Material Loss Factor Research Articles

Nonlinear behavior of piezoceramics and piezocomposites under various ac fields

A study is carried out to compare the nonlinear behavior of piezoceramics and piezocomposites. The complex material parameters including losses were determined by model fittings. An experimental system has been used to investigate the ac electric field dependence of the properties of the transducer materials, including lead zirconate titanate (PZT) and PZT/epoxy 1–3 composite rings. An analysis of the changes in the real parts of the material constants (i.e. stiffness, permittivity, and electromechanical coupling coefficients) and loss factors have been made. Under a high ac field, compared to PZT ceramics, the 1–3 composites were found to have different nonlinear behavior. This characterization is necessary for using the piezocomposite in high power transducer applications.

Experimental study on loss factor for corrugated plates by bandwidth method

The material loss factor for technically orthotropic plates was measured by half-power bandwidth method. Rectangular and trapezoidal corrugated plates of steel were considered. A simple isotropic steel plate was also considered for comparison of the results. The concept of single degree of freedom system was adopted. The tests were undertaken at very low frequency range (0–100) Hz. The plate models were suspended freely with two wires to minimize or prevent excessive extraneous energy dissipation. Out of plane point force, random in nature was applied to the top middle of the plates and the responses were measured from the middle point of the plates by FFT analyzer using miniature small mass accelerometer as sensor. The aim of these tests is to investigate the effects of bending rigidity and mode orders over material loss factor. The values of estimated modal damping loss factors are compared and tabulated for the plates models considered. Natural frequencies of some of the initial modes of the plates are also presented. It is observed that the higher the value of bending rigidity of the plates, the larger the values of loss factor of it. There was a significant increase in value of loss factor in corrugated plates to that of the isotropic plate.

Rotor vibration reduction with polymeric sectors

This work has been undertaken principally with an idea to improving the dynamic performance of rotor–shaft systems, which often suffer from two major problems (a) resonance and (b) loss of stability, resulting in excessive vibration of such systems. Polymeric material in the form of sectors has been considered in this work as bearing supports. Polymeric material has been considered in this work as both stiffness and loss factor of such materials varies with the frequency of excitation. Stiffness and loss factor have been found out for the proposed support system comprising of polymeric sectors. Depending upon the frequency of excitation the system matrix, in this case, changes and dynamic performance of the rotor–shaft system also changes accordingly. Here in this work avoidance of resonance and application of optimum damping in the support have been investigated by finding out the optimum dimension, i.e., the optimum thickness and optimum length of the sectors. It has been theoretically found that use of such sectors reduces the rotor unbalanced response, increases the stability limit speed for simple rotor–shaft systems and thus improves the dynamic characteristics. Parameters of the system have been presented in terms of non-dimensional quantities. Many examples have been presented in support of the conclusion. The life of such supports, particularly in the presence of chemicals and other reagents has not been investigated.

518 減衰を考慮した偏平シェルの振動特性について

An analysis for vibration of cylindrical shallow shells with a constrained viscoelastic layer and metal layers is presented. In this paper, vibration damping properties of three layer type shallow shells with viscoelastic material are analyzed from both of SEM (Strain energy method) and CEM (Complex eigenvalue method). Furthermore, behavior and accuracy of each solution are examined. Eigenvalue and eigenvector (displacement functions) are analyzed based on the Ritz method, when natural frequency, modal loss factor and strain energy are obtained. In method (CEM), the elastic modulus of viscoelastic material is dealt with complex quantity considering material loss factor. The eigenvalue problem that is derived by means of minimizing the energy functional, is solved to determine the natural frequencies and modal loss factors. In method (SEM), modal loss factor is defined as a ratio of damping energy (strain energy consumed in viscoelastic layer) dissipated during a vibration cycle and total strain energy of the shell. The accuracy and validity of the present results from two methods are illustrated through investigation of convergence and comparison with the established results from the literature. From thebehavior of the solution, consideration and interpretation are tried with respect to accuracy and characteristic of each solutionmethod.

A Double Cantilever Sandwich Beam Method for Evaluating Dynamic Characteristics of Rubber Materials

A double cantilever sandwich-beam method is proposed for the evaluation of the frequency dependence of the dynamic elastic modulus and material loss factor of rubber materials. The flexural vibration of a double cantilever sandwich-beam specimen with an inserted rubber layer was studied using a finite element simulation in combination with a sine-sweep test. Effects of the rubber layer length on the dynamic characteristics were also investigated such that reliable values were measured when the length of the inserted rubber layer was larger than or equal to 50% of the effective specimen length. The values were compared with those obtained by dynamic mechanical analysis and a simple resonant test. The relationships of the dynamic characteristics of rubber materials with frequency could be determined using the least squares estimation method.

Summary of energy flow measurements and calculations made on the INCE standard test structures

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.

Analytical Evaluation of Damping in Composite and Sandwich Structures

Two methodologies are outlined for the analytical evaluation of the loss factor in composite laminates and in sandwich structures. One of these methods is based on the analysis of free vibrations, whereas the second approach utilizes mechanics of materials. Both methods yield similar results. The loss factor is predicted both for specially orthotropic as well as for generally orthotropic laminas, subjected to axial stresses and/or transverse shear. The results for the loss factor of the laminas are in good agreement with available experimental data. As follows from the numerical analysis, the loss factor of laminas of the facings is significantly affected by the angle of lamination. The loss factor of a sandwich beam is relatively insensitive to the frequency of vibrations, although the effect of this frequency on the loss factors of constituent materials may alter this conclusion.

양팔 샌드위치보 시험법에 의한 EPDM고무의 동특성 평가 연구

A double cantilever sandwich-beam method has been applied to the evaluation of the frequency dependence of dynamic elastic modulus and material loss factor of EPOM rbbbers. The flexural vibration of a double cantilever sandwich-beam specimen with an inserted rubber layer was studied using a finite element simulation in combination with the sine-sweep test. Effects of the rubber layer length on the dynamic characteristics were also investigated: reliable values were measured when the length of the inserted rubber layer was larger than and equal to 50% of the effective specimen length. The values were compared with those obtained by the dynamic mechanical analysis and the simple resonant test. Relationships of the dynamic characteristics of rubbers with frequency could be determined using the least square error method.

An Acoustical Technique for Determining the Loss Factor of Solid Materials

A technique is presented here for evaluating the loss factor of a solid material element. This technique is commonly used in room acoustics to evaluate the reverberation time (RT) of rooms, and is therefore reviewed in this paper for applications in solid materials. The reverberation time is a quantity that describes the rate of decay of the sound level in the room, and is inversely proportional to the amount of sound absorption in the room. The loss factor is a measure of the proportion of vibrational energy that is dissipated during one cycle of vibration. Hence, interest is focused in this study on the damping characteristics of the material in terms of the loss factor, which is inversely proportional to RT. The reverberation time may be assessed relatively easily and rapidly from the impulse response of the test specimen as measured with the help of a smart technique. The example of a wood beam-like specimen with artificial defects in the form of voids is presented.

LOSS FACTOR PEAK OF VISCOELASTIC MATERIALS: MAGNITUDE TO WIDTH RELATIONS

The loss factor of viscoelastic materials as a function of frequency has at least one peak. The relation between the magnitude and width of the loss factor peak is investigated in this paper by means of the fractional derivative Zener model with special reference to polymeric materials used for sound and vibration damping. It is shown that the magnitude and width are interrelated through the dispersion of dynamic modulus and the rate of frequency variation of loss factor. Moreover, it is proved that the relation between the magnitude and width of the loss factor peak is not unequivocal; either proportionality or inverse proportionality may exist between them. The important consequence of prediction on the proportionality is that, in contrast to the common belief concerning polymers, it is physically possible to increase the loss factor while simultaneously broadening the peak. The validity of model predictions is discussed and it is proved that the predictions are of a general nature, because they obey fundamental physical principles. Experimental data supporting the theoretical predictions are presented.

典型的な多層多スパンモデルにおける固体音伝搬性状の実験結果と波動的逐次計算予測値との比較検討 : 建築躯体における固体音伝搬性状の研究 第6報

In this report : part-6, Calculations and experiments on structure-borne sound propagation in multi-storied plate construction model are compared. And they are shown that calculated values are fairly coincided with measured values, by introducing some corrections for lower frequency range. This calculating method is able to predict(estimate) frequency characteristics at important frequency range. But at the higher frequency range, measured values tend to show lower values than calculated. Additionally calculation programs are applied to study of the relation between the loss factor of material and the additional structure caused mechanical damping. The relation between experimental frequency response and material loss factor are explained as structural damping by calculated values.

Space Environment Effects on Damping of Polymer Matrix Carbon Fiber Composites

Theeffectsof thelow-Earth-orbitenvironmentonthemechanical propertiesof somecarbon-reinforcedpolymer matrix composites are reported. Material damping loss factors and glass transition temperatures of control and e ightspecimensweremeasured. Flight specimenswereattached totheleading edgeoftheLongDurationExposure Facility, and control specimens were maintained at the NASA Marshall Space Flight Center. Changes in the glass transition temperatures and damping were due to combined exposure to 1 )atomic oxygen, 2 )UV radiation, and 3 ) thermal cycling. High atomic oxygen exposure during the e nal year of the Long Duration Exposure Facility e ight, however, eroded away much of the material that would have been affected by UV radiation. The glass transition temperatures of the e ight samples were slightly greater than those of the controls, whereas the material loss factors were nearly the same. From a practical point of view, these changes were not very signie cant. However, the relaxation data presented herein may beuseful forunderstandingthedetailsoftheeffectsofthespaceenvironment on composite materials and may aid researchers in developing composites that maintain their properties for extended periods in the harsh environment of low Earth orbit.

Investigation of mechanical loss factors of some candidate materials for the test masses of gravitational wave detectors

This Letter describes the results of investigations into the mechanical losses of a selection of crystalline materials with the potential for use as the test masses in advanced gravitational wave detectors. We have measured loss factors of 3.7×10 −9 for HEM sapphire, to our knowledge the lowest measured loss factors of sapphire grown by a method suitable to produce test masses of the size and quality needed for use in advanced interferometric detectors. We also present the first measurements of the mechanical loss factors of YAG and Spinel at frequencies of interest for gravitational wave detection.

Reduced-Order Models of Structures with Viscoelastic Components

A useful method of modeling viscoelastic effects in structures for transient response analysis is to treat the frequency dependence of the usual damping model through the introduction of extra dissipation coordinates or internal variables. These new coordinates require a curve e t to the material loss factor data over a range of frequencies. Such a method has the disadvantage of introducing a large number of extra degrees of freedom that make response calculations and controller design very computationally intensive. Methods are examined to reduce the model size and, hence, ease this burden. Eigensystem truncation and balanced realizations are used to successfully reduce the full model. It is demonstrated that methods where the reduction transformation is based on the undamped model produce poor results. An iterative method to calculate the full eigensystem is introduced, using the frequency-dependent material modulus. In an alternative scheme, the model based on the physical degrees of freedom is reduced before the extra dissipation coordinates for the Golla ‐Hughes‐McTavish method are introduced. Also considered is the possibility of reducing the model at the element level, before assembly, although this approach has dife culty retaining the damping characteristics of the full model.

A NON-DIMENSIONAL PARAMETRIC STUDY OF ENHANCED ACTIVE CONSTRAINED LAYER DAMPING TREATMENTS

The purpose of this research is to extend the previous work of Liao and Wang [1, 2] (Journal of Smart Materials and Structures5, 638–648;Journal of Vibration and Acoustics120, 894–900) on the Enhanced Active Constrained Layer (EACL) damping treatments and provide more comprehensive results that can be better generalized. For given strain distributions in the host structure and utilizing a self-sensing control law, closed form solutions to the longitudinal motion of the active cover sheet of the EACL are derived. Active, passive, and hybrid (total) loss factors are defined to discuss the damping properties of the treatments. With a non-dimensionalized formulation, this research identifies and examines the major factors that effect the EACL damping characteristics. These factors are: the bending stiffness ratio between the host structure and the constraining layer, the offset distance of the constraining layer from the host structure, the strain distribution in the host structure, the active control gain, the characteristic length of the EACL, the Viscoelastic Material (VEM) loss factor, and the stiffness distribution of the edge elements. The effects of these factors on open-loop and closed loop damping characteristics of the treatment are discussed. This investigation provides insights and design guideline to generic one-dimensional EACL surface damping treatments.

A Rolling Resistance Simulation of Tires Using Static Finite Element Analysis

Abstract A practical rolling resistance simulation method for tires using a static finite element method is presented that fulfills three requirements: (1) easy input data preparation, (2) shorter computation time, and (3) adequate accuracy. The method implements a static deflection analysis first and the stress and strain thus obtained, together with the loss factors of the materials determined separately, are used to estimate the energy dissipation of a rolling tire. First, the stress and strain profiles of all element groups that have the same cross-sectional coordinates and are located along the circumferential direction are obtained. Second, hysteresis loops are computed by introducing a viscoelastic phase lag between the stress and strain profiles. The sum of the areas of the hysteresis loops is regarded as the dissipation energy density of the element group. The loss factors of the rubber materials are experimentally obtained and the effective loss tangents of the fiber-reinforced rubber are determined by the homogenization theory of dynamic viscoelasticity. The rolling resistance simulation of a passenger radial tire using this approach accurately captures the trends of an actual tire.

An algorithm for calculation of material loss factors using single degree of freedom method and digital data measured by FFT analyzer

The half-power band-width method that is conventionally used to calculate material loss factors cooperated with one single degree of freedom method using data of each resonance response of a material bring out estimation errors caused by approximation of resonance frequency due to discrete frequency when data are measured with FFT analyzer. The proposed new algorithm is able to determine the actual resonance frequency, and its amplitude directly from digital data and loss factors without approximation.

VIBRATION ANALYSIS OF BEAMS WITH MULTIPLE CONSTRAINED LAYER DAMPING PATCHES

A new analytical, energy based approach is described that predicts the harmonic vibration response of a damped beam with multiple viscoelastic patches. Each damping patch consists of a metallic constraining layer and an adhesive viscoelastic layer with spectrally-varying material properties. Since this approach relates all deformation variables in various layers, only flexural shape functions need to be incorporated in the complex eigenvalue problem. Consequently flexural, longitudinal and shear deformation eigenvectors can be calculated. In particular, the shear deformation modes of the viscoelastic core provide useful information regarding the effect of patch damping. The proposed method has been validated by comparing predictions with modal measurements and with those published in the literature. Also, an estimation technique is developed that determines the shear modulus and loss factor properties of two different viscoelastic materials used in experimental studies. An uncertainty study is also performed to establish the error bounds of the estimated material loss factors. Effects of patch boundary conditions, patch cutouts and locations, and mismatched patch combinations are analytically and experimentally examined.

An experimental-numerical technique for evaluating the bulk and shear dynamic moduli of viscoelastic materials

An experimental/numerical technique has been implemented to determine simultaneously the bulk and shear dynamic moduli (and loss factor) of viscoelastic materials of arbitrary shape under low-frequency (0.5–2.5 kHz) harmonic excitation. The method consists of measuring the dynamic response of the sample at several points on the surface with a set of five independent laser interferometers, and matching the response with the predictions from a finite element code in which the two complex elastic moduli are the adjustable parameters. Results are presented for measurements made in air, under standard pressure and temperature conditions, and compared with predictions based on Kerner’s model.

A vibration method for measuring mechanical properties of composite, theory and experiment

This paper presents a method for identifying elastic and damping properties of composite laminates by using vibration test data. The analysis model is established based on a finite element model which considers the effect of transverse shear deformation and hysteretic damping. The reduced elastic constants and material loss factors are selected as the updated parameters. Since the damping mainly causes a change of the imaginary part in eigenvalues and eigenvectors, the complex modal parameters are measured. The selected parameters are identified by minimizing an error function containing the deviations of eigenvalues and responses between experiment and analysis. The numerical study shows that satisfactory results including transverse shear moduli can be obtained by designing a suitable plate specimen. Experimental results demonstrate the efficiency of the proposed method. In principle, the present method allows all elastic constants and damping factors to be determined simultaneously.