Vibroacoustic optimization using a statistical energy analysis model

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.

An algorithm is presented to predict the statistical energy analysis (SEA) parameters of structures in a thermal environment. An energy flow model considering thermal effects is established by the finite element method, and the SEA parameters of the structure under a thermal environment are obtained by a power injection method. The proposed algorithm is applied to a simply supported L-shaped folded plate under rain-on-the-roof excitation. The accuracy of proposed method is verified by the travelling wave approach, and the influence of thermal effects on the SEA parameters is further investigated. The results show that, when only the effect of temperature-dependent material properties is considered, both the coupling loss factor (CLF) and the modal density have an opposite trend with the changing of the elastic modulus and shear modulus; when only the effect of additional stiffness due to thermal stresses is considered, the internal loss factor (ILF) and CLF decrease with the increase of temperature; when both the effects of the temperature-dependent material properties and the additional stiffness due to thermal stresses are taken into account, the ILF and CLF decrease with the increase of temperature. Furthermore, when the structure is exposed to a nonuniform thermal environment, the modal density, ILF, and CLF will decrease with the increase of the temperature gradient.

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

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 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.

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.

A direct transmissibility formulation for experimental statistical energy analysis with no input power measurements

This report is about response analysis using Statistical Energy Analysis (SEA) with FEM for two panels connected in L-type shape. We adopt two panels with viscoelastic damping layers and the panel connected in L-type shape as substructures. One of the panels has a curved surface and the other panel is flat. There are viscoelastic layers on the panels. Usually, modal damping is influenced by shape of panels and forms of the connection. Therefore, to consider coupling in damping between substructures, we use FEM and MSE (Modal Strain Energy) method to identify Internal Loss Factors (ILF). We get the Coupling Loss Factors (CLF) using the Element Energy and ILF. For us to verify whether a numerical value of the proposed method is right, we compare the results from this method and those from direct FEM. As a result, we show that this method is able to get SEA parameters (ILF and CLF) of the high precision for the damped panel having curved surface. This method shows that the precision of the response calculation in the low frequency range as well as in the high frequency range could be improved.

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

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

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.

Loss and coupling loss factors of two coupled dynamic systems

POWER TRANSMISSION BETWEEN TWO FINITE BEAMS AT LOW MODAL OVERLAP

Prediction of sound fields in rooms using statistical energy analysis

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.