Power flow through dynamically coupled subsystems

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.

Coupling loss factor is one of the most important parameters used in the statistical energy analysis (SEA). It regulates the energy flows between two subsystems. Theoretically, the coupling loss factors are usually calculated from the wave transmission coefficients derived using two semi-infinite systems. While the final system equation in the SEA is based on the powerful energy conservation principle, in the process the coupling loss factors are assumed to be unaffected by the configuration changes. In other words, the coupling loss factors which are experimentally or analytically determined under some ideal conditions are considered to be unchanged by the more complicated coupling conditions under a system configuration. The validity of this treatment needs to be carefully studied because there is a belief that the SEA method can be readily extended to lower frequencies so long as the coupling loss factors can be somehow satisfactorily determined. In this study, wave transmission coefficients are obtained by calculating the energy flows for a three-beam system coupled together in T-shape. Separately, the wave transmission coefficients are estimated by using energy flows calculated for each possible pairing of two beams. By comparing the results from these two different approaches, some insightful information has been obtained regarding the characteristics of the coupling loss factors in determining power flows in structures.

Robust estimation of coupling loss factors from finite element analysis

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

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.

Loss and coupling loss factors of two coupled dynamic systems

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.

In 1996 a series of standard test structures was conceived and manufactured by members of the Institute of Noise Control Engineering (INCE) [Cuschieri, Burroughs, and Carroll, Evaluation of Structure-Borne Noise Prediction Techniques Review, Proceedings of Noise-Con 98, April 1998, pp. 315–320]. The structures include a Lexan T-shaped beam and two ribbed panels of identical geometries but different materials: aluminum and lexan. In subsequent years, a wide variety of investigators from the U.S. and around the world have conducted experimental and numerical studies on the test structures, particularly on energy flow parameters, such as power input, power dissipation, and power flow. Most of the studies have been performed at low frequencies, and have shown phenomena such as the conversion of flexural wave power to longitudinal wave power at the T-beam joint and the nature of the structural intensity fields in the ribbed panels. Measurements and computations compare well. At high frequencies, Statistical Energy Analysis (SEA) techniques have shown that energy tends to become trapped in the drive leg of the T-beam. SEA studies on the ribbed panels show that the Lexan panel transmits less energy across the ribs than the aluminum panel does due primarily to differences in material loss factor.

<div class="htmlview paragraph">In this paper, sound transmission characteristics of typical stamped steel automotive body panels are investigated. In particular, focus was placed on the dash panel since it separates the interior space from the engine. Three dash panels were considered with the same geometry but different damping characteristics. These dash panels included a bare steel dash, a bare steel dash with a Patch Constrained Layer (PCL) and a laminated steel dash. Sound transmission loss was measured in a transmission loss suite. It was observed that the measured transmission loss of the laminated steel dash was significantly higher than the other dash panels throughout the mid and high frequency regions. A hybrid approach using both Finite Element Analysis and Statistical Energy Analysis (SEA) was used to predict and correlate the sound transmission loss for these panels. The geometry effects of the dash panels were considered while calculating SEA parameters. Coupling loss factors between the dash panel and acoustic cavity were predicted considering the effects of increased stiffness and the impedance mismatches due to discontinuities along the surface of the dash. The power contributions to the receiving cavity by resonant paths and non-resonant paths were investigated. It was observed that the resonant power contribution was significantly lower for the laminated steel dash as compared to the other dash panels. This resulted in higher transmission loss for laminated steel dash compared to the transmission loss for other two panels.</div>

This paper discusses analytical Statistical Energy Analysis (SEA) applicability to structural-acoustic coupling systems by means of Finite Elemental Method (FEM) calculation. At first, we summarize analytical equations about SEA primary parameters (power input, subsystem's energy, and coupling loss factor). Next, we calculate these parameters by using analytical SEA and FEM calculation in order to verify the equations for these parameters. FEM calculations are performed to compare power input, subsystem energies, and coupling loss factors on structural-acoustic coupling system. The analytical SEA predictions are also compared with FEM calculation results.

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.

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.

Theoretical and experimental investigation of effect of boundary conditions on SEA parameters for idealised subsystems

<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>

POWER TRANSMISSION BETWEEN TWO FINITE BEAMS AT LOW MODAL OVERLAP