below 500 Hz for the intake system subjected to the analysis, the noise contribution of the system below 500 Hz has been considered. Below that frequency band, results have lower confidence levels because of the method's statistical characteristics. Radiated noise analysis has been performed to predict the noise radiation from the air intake system part surfaces. With this method, radiated noise directivity from the air intake system part surfaces can also be predicted. This information provides an idea of noise reduction. The effect of the material on the radiated noise has been studied. At higher frequencies, the confidence level regarding the dynamical response becomes higher, such that it leads us to predict high frequency problems.

Application of Statistical Energy Analysis Method for modelling sound insulation of baffles

The article presents the model of sound insulation of single homo-geneous baffles based on the Statistical Method of Energy Analysis. The determined frequency characteristics of airborne sound insulation of the baffles obtained from the calculation model with the results of experimental tests were compared. Calculations using the Statistical Method of Energy Analysis and laboratory tests were performed for plates made of plexiglass and acrylic.

Noise Prediction and Control in a Cruise Ship

Based on the statistical energy analysis (SEA) method, the noise prediction of the cruise ship’s cabins was analyzed and the results show that the noise energy of the engine room (ER) is the highest in the whole cabins, and the energy propagates in the direction of the ship’s bow and stern with the ER centered. In order to reduce the noise of the ER, the main characteristics of the noise source were analyzed. The contribution rate of each noise source to the ER and the input power of the diesel engine structure-borne and air-borne noise to the ER were analyzed and calculated. The analysis shows that air-borne noise of diesel engine is the main noise source in the ER. Then the acoustic enclosures were applied to the diesel engine to control air-borne noise and the sound insulation effect of the acoustic enclosure under different working conditions was studied. The results shows that in the case of only considering the air-borne noise of the diesel engine, the sound pressure level(SPL) of the ER is reduced by about 36dB(A)∼62dB(A). In the case where all excitations are loaded, the SPL of the cabin is reduced by an average of about 10.8dB (A), which shows a better sound insulation effect.

Effect of Changes in Fiber Orientations on Modal Density of Fiberglass Composite Plates

As the manufacturing technologies for composites materials are advanced, the use of composites for engineering applications has increased significantly. The purpose of this work is to study the response of the idealized subsystem made up of composite material. To study the vibrational response theoretically, Statistical Energy Analysis (SEA) method is used. The S.E.A. techniques are used to predict the vibrational parameters of coupled structural elements and acoustic volumes and it depends largely on an accurate estimate of three parameters: the modal densities, damping loss factors, and coupling loss factors of the subsystems. In this paper the modal density of rectangular composite plate made up of fiberglass is obtained by experimentally and theoretically. Also experimentally analyzed the effect of changes in fiber orientations on modal density the same sized plates, with different fiber orientations.

Optimization for heat and sound insulation of honeycomb sandwich panel in thermal environments

An optimization based on sequential quadratic programming (SQP) algorithm to increase the thermal insulation and sound transmission loss of honeycomb panel in thermal environments is presented. First, heat transfer analysis is performed to reveal the steady-state thermal performance of hexagonal aluminum honeycomb sandwich panel, by using the semi-empirical Swann and Pittman formula. Next, the influences of temperature on acoustic performance of honeycomb panel based on statistical energy analysis method (SEA) is performed. Results show that increasing the thickness of the honeycomb core can improve the acoustic performance and heat insulation behavior.