Dynamic Behavior Of Viscoelastic Materials Research Articles

Properties Tests and Mathematical Modeling of Viscoelastic Damper at Low Temperature With Fractional Order Derivative

In the present paper, several dynamic properties tests of the viscoelastic damper at -5oC are conducted under different frequencies and displacements to investigate the dynamic behavior of the viscoelastic damper at low temperature. The seven-parameter fractional derivative model is modified with the temperature-frequency equivalent principle and utilized to describe the dynamic properties of the viscoelastic damper. The 9050A and ZN22 viscoelastic materials are used to verify the modified seven-parameter fractional derivative model. The experimental and numerical results reveal that the viscoelastic damper has perfect energy dissipation capacity at low temperature, and the modified seven-parameter fractional derivative model can well capture the dynamic behavior of viscoelastic materials and dampers.

A numerical and experimental study on optimal design of multi-DOF viscoelastic supports for passive vibration control in rotating machinery

Viscoelastic materials have played an important role in passive vibration control. Nevertheless, the use of such materials in supports of rotating machines, aiming at controlling vibration, is more recent, mainly when these supports present additional complexities like multiple degrees of freedom and require accurate models to predict the dynamic behavior of viscoelastic materials working in a broad band of frequencies and temperatures. Previously, the authors propose a methodology for an optimal design of viscoelastic supports (VES) for vibration suppression in rotordynamics, which improves the dynamic prediction accuracy, the speed calculation, and the modeling of VES as complex structures. However, a comprehensive numerical study of the dynamics of rotor-VES systems, regarding the types and combinations of translational and rotational degrees of freedom (DOFs), accompanied by the corresponding experimental validation, is still lacking. This paper presents such a study considering different types and combinations of DOFs in addition to the simulation of their number of additional masses/inertias, as well as the kind and association of the applied viscoelastic materials (VEMs). The results - regarding unbalance frequency response, transmissibility and displacement due to static loads - lead to: 1) considering VES as complex structures which allow improving the efficacy in passive vibration control; 2) acknowledging the best configuration concerning DOFs and VEM choice and association for a practical application concerning passive vibration control and load resistance. The specific outcomes of the conducted experimental validation attest the accuracy of the proposed methodology.

Modelling of dynamic behaviour of viscoelastic materials in the frequency domain

The modern methods of acoustical and vibration calculus require accurate material models to take properly into account the damping and dynamic elastic properties of the viscoelastic materials used for sound and vibration control. The usual modeling methods (spring-dashpot models, fractional calculus) start out of the stress to strain relations defined in the time-domain, which are then transformed into the frequency domain to find the appropriate material functions. In contrast, the damping and elastic properties are known from measurements made in the frequency domain; therefore, it seems to be reasonable to model the material behavior directly in this domain. The aim of this paper is to show that the typical dynamic behavior of solid viscoelastic materials can efficiently be modeled in the frequency domain. This modeling method is based on simple theoretical considerations, the frequency domain experiences and the causality principle. Two fundamental material models are developed in this way, namely one for the damping increasing with frequency, and the other one for the damping peak, which can be either symmetrical or asymmetrical with respect to the logarithmic frequency. The relation of the frequency domain models to the popular fractional derivative models defined in the time-domain is shown and discussed.

Dynamic properties comparisons between experimental measurements and nondeterministic numerical models of viscoelastic sandwich beams

In order to design viscoelastic sandwich structures used as passive damping treatment, many aspects should be considered. In all methods available in the literature to model Viscoelastic Materials (VEM) a crucial step is the determination of the complex modulus, usually obtained by curve fitting experimental results. Considering that dispersions are inherent to experimental tests and also those small variations in the fitted parameters lead to considerable changes on the dynamic behavior of VEMs hence a nondeterministic model seems to be more suitable than the usual deterministic ones. In that way, starting from dynamic properties of a VEM, a nondeterministic numerical model, which takes into account incertitudes in the VEM curve fitting procedure, is proposed. This model was used to evaluate the behavior of sandwich structures, showing the advantages and disadvantages of the presented methodology, comparing damping ratios and natural frequencies results of experimental tests with the ones extracted from the proposed nondeterministic numerical GHM based model, in order to establish a method to support viscoelastic sandwich beams design.

A visco-hyperelastic constitutive description of elastomer behaviour at high strain rates

A visco-hyperelastic constitutive equation in integral form is proposed to describe the large deformation response of incompressible elastomeric materials at high strain rates. It comprises two components: the first corresponds to hyperelasticity based on a strain energy density function expressed in polynomial form to characterize quasi-static nonlinear response, while the second is an integral form of first and incorporates a relaxation-time function to capture rate sensitivity and strain history dependence. Instead of a constant relaxation-time, a deformation-dependent function is proposed for the relaxation-time. The model is applied to describe the response of SHA60 rubber and Nylon-6. Material samples are subjected to quasi-static and dynamic loading using a universal testing machine and a Split Hopkinson Bar device respectively. Comparison of the proposed equation with experimental results shows a good degree of agreement and demonstrates its potential to describe the dynamic behavior of viscoelastic materials over a range of strain rates.

Calculation for the Acoustic Absorption Coefficient of Multilayered Materials by an Improved Extended Transfer Matrix Method

This paper describes an improved extended transfer matrix method to evaluate the acoustic absorption coefficient of multi-layered structure with viscoelactic materials for perpendicular incidence plane acoustic. Here, the dynamic behavior of viscoelastic materials is taken into account. By comparing the calculated and measured results, it is shown that the results calculated by the improved extended transfer matrix method are in good agreement with the results measured. This improved extended transfer matrix method can accurately estimate the sound properties of multilayered structures with viscoelastic materials.

The Biot Model and Its Application in Viscoelastic Composite Structures

Application of viscoelastic materials in vibration and noise attenuation of complicated machines and structures is becoming more and more popular. As a result, analytical and numerical techniques for viscoelastic composite structures have received a great deal of attention among researchers in recent years. Development of a mathematical model that can accurately describe the dynamic behavior of viscoelastic materials is an important topic of the research. This paper investigates the procedure of applying the Biot model to describe the dynamic behavior of viscoelastic materials. As a minioscillator model, the Biot model not only possesses the capability of its counterpart, the GHM (Golla-Hughes-McTavish) model, but also has a simpler form. Furthermore, by removing zero eigenvalues, the Biot model can provide a smaller-scale mathematical model than the GHM model. This procedure of dimension reduction is studied in detail here. An optimization method for determining the parameters of the Biot model is also investigated. With numerical examples, these merits, the computational efficiency, and the accuracy of the Biot model are illustrated and proved.

Theoretical and experimental analysis of longitudinal wave propagation in cylindrical viscoelastic rods

Wave propagation in viscoelastic rods is encountered in many applications including studies of impact and fracture under high strain rates and characterization of the dynamic behavior of viscoelastic materials. For viscoelastic materials, both material and geometric dispersion are possible when the diameter of the rod is of the same order as the wavelength. In this work, we simplify the Pochhammer frequency equation for low and intermediate loss viscoelastic materials and formulate corrections for geometric dispersion for both the phase velocity and attenuation. The formulation is then experimentally verified with measurements of the phase velocity and attenuation in commercial polymethylmethacrylate rods that are 12 and 6.4 mm in diameter. Without correcting for geometric dispersion, the usable frequency range for determining the phase velocity and attenuation for the 12 mm rod is about 20 kHz , and about 35 kHz for the 6.4 mm rod. Using the correction procedure developed here, it was possible to accurately determine the phase velocity and attenuation up to frequencies exceeding 55 kHz for the 12 mm rod and 65 kHz for the 6.4 mm rod. These corrections are applicable to many polymers and other viscoelastic materials. From thereon, the viscoelastic properties of the material can be determined over a wide range of frequencies.

Study on Dynamic Response Analysis of Artificial Knee Joint Considering Viscoelastic Property.

In the case of severely destroyed knee joint, total knee arthroplasty is applied to the knee joint as surgical treatment. The loosening problem on the contact surface between the artificial knee joint and bone, and impact property of the artificial knee joint have been investigated based on the elastic properties of the bone. We have to take into the consideration of the viscoelastic properties of the bone. In this paper, axisymmetric finite element method is developed for analyzing dynamic behavior of viscoelastic materials. The impact stress wave propagation behavior in the artificial knee joint, which is caused by strike on the distal end of tibia, is investigated using our finite element method. From the results of simulation, the impact stress acting in tibia considering viscoelasticity is about 30%∼80% of elasticity case. Maximum stress decreases toward the proximal direction. On the contact surface between the artificial knee joint and bone, maximum stress increases by double due to reflection of wave.

Finite Element Analysis of Dynamic Behavior of Viscoelastic Materials Using FFT

A new kind of finite element method is presented for analyzing dynamic behavior of viscoelastic materials. In this method, the finite element formulation can be accomplished in a simple form based on the correspondence principle between elasticity and viscoelasticity. Namely, the finite element equations for a viscoelastic problem are found by applying the Laplace transform to those for the corresponding elastic problem and then replacing elastic constants by viscoelastic functions. Laplace transforms of the nodal displacements can be obtained by solving the matrix equation represented in the Laplace domain (complex s domain). Laplace inverse transformation is subsequently performed with the FFT (fast Fourier transform) algorithm to obtain solutions in the time domain. The present method is successfully applied to analyze some typical problems, and the numerical results show the adequacy of the method.

Finite element modeling of frequency dependent and temperature-dependent dynamic behavior of viscoelastic materials in simple shear

Material dynamic mechanical behavior can depend strongly on frequency and temperature This dependence is especially significant for elastomers and polymers, such as those used in bearings and damping treatments. Previous research has yielded a time-domain model of linear viscoelastic material and structural behavior that captures characteristic frequency-dependent behavior; continuing research has addressed the accommodation of temperature dependence as well. The resulting approach is based on the notion of time-temperature superposition for thermorheologically-simple materials. In such materials, temperature effects are experienced primarily through a temperature-dependent factor multiplying the time scale. The phenomenon of “thermal runaway”, observed in some tests of helicopter elastomeric dampers, motivates a numerical example of forced vibration of a 40 x 16 x 5 mm elastomeric test specimen in simple shear. For forcing at 1500 N and 4 Hz, and the temperature on one face held constant, the temperature at the thermally free face increases by about 3 K. For forcing at 3000 N, the temperature rapidly increases more than 35 K, and displacement amplitudes increase by more than a factor of 4. The coupled-field finite element simulation evidently captures the key features of observed material response, including a rapidly increasing rate of temperature change and an accompanying stiffness reduction.

A new shift factor for the characterization of the dynamic properties of viscoelastic materials

During the course of characterizing the dynamic properties of a variety of viscoelastic materials, over the last 10 yr, the Arrhenius equation was found to be valid for describing the shift factor over the glassy, transition, and rubbery regions of the material. Based on this observation, the work described was initiated to define the activation temperature in terms of the dynamic behavior of viscoelastic materials. It will be shown, both empirically and analytically, that the activation temperature is a unique function of the dynamic behavior of viscoelastic materials, which can be accurately determined once the properties of the material have been measured for any frequency but over a wide temperature range. Two advantages exist for using this unique expression to describe the shift factor instead of the previously used ones. The first is that it eliminates the cumbersome and sometimes questionable ways of curve‐fitting the data. The second, which is more important, is that by using this unique function to reduce the data results in a smooth set of points without discontinuities; otherwise, the measured data are questionable, and their validity should be investigated.

Finite Element Analysis of Dynamic Behavior of Viscoelastic Materials by Use of FFT.

A new type of finite element method is presented for analyzing dynamic behavior of viscoelastic materials. In this method, the finite element formulation can be accomplished in simple form based on the correspondence principle between elasticity and viscoelasticity. Namely, the finite element equations for a viscoelastic problem are found by applying the Laplace transform to those for the corresponding elastic problem and then replacing elastic constants by viscoelastic functions. Laplace transforms of the nodal displacements can be obtained by solving the matrix equation described in the Laplace plane (complex s domain). Laplace inverse transformation is subsequently performed with the FFT (fast Fourier transform) algorithm to obtain solutions in the time domain. The present method is successfully applied to analyze some typical problems, and the numerical results show the adequacy of the method.