制振曲面パネルをL結合した構造における減衰の連成を考慮したFEM援用SEA応答解析

This report is about response analysis using Statistical Energy Analysis (SEA) with FEM for two panels connected in L-shape. Viscoelastic damping materials are laminated on the panels. One of the panels has a bead formed in circular ring. Usually, modal damping is influenced by shape of panels and forms of the connection. Therefore, to consider coupling in damping between substructures, we proposed calculation method using FEM and MSE (Modal Strain Energy) method to identify internal loss factors. We changed the inner diameter of the circular ring. As a result, we could identify SEA parameters in high precision. And the proposed SEA enables us to improve not only precision in high frequency but also precision in low frequency.

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 numerical method is proposed to calculate response analysis for automotive sound proof structure including elastic body, viscoelastic body and porous body using three dimensional FEM and MSKE method. Displacement vectors as common unknown variable under coupled condition. The explicit expressions of modal loss factors for the sound proof structures are derived using Modal Strain and Kinetic Energy Method (MSKE method) proposed by authors in our previous paper. Using this technique, eigenvalue analysis and frequency response analysis are performed for the automotive sound proof structure. In this report, we deal with a porous material sandwiched between a steel cover plate and a base plate (steel plate with a viscoelastic damping layer). We investigate vibration transmission characteristics from the base plate to the cover plate. Especially, we focus on the influences of curvature of the base plate on the vibration transmission. We set the curved plate as a convex upward structure, while the cover plate is leveled. Thus, the distance between the base plate and the cover plate become short locally because of the curvature. This caused sound bridge phenomena.

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

POWER TRANSMISSION BETWEEN TWO FINITE BEAMS AT LOW MODAL OVERLAP

The Power Input Method (PIM) is used both experimentally and a nalytically to estimate the system loss factor for sandwich panels with various configurations of Constrained Layer Damping (CLD) treatments over a broad frequency range. The experimental power input method is applied to both uniformly and non -uniformly da mped structures. Results are compared with results from other experimental methods. A new analytical power input method is proposed for evaluating the loss factor of built -up structures, based on the finite element model with assigned properties of the con stituents. The new analytical power input method is evaluated by comparison with the commonly used Modal Strain Energy (MSE) method. Instead of making an approximate correction of the constant material properties, this analytical power input method directl y takes into account the frequency -dependent material properties of the viscoelastic material using the MSC/NASTRAN direct frequency response solution. Results of experimental and analytical methods are presented, compared and discussed. It is shown that: 1) all three currently available experimental methods yield consistent results, while the power input method gives damping estimation other than just at several discrete frequencies basically in the low frequency range; 2) both the analytical power input m ethod and the modal strain energy method yield consistent results with the experimental power input method. Furthermore, both experimental and analytical power input methods are used to investigate how loss factors change as the excitation position change. This shows another merit of the analytical power input method, because analytical modal methods cannot take into account the change of excitation position.

The Power Input Method (PIM) is used both experimentally and a nalytically to estimate the system loss factor for sandwich panels with various configurations of Constrained Layer Damping (CLD) treatments over a broad frequency range. The experimental power input method is applied to both uniformly and non -uniformly da mped structures. Results are compared with results from other experimental methods. A new analytical power input method is proposed for evaluating the loss factor of built -up structures, based on the finite element model with assigned properties of the con stituents. The new analytical power input method is evaluated by comparison with the commonly used Modal Strain Energy (MSE) method. Instead of making an approximate correction of the constant material properties, this analytical power input method directl y takes into account the frequency -dependent material properties of the viscoelastic material using the MSC/NASTRAN direct frequency response solution. Results of experimental and analytical methods are presented, compared and discussed. It is shown that: 1) all three currently available experimental methods yield consistent results, while the power input method gives damping estimation other than just at several discrete frequencies basically in the low frequency range; 2) both the analytical power input m ethod and the modal strain energy method yield consistent results with the experimental power input method. Furthermore, both experimental and analytical power input methods are used to investigate how loss factors change as the excitation position change. This shows another merit of the analytical power input method, because analytical modal methods cannot take into account the change of excitation position.

This paper presents the analysis of modal parameters (natural frequencies, damping ratios and mode shapes) of a simply supported beam with adhesively bonded double-strap joint by the finite-element based Modal Strain Energy (MSE) method using ANSYS 4.4A software. The results obtained by the MSE method are compared with closed form analytical solutions previously obtained by the first author for flexural vibration of the same system. Good agreement has been obtained between the two methods for both the natural frequencies and system loss factors. The effects of structural parameters and material properties of the adhesive on the modal properties of the joint system are also studied which are useful in the design of the joint system for passive vibration and noise control. In order to evaluate the MSE and analytical results, some experiments were conducted using aluminum double-strap joint with 3M ISD112 damping material. The experimental results agreed well with both analytical and MSE results indicating the validity of both analytical and MSE methods. Finally, a comparative study has been conducted using various commercially available damping materials to evaluate their relative merits for use in the design of these joints.

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.

Constrained layer damping treatments are widely used in mechanical structures to damp acoustic noise and mechanical vibrations. A viscoelastic layer is thereby applied to a structure and covered by a stiff constraining layer. When the structure vibrates in a bending mode, the viscoelastic layer is forced to deform in shear mode. Thus, the vibration energy is dissipated as low grade frictional heat. This paper documents the efficiency of passive constrained layer damping treatments for low frequency vibrations of cylindrical composite specimens made of glass fibre-reinforced plastics. Different cross section geometries with shear webs have been investigated in order to study a beneficial effect on the damping characteristics of the cylinder. The viscoelastic damping layers are placed at different locations within the composite cylinder e.g. circumferential and along the neutral plane to evaluate the location-dependent efficiency of constrained layer damping treatments. The results of the study provide a thorough understanding of constrained layer damping treatments and an improved damping design of the cylindrical composite structure. The highest damping is achieved when placing the damping layer in the neutral plane perpendicular to the bending load. The results are based on free decay tests of the composite structure.

Loss and coupling loss factors of two coupled dynamic systems

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.

Robust estimation of coupling loss factors from finite element analysis

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.

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.