Asymptotic modal analysis and statistical energy analysis of dynamical systems

Spatially Averaged Frequency Response Envelopes For One- And Two-dimensional Structural Components

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

A structural-acoustic system consisting of an enclosed cavity with flexible wall panels is considered to evaluate the effect of sound radiation-damping resulting from the panel vibration on the sound pressure level in the cavity. The interior cavity pressure can excite the flexible wall panels that will radiate noise to the exterior that in turn can reduce the interior noise due to the energy loss to the exterior surroundings. This energy loss is described as radiation damping of the interior cavity system. An enclosed rectangular cavity-plate system subjected to external random pressure excitation is used to evaluate the effect. The radiation damping is evaluated using a modal approach (FEM, BEM) to determine the radiation efficiency of the vibrating panels. The effect of the radiation damping for the example of a box-plate structure is evaluated using the CMA (classical modal analysis) method for the low-frequency range and the AMA (asymptotic modal analysis) method for the mid- and high-frequency ranges. The inclusion of radiation damping due to rigid body cavity mode excitation is shown to provide an improved prediction of the sound transmission loss especially in the low-frequency range.

To develop a high performance yacht is the target of what the Taiwan Yacht Builders pursue. One of the main requirements of high performance yacht is the ”comfort”. This means low noise and vibration level. Unlike other structure, however, ship structure is much more complex and is affected by external forces from wave impacts, propulsion system (e.g. main engine, propeller), and auxiliary machines, etc. Besides, there is a variety of combination of fiber sheet, resin, and core material in use to form the major hull and cabin structures in FRP boats. Thus, the prediction of shipboard noise in FPR ship is more difficult than in boat with steel or aluminum structures. The goal of this paper is to predict cabin noise level in a FRP fast boat using Statistical Energy Analysis (SEA) method. First, twelve FRP test specimens were built with different lamination scheme according to their locations on the target boat, and vibration tests were performed to obtain the Damping Loss Factors and Coupling Loss Factors for these FRP laminates. These data were then put into the SEA model to predict the cabin noise under different operating conditions. The results show that the predicted noise levels coincide well with the measured data except at fore cabin under transit conditions. And this validates SEA as a potential tool for the noise prediction for FRP boats.

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.

Predicting the vibration of the switched reluctance motor (SRM) is the key to design low vibration motor. In this paper, a comprehensive study of SRM vibration prediction from low frequency to high frequency is presented. For the low frequency vibration, the prediction model based on transfer function is proposed. The transfer function is calculated using modal analysis and mechanical harmonic analysis by 3D FEM. A detailed lookup table of radial force versus phase current and rotor angle is constructed. For the high frequency vibration, the statistical energy analysis (SEA) is employed. The SEA model of SRM including 4 subsystems is built. The internal loss factor and the coupling loss factors are measured through the power injection method; the analytical calculation method of input power is deduced. Both methods are verified by experiments. The comparison between the predicted results and the measured results demonstrates the accuracy of the transfer function based method and the SEA method for SRM low frequency and high frequency vibration prediction, respectively.

This article presents a fluid–structure interaction modelling, based on a coupling between component mode synthesis or finite element and statistical energy analysis (SEA). The hybrid strategy is applied on a panel–cavity coupled system using a modal analysis with uncoupled modes of the subsystems and through a finite element model of the coupled system. The determination of the energy transfer parameters is then considered. The hybrid SEA model is then validated in the high-frequency domain by comparison with an SEA model. Finally, a parametric survey is offered through the established modelling and conclusions on its validity domain are drawn.

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.

Statistical energy analysis (SEA) is applied to predict the responses on the printer unit. First, the selection of SEA subsystems is discussed using the initial slope ratio techniques. Then, an SEA model is constructed experimentally. The vibration energy level on each SEA subsystem predicted by the constructed SEA model is compared with the measured levels under impact test. It is shown that the vibration analysis on the printer unit is suitable for SEA. Next, the power input under the operating is identified using the built SEA model. The identified input power is obtained in some small time intervals. It is difficult to identify the power input by the other methods. It is concluded that the product of plastic mold is available to analyze the vibration responses predicted by SEA.

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.

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

<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>