Dynamic characterization of high damping viscoelastic materials from vibration test data

The numerical analysis and design of structural systems involving viscoelastic damping materials require knowledge of material properties and proper mathematical models. A new inverse method for the dynamic characterization of high damping and strong frequency-dependent viscoelastic materials from vibration test data measured by forced vibration tests with resonance is presented. Classical material parameter extraction methods are reviewed; their accuracy for characterizing high damping materials is discussed; and the bases of the new analysis method are detailed. The proposed inverse method minimizes the residue between the experimental and theoretical dynamic response at certain discrete frequencies selected by the user in order to identify the parameters of the material constitutive model. Thus, the material properties are identified in the whole bandwidth under study and not just at resonances. Moreover, the use of control frequencies makes the method insensitive to experimental noise and the efficiency is notably enhanced. Therefore, the number of tests required is drastically reduced and the overall process is carried out faster and more accurately. The effectiveness of the proposed method is demonstrated with the characterization of a CLD (constrained layer damping) cantilever beam. First, the elastic properties of the constraining layers are identified from the dynamic response of a metallic cantilever beam. Then, the viscoelastic properties of the core, represented by a four-parameter fractional derivative model, are identified from the dynamic response of a CLD cantilever beam.     

Experimental investigation of the adhesive contact of an elastomer

The present work is an experimental study of adhesion between an elastomer and a rigid cylindrical indented The experimental characterization was carried out using a specially developed apparatus. Adhesive force was measured as function of contact geometry, pull-off velocity, normal force, temperature, waiting time, and material properties. Experimental results are compared with existing theoretical models for adhesion of elastic and viscoelastic bodies. Our study shows that the adhesive force between the studied elastomer and a steel cylinder is determined by completely different mechanisms than assumed in the Kendall’s theory. In particular, it does not depend on the surface energy and is almost entirely dominated by the viscosity of the elastomer.     

Rayleigh-Lamb wave propagation on a fractional order viscoelastic plate

A previous study of the authors published in this journal focused on mechanical wave motion in a viscoelastic material representative of biological tissue [Meral et al., J. Acoust. Soc. Am. 126, 3278-3285 (2009)]. Compression, shear and surface wave motion in and on a viscoelastic halfspace excited by surface and sub-surface sources were considered. It was shown that a fractional order Voigt model, where the rate-dependent damping component that is dependent on the first derivative of time is replaced with a component that is dependent on a fractional derivative of time, resulted in closer agreement with experiment as compared with conventional (integer order) models, such as those of Voigt and Zener. In the present study, this analysis is extended to another configuration and wave type: out-of-plane response of a viscoelastic plate to harmonic anti-symmetric Lamb wave excitation. Theoretical solutions are compared with experimental measurements for a polymeric tissue mimicking phantom material. As in the previous configurations the fractional order modeling assumption improves the match between theory and experiment over a wider frequency range. Experimental complexities in the present study and the reliability of the different approaches for quantifying the shear viscoelastic properties of the material are discussed.     

Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium

The effect of longitudinal magnetic field on vibration response of a sing-walled carbon nanotube (SWCNT) embedded in viscoelastic medium is investigated. Based on nonlocal Euler-Bernoulli beam theory, Maxwell’s relations, and Kelvin viscoelastic foundation model, the governing equations of motion for vibration analysis are established. The complex natural frequencies and corresponding mode shapes in closed form for the embedded SWCNT with arbitrary boundary conditions are obtained using transfer function method (TFM). The new analytical expressions for the complex natural frequencies are also derived for certain typical boundary conditions and Kelvin-Voigt model. Numerical results from the model are presented to show the effects of nonlocal parameter, viscoelastic parameter, boundary conditions, aspect ratio, and strength of the magnetic field on vibration characteristics for the embedded SWCNT in longitudinal magnetic field. The results demonstrate the efficiency of the proposed methods for vibration analysis of embedded SWCNTs under magnetic field.     

A dynamic visco-hyperelastic model of dielectric elastomers and their energy dissipation characteristics

In this paper, we present a model describing the nonlinear dynamic visco-hyperelastic behaviors of dielectric elastomers (DE), with the purpose to explain the material’s dynamic energy dissipation mechanism, and provide convenience for actual design of DE devices. On the basic mechanical properties of the material, a visco-hyperelastic constitutive relationship, derived from Kelvin–Voigt rheological model and expressed as complex modulus, is created at first. Then, from the approximate relationship between harmonic motion frequency and the stretch rate (as well as the amplitude of stretch ratio) of the film, a new model-fitting approach is put forward to obtain the three intrinsic parameters, based on the uniaxial tensile tests for VHB 4910 DE film at different stretch rates (from 0.029 to 0.71 s^?1). Applying the proposed parameters, the hysteresis and energy dissipation behaviors of the DE film are subsequently predicted, showing good agreement with the experimental results. Finally, the influences of the kinematic variable pair on energy dissipation properties are quantitatively investigated.     

Forced response of FRP sandwich panels with viscoelastic materials

In this paper a new analytical model is presented that accurately predicts the forced response of fibre reinforced plastic (FRP) sandwich plates subjected to transverse applied loads. It is based on Reddy's refined high order shear deformation theory and offers the feasibility of accounting for the viscoelastic properties of the constitutive materials without restriction to the steady state motion. This is achieved by modelling the viscoelastic behaviour of the constitutive materials using the Golla Hughes McTavish mathematical tool. Validation of the new approach is achieved by comparing results under harmonic loading conditions against data obtained using the proposed new analytical model. Subsequently, predicted responses for a given FRP sandwich plate under various transverse applied loads are presented. The results outline the importance of being able to account for the viscoelastic properties of the constitutive materials when modelling the dynamic behaviour of sandwich structures.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss (gain) behavior when the elasticity parameter of the medium is larger (smaller) than the critical value for Kelvin (Maxwell) viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss （gain） behavior when the elasticity parameter of the medium is larger （smaller） than the critical value for Kelvin （Maxwell） viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM

The objective of this study is to investigate the influence of the rotary inertia on dynamic behavior of linear viscoelastic cylindrical and conical helixes by means of the Laplace transform-mixed finite element formulation and solution. The element matrix is based on the Timoshenko beam theory. The influence of rotary inertias is considered in the dynamic analysis, which is original in the literature. Rectangular, sine and step type of impulsive loads are applied on helices having rectangular cross-sections with various aspect ratios. The Kelvin and standard models are used for defining the linear viscoelastic material behavior; and by means of the correspondence principle (the elastic-viscoelastic analogy), the material parameters are replaced with their complex counterparts in the Laplace domain. The analysis is carried out in the Laplace domain and the results are transformed back to time space numerically by modified Durbin?s algorithm. First, the solution algorithm is verified using the existing open sources in the literature and afterwards some benchmark examples such as conical viscoelastic rods are handled.     

Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids

Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.     

Fractal description of significant nano-effects in polymer composites with nanosized fillers. Aggregation,phase interaction,and reinforcement

The paper analyzes experimental data obtained on physical and mechanical properties of nanostructured particle-reinforced composites with elastomer matrices and nano- and microsized carbon-containing particles by scanning probe microscopy and nanoindentation with specialized 3D computer processing. The nano-effects observed in the elastomer matrices are described using the fractal approach. A fractal model of nanoparticle aggregation in a polymer matrix is proposed. Phase interactions in the nanostructured polymer materials are described and fractal relations that predict the reinforcing effect of this type of media are presented. It is shown that interphase regions in the nanostructured composites are the same reinforcing elements as a nanofiller for the medium. It is found that reinforcement of elastomer composites by nanosized particles is a true nano-effect.     

Effect of sample tilt on nanoindentation behaviour of materials

Analysis of nanoindentation is based on the elastic solution of a rigid indenter perpendicularly penetrating a flat contact surface. In reality, nanoindentation is often performed on a tilt sample surface due to sample tilt mounting or the existing roughness of a polished or raw surface. In this study, finite element simulations as well as nanoindentation experiments on a fused-quartz sample with different tilt angles were carried out to investigate the influence of sample tilt on nanoindentation behaviour of materials. It was found that sample tilt results in increases in the indentation load, contact area and contact stiffness at the same penetration depth. The contact area increase caused by sample tilt cannot be accounted for by Sneddon's equation, commonly used in nanoindentation analysis. This results in a significant underestimation of indentation projected contact area, which in turn leads to an overestimation of the mechanical properties measured by nanoindentation.     

Nanoindentation study of the time-dependent mechanical behavior of materials

The methodological aspects of studying the time-dependent mechanical properties of materials subjected to nanoindentation under pulsed loading and unloading of a Berkovich indenter are considered. It is shown that the viscosities and relaxation times of viscoelastic materials can be determined from nanoindentation experiments. The advantages of the pulsed nanoindentation technique are demonstrated with the photoplastic effect in chalcogenide glasses.     

An experimentally-based viscoelastic constitutive model for polyurea,including pressure and temperature effects

Presented here are the results of a systematic study of the viscoelastic properties of polyurea over broad ranges of strain rates and temperatures, including the high-pressure effects on the material response. Based on a set of experiments and a master curve developed by Knauss (W.G. Knauss, Viscoelastic Material Characterization relative to Constitutive and Failure Response of an Elastomer, Interim Report to the Office of Naval Research (GALCIT, Pasadena, CA, 2003.) for time–temperature equivalence, we have produced a model for the large deformation viscoelastic response of this elastomer. Higher strain-rate data are obtained using Hopkinson bar experiments. The data suggest that the response of this class of polymers is strongly pressure dependent. We show that the inclusion of linear pressure sensitivity successfully reproduces the results of the Hopkinson bar experiments. In addition, we also present an equivalent but approximate model that involves only a finite number of internal state variables and is specifically tailored for implementation into explicit finite-element codes. The model incorporates the classical Williams–Landel–Ferry (WLF) time–temperature transformation and pressure sensitivity (M.L. Williams, R.F. Landel, and J.D. Ferry, J. Am. Chem. Soc., 77 3701 (1955)), in addition to a thermodynamically sound dissipation mechanism. Finally, we show that using this model for the shear behaviour of polyurea along with the elastic bulk response, one can successfully reproduce the very high strain rate pressure–shear experimental results recently reported by Jiao et al. (T. Jiao, R.J. Clifton and S.E. Grunschel, Shock Compression of Condensed Matter 2005 (American Institute of Physics, New York, 2005.).     

Dynamic viscoelastic effects on sound wave scattering by an eccentric compound circular cylinder

The classical method of separation of variables in conjunction with the translational addition theorem for cylindrical wave functions are employed to obtain an exact solution for two-dimensional interaction of a harmonic plane acoustic wave with an infinitely long (visco)elastic circular cylinder which is eccentrically coated by another (visco)elastic material and is submerged in an ideal unbounded acoustic medium. The novel features of Havriliak-Negami model for dynamic viscoelastic material behaviour are used to take the rheological properties of the coating (and/or core) material into consideration. The analytical results are illustrated with numerical examples in which a steel rod eccentrically coated with (an eccentric steel shell filled with) dissipative materials of distinct viscoelastic properties is insonified by plane sound waves at selected angles of incidence. The effects of incident wave frequency, angle of incidence, core eccentricity and dynamic viscoelastic material properties on the backscattered form function spectra are examined. Limiting cases are considered and fair agreements with available solutions are obtained.     

冲击载荷下土的动态力学性能研究

 利用分离式霍普金森压杆（Split Hopkinson Pressure Bar,SHPB）技术,研究了土体在不同应变率条件下的冲击动态力学性能,发现土体有明显的应变率效应,与静载相比,冲击载荷下土的动强度和动模量均有很大的提高。根据实验曲线的特征,以一根线性弹簧和两个不同松弛时间的Maxwell体并联的粘弹性模型来表达土体的损伤型粘弹性本构模型,两个Maxwell体分别表示土体的低应变率响应和高应变率响应,模型的数值拟合曲线与实测动态本构曲线具有较好的一致性。拟合参数表明,土体对低应变率的响应与混凝土相同,对高应变率的敏感性远远高于混凝土。     

Analysis of Laser-generated Rayleigh wave on viscoelastic materials

In order to understand the viscoelasticity of material, this research has been conducted to study the propagation characteristics of viscoelastic Rayleigh wave theoretically. A model is presented for the pulsed laser generation of ultrasound on viscoelastic medium surface. Referred to the Kelvin model, the frequency equation and the normal displacement of viscoelastic Rayleigh wave were derived, the influence of the viscoelastic modulus on dispersion and attenuation was discussed. From the theoretical calculation, it is shown that the effect of viscoelasticity on the attenuation of Rayleigh wave is more than that on its dispersion. In the case of a weak viscosity, the attenuation of viscoelastic Rayleigh wave is directly proportional to viscosity modulus; the effect of shear viscosity on the attenuation is much more than that of bulk viscosity. The transient response of viscoelastic Rayleigh wave was also simulated using Laplace and Hankel inversion transform, which are showed in good agreement with the theoretic predictions. The model provides a useful tool for the determination of viscoelastic parameters of medium.     

Viscoelastic Models for Passive Arterial Wall Dynamics

This paper compares two models predicting elastic and viscoelastic properties of large arteries. Models compared include a Kelvin (standard linear) model and an extended 2-term exponential linear viscoelastic model. Models were validated against in-vitro data from the ovine thoracic descending aorta and the carotid artery. Measurements of blood pressure data were used as an input to predict vessel cross-sectional area. Material properties were predicted by estimating a set of model parameters that minimize the difference between computed and measured values of the cross-sectional area. The model comparison was carried out using generalized analysis of variance type statistical tests. For the thoracic descending aorta, results suggest that the extended 2-term exponential model does not improve the ability to predict the observed cross-sectional area data, while for the carotid artery the extended model does statistically provide an improved fit to the data. This is in agreement with the fact that the aorta displays more complex nonlinear viscoelastic dynamics, while the stiffer carotid artery mainly displays simpler linear viscoelastic dynamics.     

Generalized response of a sphere embedded in a viscoelastic medium excited by an ultrasonic radiation force

The response of an embedded sphere in a viscoelastic medium excited by acoustic radiation force has been studied in both the time- and frequency-domains. This model is important because it can be used to characterize the viscoelastic properties of the medium by fitting the response to the theoretical model. The Kelvin-Voigt model has been used exclusively in these models. An extension to the previously reported models is described so that any viscoelastic rheological model can be used. This theoretical development describes the generalized embedded sphere response both in the time and frequency domains. Comparing the results from derivations in both domains showed very good agreement with a median absolute error (MAE) ranging from 0.0044 to 0.0072. Good agreement is demonstrated with finite element model simulations and the theory with a MAE of 0.006. Lastly, results for characterization of gelatin and rubber materials with the new theory are shown where the MAE values were used to determine which rheological model best describes the measured responses.     

Transverse Vibration of Tapered Single-Walled Carbon Nanotubes Embedded in Viscoelastic Medium

Based on the nonlocal theory, Euler-Bernoulli beam theory and Kelvin viscoelastic foundation model, free transverse vibration is studied for a tapered viscoelastic single-walled carbon nanotube (visco-SWCNT) embedded in a viscoelastic medium. Firstly, the governing equations for vibration analysis are established. And then, we derive the natural frequencies in closed form for SWCNTs with arbitrary boundary conditions by applying transfer function method and perturbation method. Numerical results are also presented to discuss the effects of nonlocal parameter, relaxation time and taper parameter of SWCNTs, and material property parameters of the medium. This study demonstrates that the proposed model is available for vibration analysis of the tapered SWCNTs-viscoelastic medium coupling system.