Home HomeBrian R. Mace, The University of Auckland (New Zealand)
This paper concerns energy flow and statistical energy analysis (SEA) models of structural vibrations when modal overlap is small. In this circumstance the accuracy of SEA predictions is often poor. Particular reference is made to equipartition of energy (i.e., uniform energy density or modal energy throughout a system). It is seen, from both wave and modal analyses, that equipartition of energy does not occur in mechanical systems. Some wave analyses are reviewed. A global modal analysis is performed for the case of low modal overlap. Examples are discussed, and, in particular, results for a system comprising three coupled plates are presented. Energy density differences between different subsystems in a system are seen to exist when the modal overlap is low. This arises, in wave terms, when transmission coefficients differ from unity and, in modal terms, from the localisation of global modes within the susbsytems. Both these tend to contain energy in the driven subsystem. Effects tend to decrease for subsystems that are well coupled and irregular and if the system has many subsystems, many of which are excited.
sv970415.pdf (Scanned)
TOPKen H. Heron, DERA Farnborough
Using the wave approach, the theoretical prediction of Statistical Energy Analysis plate-to-plate coupling loss factors is based on calculating the random incidence transmission coefficient matrix associated with the equivalent infinite line junction. The 4x4 semi-infinite line wave dynamic stiffness of each plate is used to calculate the transmission coefficient for a particular angle of incidence; these angle transmission coefficients are then numerically integrated to obtain the required random incidence transmission coefficient. Many line connections in real engineering structures are in fact a series of equally spaced point connections. The spacing of these points is often neither large nor small in comparison to structural wavelengths. Furthermore each connection point may itself exhibit dynamic behaviour such as when point isolators are employed. This paper presents a theoretical solution to this problem based on the Fourier decomposition of the connection line into a series of true line connections each with a different trace wavenumber. The cross transfer matrix of a single point connection is then incorporated into the theory to model its dynamic behaviour. Experimental results are then compared with this theory using a two-plate assembly with an I-sectioned connecting beam and with various numbers and types of point connectors.
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Charles D. Coffen, United Technologies Research Center (U.S.A.)
Larry Hardin, United Technologies Research Center (U.S.A.)
Tricia Derwinski, Otis Elevator Company (U.S.A.)
An analytic prediction model was developed to identify the dominant paths of broadband (100 - 5000 Hz) acoustic energy transmission into an elevator cab enclosure. Statistical Energy Analysis (SEA) was used as the method, including analytical SEA, test based SEA, and panel transmission loss experiments. The model was validated statically with vibration and acoustic measurements made in Otis' Ride Quality Evaluation Facility, and operationally with measurements made in Otis' Bristol Research Tower. The validated AutoSEA model has provided a new means of identifying and quantifying the dominant noise sources and paths for vibro-acoustic energy flow through the elevator cab. This analysis has also demonstrated potential as a design tool for evaluating cab enclosure noise reduction concepts.
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Minoru Kamata, University of Tokyo (Japan)
Toru Yamazaki, University of Tokyo (Japan)
Kazuaki Kurosawa, University of Tokyo (Japan)
Shinichi Ohno, University of Tokyo (Japan)
This paper describes a new procedure which eases the SEA model construction (estimation of loss factors) and enables the prediction of vibration energy distribution in subsystems. In the construction of SEA model, the power flow between subsystems are directly measured using the structural intensity measurement. Compared with the power injection method which is popular for determining factors, this approach is easier because only one subsystem in the objective system is required for excitation. The SEA model gives the prediction of energy levels of subsystems, but the distribution of energy inside of a subsystem is unknown. Then, in order to predict the distribution, we use the finite element analysis in which an objective subsystem is modeled. This paper shows how the boundary and the excitation conditions in FEM are determined. These approach is tested to predict the vibration energy and the energy distribution of a box-like structure both numerically and experimentally. As a result, the SEA model constructed by the structural intensity measurement is good for energy prediction, and the finite element model of ever-y subsystem gives us the proper prediction of energy distribution.
sv970422.pdf (Scanned) TOP
P.J. Shorter, The University of Auckland (New Zealand)
Brian R. Mace, The University of Auckland (New Zealand)
This paper is concerned with the prediction of the distribution of vibrational energy throughout a structure. The paper illustrates how the results from a finite element model can be rephrased in terms of subsystem powers and energies using component mode synthesis. Equations are derived for the response, and frequency averages are obtained from them analytically. The technique is then illustrated by considering a system comprising three coupled plates, each plate being coupled along two of its edges. Ensemble and frequency averaged numerical results are compared with SEA predictions. It is seen that SEA predictions can be in error, this being attributable to coherence effects which arise because the system is strongly coupled, and the effects of averaging over narrow frequency bands.
sv970414.pdf (Scanned) TOP
Ruisen Ming, The University of Western Australia (Australia)
Jie Pan, The University of Western Australia (Australia)
This paper presents a numerical study of SEA prediction accuracy in a coupled plate system. It was shown that the parameters controlling the prediction accuracy are the geometric mean of modal overlap factor M and number of coupled modes N in the frequency band of analysis. In the low frequency bands where few coupled modes are present, both prediction error and standard deviation of numerical results are large. The "travelling wave" model and SEA may not be appropriate. In the medium frequency bands where N is neither large nor small, the "travelling wave" model and SEA are applicable but their prediction errors are not negligible. The prediction error and standard deviation generally decrease as M increases. However, M cannot be used as a sole parameter for judging the prediction accuracy. For same M but different dissipation loss factors, the prediction errors could be different. The increase of modal number can reduce fluctuation and standard deviation, but cannot reduce the prediction error. The increase of dissipation loss factors can reduce not only fluctuation and standard deviation but also the prediction error. In the high frequency bands where both M and N are large, the standard deviation becomes small and the prediction error is negligible.
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Sang R. Kim, KIMM (Korea)
Jae S. Kim, KIMM (Korea)
Hyun S. Kim, KIMM (Korea)
Hyun J. Kang, KIMM (Korea)
It is well known that Statistical Energy Analysis (SEA) is one of very attractive analytical methods to solve shipboard noise problems. With reasonable successes, many applications of SEA to shipboard noise prediction have been reported. However when one wishes to obtain theoretical preductions by using SEA in practical systems, he will find difficulty in modeling of source systems, that is, foundations where to place main engine, generator, compressor, and so on. Also, he will find that it is hard to determine the amount of power flow from machinery to structures. In this paper, SEA of a simple foundation model was carried out using three kinds of the estimated amount of power flow from source; a averaged square-velocity level, mobility method, and actually measured power. The comparison of these results is presented. That comparison shows a method to get structure-borne noise power from the combination of machinery and foundation. This preduction method gave a good result for a air-compressor mounted on a model foundation. The method is expected to give a reasonable power output in practical problems.
sv970315.pdf (Scanned) TOPAnders M. Wilson, Chalmers University of Technology (Sweden)
The Finite Element Method (FEM) is frequently and mostly successfully used to model low frequency vibration behavior in built up structures. Although this tool has proven successful in many areas, it has been found to have severe limitations for noise and high ferquency vibration prediction. The Statistical Energy Analysis (SEA) technique has become increasingly interesting and important for high frequency vibration and noise prediction. Up till now, the techniques mentioned above have mostly been used separately. Since FEM and SEA have their compoutational strengths in different frequency ranges, an analytical means of combining these two methods and taking advantage of each method's strengths is sought for in the current project. The procedure used to combine SEA and FEM, is separate modeling of the different regions of the structure according to modal density and structural configuration, and then applying an energy based optimization to fullfill local and global restraint equations. To allow large FEM models in the analysis and to extend the frequency range for the part analyzed by FEM, dynamic substructuring is incorporated in the analysis.
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