Structural Damping Loss Factor Research Articles

Vibrational Energy Flow Model for a High Damping Beam with Constant Axial Force

The energy flow analysis (EFA) method is developed to predict the energy density of a high damping beam with constant axial force in the high-frequency range. The energy density and intensity of the beam are associated with high structural damping loss factor and axial force and introduced to derive the energy transmission equation. For high damping situation, the energy loss equation is derived by considering the relationship between potential energy and total energy. Then, the energy density governing equation is obtained. Finally, the feasibility of the EFA approach is validated by comparing the EFA results with the modal solutions for various frequencies and structural damping loss factors. The effects of structural damping loss factor and axial force on the energy density distribution are also discussed in detail.

Application of the energy finite element analysis to vibration of beams with stepped thickness and variable cross-section

Energy finite element analysis (EFEA) has been developed to compute the energy distribution of vibrating structures. The method adopts the energy density as the basic variable of differential equation. The energy density can be used to analyze the behavior of vibrating beams. Firstly, an EFEA equation is obtained from the classical displacement equation. In the applications of uniform and non-uniform beams, the EFEA results are compared with the analytical and FEA results. Secondly, a junction formulation solving the discontinuity problem of energy density at the junction of two beams with stepped thickness is proposed. The EFEA equation combined with junction formulation is used to solve the energy transmission problem of the coupling beams with stepped thickness and variable cross-section. The smoothed results of coupling beams are achieved, and the differences of energy density at the junctions are analyzed. The feasibility of the EFEA approach is validated by using several design examples under the various frequencies and structural damping loss factors.

Progressive phase trends in plates with embedded acoustic black holes.

Acoustic black holes (ABHs) have been explored and demonstrated to be effective passive treatments for broadband noise and vibration control. Performance metrics for assessing damping concepts are often focused on maximizing structural damping loss factors. Optimally performing damping treatments can reduce the resonant response of a driven system well below the direct field response. This results in a finite structure whose vibration input-output response follows that of an infinite structure. The vibration mobility transfer functions between locations on a structure can be used to assess the structure's vibration response phase, and compare its phase response characteristics to those of idealized systems. This work experimentally explores the phase accumulation in finite plates, with and without embedded grids of ABHs. The measured results are compared and contrasted with theoretical results for finite and infinite uniform plates. Accumulated phase characteristics, their spatial dependence and limits, are examined for the plates and compared to theoretical estimates. The phase accumulation results show that the embedded acoustic black hole treatments can significantly enhance the damping of the plates to the point that their phase accumulation follows that of an infinite plate.

Analytical model of high-frequency energy flow response for a beam with free layer damping

Energy flow analysis (EFA) is developed to predict the vibrational energy density of beam structures with both full free layer damping (FFLD) and partial free layer damping (PFLD) treatments in the high frequency range. Both equivalent flexural stiffness and structural damping loss factor of a beam with free layer damping are obtained using the equivalent complex stiffness method. Then the energy density governing equation considering high damping effect is derived for a beam with FFLD treatment. Following obtainment of the energy transfer coefficients at both ends of free damping layer, the energy density within a beam with PFLD treatment is evaluated by solving the presented energy governing equation. To verify the proposed formulation, numerical simulations are performed for the pinned-pinned beams with FFLD and PFLD treatments. The EFA results are compared with the exact solutions from wave analysis at various frequencies, and good correlations are observed between the developed EFA results and the exact solutions.

Study on vibration damping of composite sandwich cylindrical shell with pyramidal truss-like cores

The vibration and damping characteristics of free–free composite sandwich cylindrical shell with pyramidal truss-like cores have been conducted using the Rayleigh–Ritz model and finite element method. The predictions for the modal properties of composite sandwich cylindrical shell with pyramidal truss-like cores showed good agreement with the experimental tests. The influences of fiber ply angles on the natural frequency and damping loss factor were investigated. Three types of such composite sandwich cylindrical shells were manufactured using a hot press molding method and the relevant modal characteristics of various sandwich cylindrical shells could be obtained by modal tests. It can be found that modal strain energy approach was effective to estimate the structural damping loss factors and the variation of damping for each vibration modes could be explained suitably through the contributions of each strain energy components. Results showed that the structural damping loss factors not only depended on inherent material damping, but also relied on the vibration modes. The natural frequencies of composite sandwich cylindrical shell increased with the increasing of the ply angle of the inner and outer curve face sheets, whereas the damping loss factors of present shells did not increase monotonically.

Core material effect on wave number and vibrational damping characteristics in carbon fiber sandwich composites

A sandwich composite is typically designed to possess high bending stiffness and low density and consists of two thin and stiff skin sheets and a lightweight core. Due to the high stiffness-to-weight and strength-to-weight ratios, sandwich composite materials are widely used in various structural applications including aircraft, spacecraft, automotive, wind-turbine blades and so on. However, sandwich composite structures used in such applications often suffer from poor acoustic performance. Ironically, these superior mechanical properties make the sandwich composites “excellent” noise radiators. There is a growing interest in optimizing and developing a new sandwich composite which will meet the high stiffness-to-weight ratio and offer improved acoustic performance. The focus of this study is to investigate the structural–vibrational performance of carbon-fiber face sheet sandwich composite beams with varying core materials and properties. Core materials utilized in this study included Nomex and Kevlar Honeycomb cores, and Rohacell foam cores with different densities and shear moduli. The structural–vibrational performance including acoustic and vibrational damping properties was experimentally characterized by analyzing the wave number response, and structural damping loss factor ( η ) from the frequency response functions, respectively. It was observed that the relationship between the slopes of the wave number data for frequencies above 1000 Hz is inversely proportional to the core material’s specific modulus ( G / ρ ). The analysis also showed the importance of using a honeycomb core’s effective properties for equal comparison to foam-cored sandwich structures. Utilizing analytical modeling, the loss factors of the core materials ( β ) was determined based upon the measured structural loss factors ( η ) for a frequency range up to 4000 Hz. It was determined that low shear modulus cores have similar material damping values to structural damping values. However as the core’s shear modulus increases, the percent difference between these values is found to increase linearly. It was also observed that high structural damping values correlated to low wave number amplitudes, which correspond to reductions in the level of noise radiation from the structure.

Effect of core thickness on wave number and damping properties in sandwich composites

Due to their higher strength-to-weight and stiffness-to-weight ratios compared to metals, fiber reinforced composite materials are a great alternative for use in many structural applications. However these properties lead to poor acoustic performance as composite materials are excellent noise radiators. This is particularly true for sandwich composite structures. Therefore the focus of this study is to investigate the effect of a core thickness change on the vibrational properties of Rohacell foam/carbon-fiber face sheet sandwich composite beams. Four different foam core thicknesses were explored, using a combination of experimental and analytical methods to characterize sound and vibrational properties of the sandwich beams. First, the wave number responses of the beams were obtained, from which coincidence frequencies were identified. Second, from the frequency response functions the structural damping loss factor, η, was determined using the half-power bandwidth method. Experimental and analytical results show that the relationship between core thickness and coincidence frequency is non-linear. A drastic increase in coincidence frequency was observed for the sandwich beam with the thinnest core thickness due to the low bending stiffness. Moreover this low bending stiffness results in low damping values, and consequently high wave number amplitude responses at low frequency ranges (<1000Hz).

Acoustic Radiated Calculation of a Finite Cylindrical Shell and Interface Design of the Programs

Based upon the vibratory equation and sound radiation impedance of a cylindrical shell, the sound field distribution of a finite cylindrical shell simply-supported at two infinite rigid cylindrical shells were resolved with considering the structural loss. An interface containing some buttons connected with all the programs was designed by using Matlab, and their data were all stored in a file. It has been shown that the sound radiation power of the cylindrical shell decreases and the radiation efficiency increases with increasing of structural damping loss factors; when the frequency of the driving force is low, the sound field shapes “∞” directivity pattern; When the frequency of the driving force grows higher the sound directivity pattern becomes complex due to superposition of axial modes and circumferential modes; Only when the radiation of the end plates is much weaker than the cylindrical shell the analytical results of the shell simply-supported at two infinite rigid cylindrical shells can be utilized to illustrate the sound radiation by a finite cylindrical shell with two end plates.

Upper Bound of Vibration Response of Satellite Panel Under Diffused Acoustic Field Excitation

Severe random vibration is easily induced to satellite structure during the flight. Acoustic test at ground is applied to verify the structural design and abnormal function of equipment. An accurate prediction of acoustic induced vibration response of equipment, therefore, is critical for design purposes. Especially for a satellite exterior panel, it has been shown that two subsystem statistical energy analysis model composed of an acoustic chamber and a single panel will simplify the analyses approach and gives a satisfactory result. This paper derives two subsystem SEA model for the prediction of the exterior satellite panel and formulates the damping loss factor equation based on the experiment data. Moreover, the upper bound value of the two subsystem SEA model is presented for further simplification with which response is obtained without structural damping loss factor and radiation coupling loss factor. These two models were validated well by acoustic tests of eleven satellite honeycomb panels.

The radiation efficiency of baffled plates and strips

The average radiation efficiency of point-excited rectangular plates, including those with a very large aspect ratio (‘strips’), is investigated by using a modal summation method based on the farfield sound intensity. By taking an average over all possible forcing positions on the plate, the cross-modal contributions average out to zero. The numerical results from the modal summation are compared with established formulae for rectangular plates. For wavenumbers where acoustic circulation takes place, it is shown that the previously published formulae are not applicable for predicting the average radiation efficiency for a strip. The analysis for the strip reveals that the radiation efficiency at frequencies below the first structural natural frequency of the strip is proportional to the square of the shortest edge length. At frequencies between the fundamental natural frequency and that of the second order mode of bending across the strip, the average radiation efficiency is found to be proportional to the structural damping loss factor, but differs from the results obtained from the usual model of the nearfield radiation from the forcing point of a rectangular plate. Approximate expressions for calculating the average radiation efficiency of the strip are derived. The maximum radiation efficiency around the critical frequency is found to vary less with Helmholtz number k c a, where k c is the wavenumber at the critical frequency and a is the width, than previously published models suggest.

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.