307 SEAによるレーザプリンタの振動解析 : 印刷時の入力パワー同定

In practical applications of the statistical energy analysis (SEA) or other power flow techniques, the calculation of the power flow between subsystems is of fundamental concern. When the subsystems are connected by multimodal structures, for instance, vibration mounts, values for the coupling loss factors as found in the literature are not suitable. In this paper we present a general theoretical framework for calculating the coupling loss factor when the coupler is numerically modeled by classical dynamics, notably by means of a finite element analysis (FEA). After presenting some pertinent results and definitions from SEA, FEA, and structural dynamical theory, an expression for the “coupling” impedance matrix, which relates the forces and free velocities at nodes along the subsystem/coupler boundaries, is derived. This impedance is formed from the admittance matrix of the coupler, calculated using FEA, and input impedances for the systems, analytically calculated. From the coupling impedance, expressions for the coupling loss factors are derived for the cases where the SEA subsystems are plates or beams and include flexural, longitudinal, and torsional forms of energy transmission. Finally, numerical examples are given for the application of this technique to structures consisting of two beams or plates connected by a multimodal coupler.

Is it possible to treat confidentially SEA the wolf in sheep's clothing?

This work uses statistical energy analysis (SEA) to study noise transmission through a commercial motor vehicle and in order to do this various sound and vibration power inputs associated with flanking transmission via the exhaust and engine noise are calculated. A modern commercial motor vehicle that has an exhaust noise sensitivity problem is studied in this work. The aim of this work is to demonstrate the application of SEA and to study the effects on noise transmission when the exhaust is incorrectly fitted (misaligned). Airborne and structural paths for sound and vibration transmission to a vehicle saloon are considered. Also, the SEA framework is used to identify the relative importance of each structural and airborne power input in relation to the sound power that is transmitted to the vehicle saloon. It is shown that the importance of each sound power input varies with frequency. At low frequencies, sound transmission through the vehicle structure is most important. At high frequencies, airborne flanking noise transmission to the floor is important. In this case, exhaust vibration transmission is most important at frequencies between 250 Hz and 1 kHz when the engine is running at 5700 r/min, and the SEA model predicts the change in performance associated with exhaust misalignment.

The well known text by Lyon on Statistical Energy Analysis (SEA) [R. H. Lyon, Statistical Energy Analysis of Dynamical Systems: Theory and Applications (MIT Press, Cambridge, MA, 1975)] is the standard reference on the subject. As originally conceived SEA was based upon several plausible hypotheses. Various authors have considered the underlying basis for SEA and thereby advanced our understanding of it. In the present paper, the relationship between classical modal analysis (CMA) and SEA is studied. It is shown how the results of SEA may be obtained as an asymptotic limit of CMA. The present work only considers the response of a single general linear structure under a random or sinusoidal load. However future plans will consider (a) the structural acoustic response of an enclosure bounded by a flexible wall and excited by external forces and (b) two (or more) coupled structural systems. Here the emphasis is on (1) a new derivation of the SEA results from CMA for a single structure under a random load, (2) the generalization of the usual SEA result to show that, asymptotically, all points on the structure have the same response. In the literature this is sometimes invoked as an assumption. Here the result is derived as part of the asymptotic limit of CMA. (3) A numeriCal example which displays the manner in which the asymptotic limit is approached for random loading and (4) an extension of the usual SEA result for sinusoidal loading. In view of the above, the present results might be called more appropriately Asymptotic Modal Analysis (AMA) rather than SEA.

Sound and vibration transmission modeling methods are important to the design process for high quality automotive vehicles. Statistical Energy Analysis (SEA) is an emerging design tool for the automotive industry that was initially developed in the 1960’s to estimate root-mean-square sound and vibration levels in structures and interior spaces. Although developed to estimate statistical mean values, automotive design application of SEA needs the additional ability to predict statistical variances of the predicted mean values of sound and vibration. This analytical ability would allow analysis of vehicle sound and vibration response sensitivity to changes in vehicle design specifications and their statistical distributions. This paper will present an algorithm to extend the design application of the SEA method through prediction of the variances of RMS responses of vibro-acoustic automobile structures and interior spaces from variances in SEA automotive model physical parameters. The variance analysis is applied to both a simple, complete illustrative example and a more complex automotive vehicle example. Example variance results are verified through comparison with a Monte Carlo test of 2,000 SEA responses whose physical parameters were given Gaussian distributions with means at design values. Analytical predictions of the response statistics agree with the statistics generated by the Monte Carlo method but only require about 1/300 of the computational effort.

Prediction of structure-borne sound transmission on built-up structures at audio frequencies is well-suited to Statistical Energy Analysis (SEA) although the inclusion of periodic ribbed plates presents challenges. This paper considers an approach using Advanced SEA (ASEA) that can incorporate tunneling mechanisms within a statistical approach. The coupled plates used for the investigation form an L-junction comprising a periodic ribbed plate with symmetric ribs and an isotropic homogeneous plate. Experimental SEA (ESEA) is carried out with input data from Finite Element Methods (FEM). This indicates that indirect coupling is significant at high frequencies where bays on the periodic ribbed plate can be treated as individual subsystems. SEA using coupling loss factors from wave theory leads to significant underestimates in the energy of the bays when the isotropic homogeneous plate is excited. This is due to the absence of tunneling mechanisms in the SEA model. In contrast, ASEA shows close agreement with FEM and laboratory measurements. The errors incurred with SEA rapidly increase as the bays become more distant from the source subsystem. ASEA provides significantly more accurate predictions by accounting for the spatial filtering that leads to non-diffuse vibration fields on these more distant bays.

The use of statistical energy analysis (SEA) for the solution of vibroacoustic problems that occur with the operation of machinery, has only recently become practicable. This paper charts the developments that led from the early ideas of energy accountancy (EA) to the current SEA modeling techniques. The basic concept of EA, which was conceived to show the influence of the overall design parameters on the radiated noise, is explained and its limitations discussed. The paper then goes on to describe how the various practical difficulties preventing the application of SEA were overcome to the point where it could be used as a practical tool. Finally, a case history is presented in which an experimental SEA model is used to determine input (exciting) powers, power flow and sensitivity of the noise to parameter changes. In addition, the use of an optimization algorithm for driving the noise level down to a target spectrum within parameter and weight constraints is also demonstrated.

<div class="section abstract"><div class="htmlview paragraph">Statistical Energy Analysis (SEA) is the standard analytical tool for predicting vehicle acoustic and vibration responses at high frequencies. SEA is commonly used to obtain the interior Sound Pressure Level (SPL) due to each individual noise or vibration source and to determine the contribution to the interior noise through each dominant transfer path. This supports cascading vehicle noise and vibration targets and early evaluation of the vehicle design to effectively meet NVH targets with optimized cost and weight.</div><div class="htmlview paragraph">A common misconception is that SEA is only capable of predicting a general average interior SPL for the entire vehicle cabin and that the differences between different locations such as driver's ear, rear passenger's ear, lower interior points, etc., in the vehicle cannot be analytically determined by an SEA model. However, because the interior acoustic energy distribution varies due to absorption and distance effects that can be modeled, an SEA model is capable of predicting the SPL at different interior locations with good accuracy at high frequencies.</div><div class="htmlview paragraph">This paper discusses the SEA modeling assumptions used to generate a typical model of a vehicle cabin interior and surrounding structure. The distribution of acoustic absorption and its effect on the local interior SPL responses are addressed. Measurements of transfer functions to various points of the vehicle interior from exterior and interior acoustic sources and structureborne sources for a typical vehicle are presented and compared to SEA model predictions. Observations and recommendations about typical interior transfer function correlation, modeling limitations, and use of the SEA model as a design tool are given.</div></div>

Coincidence effect which occurs in a certain frequency range will impairs the sound insulation of walls. For the purpose to predict the phenomenon of coincidence effect that is unlikely predicted theoretically by the mass law, the Statistical Energy Analysis (SEA) theory are adopted in studying coincidence effect of sound insulation of the light weight single-leaf wall. The comparison among predicted by SEA, by mass law and measured was performed. Therefore, the comparison results show that sound insulation prediction by SEA is more precise and agrees with the measured date. Moreover, the coincidence effect and its effect on sound insulation were predicted by SEA. Eventually, it is likely to select appropriate building materials and configuration to achieve a better sound environment theoretically.

In the analysis of the vibration response and structure-borne vibration transmission between elements of a complex structure, statistical energy analysis (SEA) or finite element analysis (FEA) are generally used. However, an alternative method is using vibrational power flow techniques which can be especially useful in the mid frequencies between the optimum frequency regimes for FEA and SEA. Power flow analysis has in general been used on one-dimensional beam-like structures or between structures with point joints. In this paper, the power flow technique is extended to two-dimensional plate like structures joined along a common edge without frequency or spatial averaging the results, such that the resonant response of the structure is determined. The power flow results are compared to results obtained using FEA at low frequencies and SEA at high frequencies. The agreement with FEA results is good but the power flow technique has an improved computational efficiency. Compared to the SEA results the power flow results show a closer representation of the actual response of the structure.

<div class="htmlview paragraph">High frequency responses of structural-acoustic systems may be predicted by statistical energy analysis (SEA) or energy finite element method (EFEM). To combine the good features of these two techniques, a simplified energy finite element method, referred to as EFEM<sup>0</sup>, has been developed recently. The EFEM<sup>0</sup> technique, which is compatible with SEA, integrates the joint coupling procedures for discontinuous systems and the finite volume formulation for continuous system. The EFEM<sup>0</sup> models have been verified either analytically or experimentally for one- and multi-dimensional systems.</div> <div class="htmlview paragraph">In this study, the EFEM<sup>0</sup> technique is applied to a passenger van for a noise control investigation. The general scheme is to incorporate the EFEM<sup>0</sup> coupling factors into a SEA model in order to release some SEA assumptions and improve the SEA model, especially for relatively high damping, strong coupling and direct field cases. The EFEM<sup>0</sup>-SEA integrated model for the trimmed van is validated by experimental data. Several noise control strategies will be discussed for the integrated model to optimize the sound package.</div>

In this paper, based on statistical energy analysis (SEA), the noise attenuation effect of highway sound absorbing barrier is predicted. The theoretical formula value is compared with the calculated value of statistical energy analysis (SEA) to verify its effectiveness in the prediction of sound barrier. And the insertion loss of sound barrier of mineral wool with diverse material thicknesses and coverage are calculated. The results showed that the noise attenuation of the sound barrier increased by 1.5 dB when the sound absorbing materials are attached to the sound barrier near the acoustic source. The noise attenuation effect of mineral wool is improved in the frequency band below 600 Hz when the thickness is increased. The coverage of mineral cotton increased by 25%, and the noise attenuation increased by 0.4 dB. Meanwhile, it also reflects the advantages of fast and convenient statistical energy analysis (SEA) – only one time modelling and changing its parameters can obtain the corresponding statistical results, which has some excellent reference function.

Sound insulation of brick diaphragm walls—I. Scale model measurement and statistical energy analysis

<div>In this article, the method based on the combination of the acoustic perturbation equations and the statistical energy analysis has been used to simulate and optimize the interior aerodynamic noise of a large sport utility vehicle model. The reliability of the method was verified by comparing the analysis results with the wind tunnel test. Influenced by the main noise sources such as A-pillar, exterior rearview mirror, and front sidewindow, the wind noise of the model was significantly greater than that of the same class. To improve the wind noise performance, the side mirror was optimized with the method, including the minimum distance between the rearview mirror and the triangle trim cover, the angle between the rearview mirror and the front sidewindow, and the shell groove of the rearview mirror. The simulation results show that the overall sound pressure level in the car decreases by 2.12 dBA and the articulation index increases by 4.04% after optimization. The development target of wind noise performance was achieved finally. The research demonstrates that the method combining the acoustic perturbation equations and the statistical energy analysis could be effectively utilized in the design optimization of the exterior shape to improve the wind noise performance of the vehicle during the conceptual design stage of the vehicle development.</div>

Sound transmission loss of foam-filled honeycomb sandwich panels using statistical energy analysis and theoretical and measured dynamic properties