Prediction of sound fields in rooms using statistical energy analysis

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.

A simple formula for insertion loss prediction of large acoustical enclosures using statistical energy analysis method

The method of the statistical energy analysis (SEA) has become a useful technique to predict the sound insulation and structural vibration in buildings. The accuracy of the prediction depends on the model of interaction of waves of different types and wave transmission through joints of structural elements. The method of SEA requires exact calculations of modal densities of waves of different types in structures. At high frequency, the correction based on the theory by Rayleigh, R.D. Mindlin and J.H. Rindel gives more accurate dispersion relations for phase velocities of longitudinal and bending waves in thick beams and plates.

<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>

Acoustic enclosure design is a complex problem that involves the interaction of multiple components. Yet the present conventional approach uses two-dimensional closed form solution to evaluate transmission loss of acoustic wall. In this paper, Statistical Energy Analysis (SEA) was first studied for simple cases of radiation efficiency, transmission loss, and flanking path calculations. The effectiveness of the SEA method for complex system was then demonstrated through a practical design application to gas turbine enclosure. It was found that SEA was a useful tool for gas turbine acoustic enclosure design.

Acoustic enclosure design is a complex problem that involves the interaction of multiple components. Yet the present conventional approach uses a two-dimensional closed-form solution to evaluate transmission loss of acoustic wall. In this paper, Statistical Energy Analysis (SEA) was first studied for simple cases of radiation efficiency, transmission loss, and flanking path calculations. The effectiveness of the SEA method for complex systems was then demonstrated through a practical design application to gas turbine enclosure. It was found that SEA was a useful tool for gas turbine acoustic enclosure design.

Traffic induced structural vibrations and noises of railway station structures are analyzed and estimated in this paper. Two finite element models, train-bridge model and frame model, are used to simulate the dynamic behavior of the station structure. The analytical model for the train-structure system is presented. The method of statistical energy analysis is used to estimate the structural noises. The relationship between structural vibration and noise is determined through computer simulation on the basis of radiation ratio and statistical energy analysis. Several factors, such as structural forms, materials, support conditions, train speed, etc., affecting the noise are discussed. By comparison of the noise level expressed with sound power radiation, some conclusions are obtained. The results show that the method can be used as reference for the plan, design and material selection of elevated station structures.

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

<div class="htmlview paragraph">The Energy Flow Method (EFM), which is based on a Finite Element Analysis (FEA) model and its modal frequency response solution is presented in this paper. The energy and power for each subsystem are the primary response and excitation parameters as in the Statistical Energy analysis (SEA) method. This gives a broad-brush prediction by averaging over both frequency and spatial domain. This prediction is useful when uncertainties exist in the model. The FEA model is used to capture the geometry detail, which is critical in mid-frequency vibration. As an example, a five-plate system is studied using various methods, including traditional FEA, SEA and EFM. The last one has been implemented in MSC/NASTRAN. A discussion is given to understand the limitation of SEA and FEA application in mid frequency response.</div>

In this paper, an optimization technique for medium-high frequency dynamic problems based on Statistical Energy Analysis (SEA) method is presented. Using a SEA model, the subsystem energies are controlled by internal loss factors (ILF) and coupling loss factors (CLF), which in turn depend on the physical parameters of the subsystems. A preliminary sensitivity analysis of subsystem energy to CLF׳s is performed to select CLF׳s that are most effective on subsystem energies. Since the injected power depends not only on the external loads but on the physical parameters of the subsystems as well, it must be taken into account under certain conditions. This is accomplished in the optimization procedure, where approximate relationships between CLF׳s, injected power and physical parameters are derived. The approach is applied on a typical aeronautical structure: the cabin of a helicopter.

Based on the dynamic receptance method, a vehicle–track–bridge interaction model was developed to calculate the wheel–rail interaction forces and the forces transmitted to the bridge in an elevated urban rail transit system. A prediction model integrating the finite element method–boundary element method (FEM-BEM) and the statistical energy analysis (SEA) method was established to obtain the noise from the main girder, track slab, and wheel–rail system for elevated urban rail transit. The calculated results agree well with the measured data. Thereafter, the noise radiation characteristics of a single source and the total noise of elevated urban rail transit systems with resilient fasteners, trapezoidal sleepers, and steel spring floating slabs were investigated. The results demonstrate that the noise prediction model for elevated urban rail transit that was developed in this study is effective. The diversity of track forms altered the noise radiation field of elevated urban rail transit systems significantly. Compared to monolithic track beds, where the fastener stiffness is assumed to be 60 × 106 N/m (MTB_60), steel spring floating slab tracks (FSTs), trapezoidal sleeper tracks (TSTs), and resilient fasteners with a stiffness of 40 × 106 N/m (MTB_40) and 20 × 106 N/m (MTB_20) can reduce bridge-borne noise by 24.6 dB, 8.8 dB, 2.1 dB, and 4.2 dB, respectively. These vibration-mitigating tracks can decrease the radiated noise from the track slab by −0.7 dB, −0.6 dB, 2.5 dB, and 2.6 dB, but increase wheel–rail noise by 0.4 dB, 0.8 dB, 1.3 dB, and 2.4 dB, respectively. The noise emanating from the main girder and the track slab was dominant in the linear weighting of the total noise of the elevated section with MTBs. For the TST and FST, the radiated noise from the track slab contributed most to the total noise.

<div class="section abstract"><div class="htmlview paragraph">Squeak and Rattle are the most obnoxious noises, affecting the perceived quality of an automobile interior. Minimizing or eliminating these transient events poses a great challenge in vehicle construction as they are generally discovered late in the product development cycle. Identifying and quantifying these issues at the design and virtual validation stage is of prime importance. Current simulation methodologies estimate the occurrence of these events by measuring the relative displacement between the interacting parts. Solving this problem using linear simulations do not accurately reflect real-world non-linear mechanical behavior and most importantly, quantifying the noise caused by these impact events. Capturing a suitable impact behavior is essential along with the quantification of noise generated by these events is necessary for understanding the severity of the problem. This paper suggests a method based on non-linear impact analysis for quantifying the noise produced during a rattle event. To represent this rattle event a simplified geometry consisting of two plates was considered. Contacts were defined at the impact points, and a non-linear transient simulation was run with a sinusoidal load as the input. The impact forces were measured at the contact interfaces and then used to calculate the SPL using the Statistical Energy Analysis (SEA) method at a suitable distance from the impacting event. In addition, a comparison study was performed to observe the effect of increase in excitation frequency. The implemented method would provide an advanced approach to assess noise produced due to impact, and it could be scaled up to undertake assessments for various sub-systems and vehicle assemblies, especially the interior trim parts to attenuate the noise generated by rattle events.</div></div>

In this study, dynamic receptance analysis (DRA) is proposed and combined with hybrid finite element (FE)-statistical energy analysis (SEA) method to accurately predict structural noise from long-span cable-stayed bridge (LSCB) with steel box composite girder (SBCG) in urban rail transit (URT). To begin with, a vertical vehicle–track coupling model in frequency domain is established based on DRA, in which the rail is represented by an infinite Timoshenko beam supported by a series of fasteners that are regarded as springs with complex stiffness. The floating slab is regarded as the Euler beam with both ends free supported by steel springs. Using this model, the spectrums of the wheel–rail force and the forces transferred to the bridge can be efficiently obtained by taking rail roughness as the excitation. Due to the low modal density of the concrete deck, the hybrid FE-SEA method is introduced to establish the noise prediction model, in which the discontinuity caused by using distinct models for different frequency bands is avoided. Then the on-site noise tests of a LSCB with SBCG in URT are carried out to verify of the proposed method. Finally, based on the prediction method, the acoustic contributions of the bridge components are analyzed in detail. The force transfer characteristics as well as the noise reduction effects of different track structures are thoroughly investigated, so as to provide reference for the future research on bridge-borne noise control.

Sound fields in realistic rooms were simulated by different kinds of computational methods, and comparisons were conducted. One is based on the wave acoustics and the other is based on the geometrical acoustics, i.e., the finite-element method (FEM) and the conical beam method (CBM). As for the software applied here, the authors have developed their own FEM code, namely LsFE-SFA, to conduct FEM computations, and they employed commercial software, i.e. raynoise, to conduct CBM computations. First, theoretical basis of LsFE-SFA was given briefly. Next, sound-pressure distributions in a reverberation room with the volume of 165 cubic meters were computed by both methods to compare the agreement with measured sound-pressure levels. The boundary conditions due to the sound absorption were changed to examine the relation between the absorbent condition and the agreements. The agreement between FEM and measurement were found to be better throughout the examination. Next, both FEM and CBM were applied onto the analysis of large-scale sound fields in a multipurpose hall with the volume of 37<th>000 cubic meters to discuss the agreement and difference in detail.

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.