Structural Loss Factor Research Articles

Effect of modal overlap factor on the ray tracing analysis of the curved beam structure: A computational study

Ray tracing method (RTM) of the geometrical acoustics area is recently known to be useful for the evaluation of spatial distribution of energy density and power flow of vibrating structures at high frequencies. In this study, the spatial distribution of vibrational energy and power flow of curved beam and its connected structures are of interest. Longitudinal, flexural, and torsional waves are considered using the Euler–Bernoulli beam theory. In the analysis of spatial distribution, the band-averaged RTM result varies smoothly in space without local fluctuations. This means that the RTM result can represent a similar tendency to the traveling wave solution. An accuracy of the analysis depends on the modal overlap factor (MOF), which is the function of the length of the beam, frequency range, and structural loss factor. The effect of changing each parameter is investigated and discussed. Similar to other high frequency methods such as statistical energy analysis and power flow analysis, the results become close to the traveling wave solutions as the modal overlap factor increases. [Work supported by the BK21 project and NRL.]

Mechanics and finite elements for the damped dynamic characteristics of curvilinear laminates and composite shell structures

Integrated mechanics and a finite element method are presented for predicting the damping of doubly curved laminates and laminated shell composite structures. Damping mechanics are formulated in curvilinear co-ordinates from ply to structural level and the structural modal loss factors are calculated using the energy dissipation method. The modelling of damping at the laminate level is based on first order shear shell theory. An eight-node shell damping finite element is developed. Comparisons of the present model with classical and discrete layer laminate damping theory predictions are shown. Modal damping and natural frequencies of composite plates and open cylindrical shells were measured and correlated with predicted results. Parametric studies illustrate the effect of curvature and lamination on modal damping and natural frequency.

Sound Radiation due to Tire Tread Vibration

A theoretical model was studied to describe the sound radiation created by surface vibration of in-service tires. The tire is modeled as a circular ring model. The effects of normalized frequency and the structural loss factor are included. The radiation sound power is calculated as a function of the normalized frequency and the structural loss factor through numerical integration of the sound pressure. The basic sound radiation mechanism is shown to be a damped progressive wave field on the structure in the vicinity of the applied force. The result indicates that the potential sound reduction might be obtained if the values of the normalized frequency and structural loss factor are determined.

Vibrations of infinite plates and the mean value vibrations of finite plates excited by turbulent boundary layer flows

The vibration response of a turbulent boundary layer (TBL) excited flat plate is analyzed using a finite-element model and infinite plate theory. For the finite-element models, discretization sufficient to resolve the convective fluctuations in the flow excitation field is used for the study. Clamped boundary conditions are assumed for the finite-element models and analyses are conducted at a variety of flow speeds and structural loss factors. Two equivalent TBL wall pressure excitation models are applied to the plates: (1) a modified Corcos cross-spectrum model for the finite-element models, and (2) a wave-vector-frequency spectrum model (the Fourier transform of the modified Corcos cross spectra) for the infinite plate theory. The TBL wall pressure autospectrum is approximated using the model derived by Smolyakov and Tkachenko. The infinite plate predicts the mean value response of the finite plate very well for all speeds and loss factors considered, showing consistency with Skudrzyks mean value theory and its usefulness for generating sound and vibration estimates.

205 SEA理論に基づく機械構造物の振動解析(OS2-2 SEA理論)(OS2 振動の解析と制御)

We discuss a way to estimate the Coupling Loss Factors(CLF) of complex structures by predictive SEA. The formulations of main SEA paremeters are firstly arranged. Then, some guidelines for modeling in predictive SEA are derived using some simple structures. Finally the guidelines are applied to evaluate the CLFs on an automotive parts. As a result, we can get the reasonable CLFs.

VIBRATIONAL ENERGY ANALYSIS OF GROUND/STRUCTURE INTERACTION IN TERMS OF WAVE TYPE

The vibrational interaction of underground structures such as tunnels or building foundations with the ground involves different types of waves both in structures and in ground. In this paper, a wave approach is used to study these waves in the simple case of an infinite slab laying on a half-space homogeneous soil. The results are expressed in terms of energy quantities such as input line mobility and radiated power in the case of line force excitation of the slab and power injected to the slab in the case of forced vibration by an incoming ground borne wave. It is shown that in the case of line force excitation of the slab, the radiation loss factors obtained are 10 times higher than common values of structural loss factors, showing that the energy losses of an underground structure are mainly radiated into the ground. In the case of forced vibration by an incoming ground-borne wave, the slab wave type depends on the type of incident ground-borne waves: P waves mainly generate quasi-longitudinal waves in the slab at low frequencies and bending waves at higher frequencies; SV waves generate both bending and quasi-longitudinal waves with a percentage depending on the type of ground.

Damping of Patched Structures Subjected to Acoustic Fatigue: A Numerical Study

This numerical study seeks to evaluate a set of reinforcement/damping treatment options to alleviate the acoustic fatigue damage of the nacelle panel of the F/A-18 aircraft. This study focuses on the use of constrained layer damping to increase the structural loss factor in the nacelle region in a bid to reduce the incidence of acoustic fatigue. The findings of this report show that where add-on damping material is to be implemented on a repair/reinforcement, orthotropic material, (e.g. boron/epoxy), is a more appropriate material to use as a repair/reinforcement material than isotropic material, e.g. aluminium. In addition, the results presented in this paper revealed that boron/epoxy laminate can be used as an alternative constraining layer for the damping treatment in regions of intense acoustic excitation.

Damping of Patched Structures Subjected to Acoustic Fatigue: A Numerical Study

This numerical study seeks to evaluate a set of reinforcement/damping treatment options to alleviate the acoustic fatigue damage of the nacelle panel of the F/A-18 aircraft. This study focuses on the use of constrained layer damping to increase the structural loss factor in the nacelle region in a bid to reduce the incidence of acoustic fatigue. The findings of this report show that where add-on damping material is to be implemented on a repair/reinforcement, orthotropic material, (e.g. boron/epoxy), is a more appropriate material to use as a repair/reinforcement material than isotropic material, e.g. aluminium. In addition, the results presented in this paper revealed that boron/epoxy laminate can be used as an alternative constraining layer for the damping treatment in regions of intense acoustic excitation.

Experimental and Finite Element Analysis of Pultruded Glass-Graphite/Epoxy Hybrids in Axial and Flexural Modes of Vibration

The effects of hybridization on the extensional and flexural dynamic properties of pultruded composite materials are reported in this paper. The composite materials considered were made up of unidirectional glass, graphite fibers in an epoxy matrix, and hybrids of glass-graphite/epoxy produced by the pultrusion manufacturing process. The dynamic storage modulus and loss factor of the rectangular and circular cross-section samples were first evaluated using the nondestructive impulse-frequency response vibration technique. The long and slender flat specimens were analyzed in both extensional and flexural modes of vibration in a free-free test configuration, whereas the thicker round specimens were analyzed only in the axial mode of vibration. The properties of the monofiber type glass/epoxy and graphite/epoxy composites were used as input to the finite element model for predicting and experimental validation of various pultruded (and hypothetical) glass-graphite/epoxy hybrid combinations. The modal strain energy method was used for computing the structural loss factors of the hybrid specimens based on the element stiffness matrices and estimated mode shapes in the fundamental mode of vibration. Results of this investigation showed excellent agreement between experimental data and numerical predictions for the dynamic extensional properties of both flat and round specimens. The numerical results for dynamic flexural properties of flat specimens were found to have a similar trend as that obtained from the experimental technique. Small variations in flexural properties could be attributed to the irregular shapes (which were not taken into account in the finite element model) of layers in the hybrid combinations formed during the pultrusion manufacturing process. Results also demonstrated that while the extensional properties were independent of the fiber location and fiber packing geometry, the flexural properties were highly dependent upon these two factors. Previously reported data (which was obtained by testing these flat hybrid specimens in the flexural mode of vibration in a clamped-free boundary condition) were re-analyzed using the free-free configuration and modal strain energy method, yielding more reasonable results.

Loss factors of pipelike structures containing beads

It is found that when beads are inserted into the interior of a pipelike structure, the damping of this beaded structure may substantially exceed that of the unbeaded structure. The beads are modeled by a ‘‘beaded fluid’’ characterized by a low density, a low sound speed, and a high loss factor. Statistical energy analysis (SEA) is developed to account for the presence of the beaded fluid within the structure. It is shown that in certain frequency regimes and certain choices of the parameters that characterize the beaded fluid, relative to those that characterize the structure, the loss factor of the beaded structure can be designed to significantly exceed that of the unbeaded structure. The mechanism for the increase lies in that the stored energy in the beaded fluid may, in the ‘‘steady state,’’ be made to substantially exceed that in the structure. The bulk of the stored energy is then decimated by the high damping capability that the beaded fluid enjoys. A selected number of computer experiments are cited to illustrate the potential effectiveness of this damping mechanism and the manner by which the parameters that define the beads and the structure, control it.

Experimental measurements of vibrational energy and acoustic radiation for a 3-D truss

The MIT Structural Acoustics Group is making experimental measurements to determine the structural loss and radiation efficiency of an undamped, three-dimensional truss structure, constructed of 0.5-in. aluminum tubing connected by massive aluminum joints. The truss was excited with a shaker driven by wideband white noise out to 20 kHz. The total vibrational energy in the truss was calculated by spatially integrating the energy estimated from acceleration measurements made over the entire truss. This value and the total input power, as measured with an impedance head, allow estimation of the total loss factor for the truss as a function of frequency. Total radiated sound power was calculated by spatially integrating a set of average acoustic intensity measurements made over a grid surrounding the truss. Since the total radiated sound power is known, the total loss factor can easily be broken down into a structural loss factor and a radiation loss factor. These measurements show that the radiation loss is smaller than structural loss, but larger than radiation from an equivalent length single strut would predict. The additional radiation is accounted for by a factor due to multipath in the truss. This factor is frequency dependent and can be estimated from the data by comparing to theory. [Research supported by ARPA and ONR.]

Acoustic radiation from a 3-D truss: Direct global stiffness matrix modeling results

This study was initiated to evaluate the normalized sound power level radiated by a driven truss. The coincidence frequency for the beam elements was sufficiently high that global truss modes are not a concern. Radiation from local beam modes dominate the field. Acoustic radiation was modeled using a combination of the direct global stiffness matrix (DGSM) method and models based on radiation efficiency of cylindrical beams. Use of a nominal structural loss factor of 10−4 for the beam material (aluminum) overestimates the measured field by an order of magnitude. Earlier studies suggest that a combination of structural loss in the joints and multipath wave-type conversion in the truss leads to a loss factor of order 10−3. For this study experimental data were inverted to estimate a frequency-dependent loss factor, which confirms the prior estimate of order 10−3. When the DGSM based model was run with the estimated frequency-dependent loss factor, the model results match the measured data closely. A power balance shows that the structural loss factor dominates the total power dissipated in the system, as one might expect for a lightly fluid-loaded structure. [Research sponsored by ARPA/ONR.] a)E-mail: fricke@mit.edu

Electrorheological Material Based Adaptive Beams Subjected to Various Boundary Conditions

The semi-active vibration control capabilities of Electrorheological (ER) material based adaptive beams were investigated in this study. The adaptive nature of such ER beams was achieved by controlling the pre-yield rheology of the ER material in response to varying applied electric field levels. The cross-sectional configuration of the beams considered was based on sandwiching the ER material between elastic face plates. A dynamic model of the beam structure based on thin plate theory was developed. The resulting dynamic model was able to predict the structural vibration characteristics of the ER adaptive beam. The information determined included natural frequencies, loss factors, and transverse vibration responses at any location on the beam surface. These vibration characteristics were determined as functions of excitation frequency and applied electric field level. Also the beam model was developed for generalized boundary conditions. The boundary conditions considered in this study were: clamped-clamped, clamped-free, clamped-simply supported and simply supported. Variations in the natural frequencies, loss factors, and transverse vibration response of the adaptive structure were analyzed for the listed boundary conditions. Additionally, effects of variations of the damping layer thickness of the adaptive beam on the structural loss factor was studied. Results were compared for the boundary conditions studied, and considerable variations in beam vibration responses were observed. As a result, the semi-active control capabilities of ER material based adaptive beams were theoretically illustrated.

Computational prediction and redesign for viscoelastically damped structures

Viscoelastic materials are very effective in suppressing excessive vibrations and noise. The shear modulus of these materials has an important effect on the loss factors of damped structures. However, it changes rapidly with frequency, an effect, which has to be taken into account. This paper presents a method, namely the finite element perturbation method, which provides a simple tool for the prediction in a wide frequency range without repeated analysis. This approach also enables a simplified redesign of damping.

Frequency response analysis of laminated composite beams

The modeling of laminated composite beams has been derived systematically from the three-dimensional elasticity relations. The correctness of the solution found by using the present finite element model is verified by comparison with the results obtained by analytical solutions and other results presented in the literature. Numerical results indicate that the present technique can given accurate results for frequency response analysis for laminated composite beams. Loss factors of structures obtained by the method of complex eigenvalues and the direct frequency response method exhibit very good agreement. Optimum design of a laminated composite beam by the finite element method and the method of experiment planning has been successfully presented.

Determination of SEA total loss and coupling loss factors for built-up structures: Theory and numerical experiments.

It is the aim of this paper to develop a strategical method for the determination of SEA total loss factors (TLFs) and some of the coupling loss factors (CLFs) for built-up structures based on the recent development of in situ measurement techniques and the Statistical Energy Analysis theory. An obvious advantage of the method is that the determined TLFs would include the dissipation of coupling, and ‘automatically’ share the dissipation loss of the coupling to each coupled subsystem. The present strategy provides an applicable means for determination of total loss and some coupling loss factors of built-up structures for high frequency structure borne vibration and sound prediction. Satisfactory results of numerical experiments of the present strategy have been achieved.

Finite element analysis of vibration and damping of laminated composites

A sandwich composite beam and plate finite superelements with viscoelastic layers for vibration and damping analysis are presented. Each layer is considered as simple Timoshenko's beam or Mindlin-Reissner plate finite element. The energy dissipation in the viscoelastic layers is taken into account with complex modulus of elasticity theory. Two methods for damping analysis of laminated composite beams or plates are considered: the method of complex eigenvalues and the energy method. The first one is an ‘exact’ method, in which the modal loss factors of structure for each frequency are determined as the ratio of imaginary and real parts of complex eigenvalues. The second method is approximate, in which the modal loss factors of structure for each frequency are calculated as the ratio of dissipated and elastic strain energy for one cycle of steady-state vibrations. For sandwich beams and plates with a viscoelastic middle layer, the vibration and damping analysis for a wide range of materials and geometric parameters was carried out. Comparison of the results obtained by the two methods gives good agreement with the results of other authors.

Viscoelastic Damping Calculations Using a p-Type Finite Element Code

Damping factors of viscoelastically damped structures can be calculated using the modal strain energy method, implemented with a sequence of undamped modal analysis computations. There are significant advantages in performing these calculations using p-type finite element codes. These include ease of mesh design, an indicator of degree of solution convergence, modest computation time, and an insensitivity to element aspect ratio. Capitalizing on these advantages an algorithm is defined, which is effective in solving for the natural frequencies and modal loss factors of damped structures. The algorithm is demonstrated using a sandwiched cantilevered beam as an example.

Parametric analysis of the power flow on an L-shaped plate using a mobility power flow approach

In an earlier paper [J. M. Cuschieri, J. Acoust. Soc. Am. 87, 1159–1165 (1990)], the coupled response of two identical plate structures, determined using a mobility power flow (MPF) approach is presented. The plates’ responses are described in terms of the vibrational power input and transfer between the two plates. In this present paper, the MPF analysis for the vibrational response, power input, and transfer is presented for two coupled plates with arbitrary characteristics. Using the results from this analysis, a parametric evaluation of the plates’ responses is presented for changes in the plates’ structural parameters, which include different areas, thicknesses, materials, and structural damping loss factors. In the case of the structural damping, equal as well as different damping of the two plates are investigated. Furthermore, the response of the two plates for different excitation locations is included in the parametric evaluation. To minimize the number of results that are presented the source plate characteristics are kept constant except in the damping analysis. The results of the parametric analysis are used to determine the most critical parameters that influence the flow of vibrational power between the two coupled plates. The results obtained from the MPF approach are compared to results obtained using a statistical energy analysis (SEA) approach. The significance of the power flow results are discussed together with a discussion and a comparison between the SEA results and the MPF results.

Optimal constrained viscoelastic tape lengths for maximizing dampingin laminated composites

The results of experimental investigations conducted on glass/epoxy and graphite/epoxy composite laminated beams with constrained layer surface-damping treatments are reported. A fast Fourier transform based impulse technique is used for identifying an optimal length of damping tape to be applied for maximizing the structural loss factor.