Dynamic Properties Of Viscoelastic Materials Research Articles

A study of soft and hard impact effects in single-particle impact dampers

Single-particle impact dampers (SPIDs) are simple, yet impactful devices that mitigate vibrations in various applications such as high-rise structures, machinery, and satellites. However, the high-intensity impact forces transmitted to the host structure pose a risk to older and vulnerable structures. Therefore, this study investigates the performance of SPIDs with soft impacts, employing viscoelastic materials to minimize the impact forces and noise levels without degrading the damping performance. Four different materials (rubber, ethylene-vinyl acetate, acrylic and poly-urethane foams) exhibiting different viscoelastic properties are studied and compared with hard impact. An approximate Voigt model for the stiffness and damping coefficient of viscoelastic material is used to conduct numerical simulations and to evaluate the damping performance of SPIDs. Dynamic mechanical analyser (DMA) tests are conducted to determine the dynamic properties of viscoelastic materials. An experimental rig which includes a single-degree-of-freedom host structure, and a prototype SPID is designed and manufactured. Experiments are conducted to determine the damping performance, impact force, and noise level with soft impacts and the results are compared with hard impacts. The results reveal a 40% reduction in vibration amplitude at resonance frequency, an impressive 96% reduction in impact force at resonance, an 11.55 dB reduction in the noise level using poly-urethane foam (softest impact) compared to steel (hard impact). Although viscoelastic materials may not be suitable in harsh environmental conditions, this study demonstrates that introducing a viscoelastic material in SPID can resolve its major drawbacks such as impact forces and noise leading to a simple, cost-effective, and safe SPID.

Dynamic property evaluation of pipeline clamp based on analyzing the propagation characteristics of flexural wave in pipeline

The external clamp of hydraulic pipeline plays an important role in strengthening pipeline stiffness and improving vibration attenuation ability. In this study, wave propagation method is proposed to evaluate the translational and rotational stiffness and their loss factors of the clamp by analyzing the flexural wave propagation characteristics of pipeline. In order to validate the measured dynamic properties, experimental modal analysis was performed on the two-end elastically-supported pipeline. By modelling the pipeline with translational and rotational edge restraints, the analytical modal frequency parameters, wave numbers, and waveform coefficients were obtained. By comparing of the first-order flexural mode frequencies between experiment and analysis, the dynamic stiffness predicted by the wave propagation method was validated. The effects of the magnitude of torque, direction, clamping torque cycle, and clamp size on the complex dynamic properties of pipeline clamp were investigated. The proposed wave propagation method allows non-destructive continuous monitoring of a clamp stiffness, provides additional information about the vibration attenuation feature. It has advantages in clamp applications and is an effective methodology for measuring the dynamic properties of viscoelastic materials.

Review of Progress in Atomic Force Microscopy

The study of biological samples is one of the most attractive and innovative fields of application of atomic force microscopy AFM. Recent breakthroughs in software and hardware have revolutionized this field and this paper reports on recent trends and describes examples of applications on biological samples. Originally developed for high-resolution imaging purposes, the AFM also has unique capabilities as a nano-indentor to probe the dynamic visco-elastic material properties of living cells in culture. In particular, AFM elastography combines imaging and indentation modalities to map the spatial distribution of cell mechanical properties, which in turn reflect the structure and function of the underlying structure. This paper describes the progress and development of atomic force microscopy as applied to animal and plant cell structures.

Characterisation of static and dynamic responses of natural rubber bio-composites

Characterisation of static and dynamic behavioural are presented in this study of hybrid filled natural rubber. The hybrid filler consists of a combination of oil palm ash (OPA) and egg shell powder (ESP). Testing on the samples are conducted in three different aspects namely static compression testing, time dependent stress relaxation testing in compression and dynamic compression testing. Mechanical properties such as the static stiffnesses, hysteresis loss ratios, stress relaxation responses, dynamic stiffnesses, phase angles and damping ratios are reported. The static stiffness values of the hybrid filled rubber, although lower than rubber filled carbon black, presented potential if the ESP content were to be increased. The stress relaxation responses lacked consistency in the uploading stages but were fairly consistent in the unloading stages where the relaxation was close to that of rubber filled carbon black. The dynamic properties appear to be no significant improvement over that of rubber filled carbon black filled. All hybrid filled rubber samples conformed to general dynamic properties of viscoelastic material and did not display any unexpected behaviour. Collectively, there is a trend of improvement with increasing ESP content but no prominent improvement over rubber filled carbon black is observed.

Thermorheologically simple materials: A bayesian framework for model calibration and validation

The dynamic properties of viscoelastic materials show highly frequency-temperature dependency and numerical methods for structural systems containing this type of material require accurate mathematical models to describe their dynamical behaviour. The material behaviour here is modelled using a constitutive equation based on fractional derivative operators and considering the temperature dependence of the material under the thermorheologically simple postulate. The quest for information about the constitutive model parameters is phrased as a statistical inverse problem under the Bayesian framework. A Markov Chain Monte Carlo (MCMC) method is used to explore the posterior density of model parameters using measured data from dynamic tests at different temperatures. The agreement between measured data and the predictive capabilities of sixteen models were quantitatively assessed using two validation metrics. Based on the validation metrics analysis it is possible to conclude that the range of temperature of the calibration data set is a key-point into the implementation of the Frequency Temperature Superposition Principle (FTSP). This was verified defining some scenarios for assessing the agreement of model predictions and the set of available experimental data. The results are quite compelling due to the fact that the proposed approach is easy-handed. Furthermore, this approach could be applied on any generic constitutive model using the FTSP.

온도변화를 고려한 고무엔진마운트의 동특성 변동성 해석

Vehicle vibrations arise from engine and road surface excitations. The engine mount system of a passenger car sustains the engine weight and insulates the excitation force from the engine system. The dynamic properties of viscoelastic material used for the vehicle engine mounts have large variation due to environmental factors such as environmental temperature and humidity etc. The present study aims to investigate the variability of dynamic characteristics in rubber engine mounts considering both environmental temperature change and material model errors/uncertainty. The engine mounts for a passenger car were modeled using finite element method. Then, the dynamic stiffness variability of the engine mounts were estimated using Monte Carlo simulation method. In order to estimate the variations in the storage and loss moduli of the viscoelastic materials, the material properties of the synthetic rubber were expressed as a fractional-derivative model. Next, in order to simulate the uncertainty propagation of the dynamic stiffness for the engine mounts due to the storage and loss moduli variations, the Monte Carlo simulation was used. The Monte Carlo simulation results showed large variation of the engine-mount stiffness along frequency axis.

Optimization Based Identification of the Dynamic Properties of Linearly Viscoelastic Materials Using Vibrating Beam Technique

Sandwich structures with viscoelastic core and metal face sheets are increasingly used in automotive industry to significantly reduce the amplitude of vibration and noise radiation. Several experimental methods such as dynamic mechanical analysis (DMA) and vibrating beam technique (VBT) are used to characterize the dynamic properties of viscoelastic materials as a function of frequency and temperature. This paper investigates the use of a free-free beam setup, as an alternative solution to the classical clamped-free VBT, for a better control of the effect of boundary conditions on the laminated steel specimen. The new setup is developed in combination with a frequency response function based optimization method, to automatically derive the dynamic properties of viscoelastic core materials and generate their master curves. A solver based on the normal mode superposition method, considering the added mass effect of the impedance head, is used in the cost function of the optimization approach. The sandwich model is based on the Ross–Kerwin–Ungar equation, and the four-parameter fractional derivative model is used in conjunction with the Williams–Landel–Ferry equation to describe the frequency and temperature dependent behavior of the viscoelastic material. The master curves are a direct result of the optimization process. Several applications are described to assess the performance of the present method. In particular, a systematic comparison with both the classical VBT and DMA (when available) is presented.

Amplitude dependence of filler-reinforced rubber: Experiments, constitutive modelling and FEM – Implementation

The focus of the present paper is the experimental investigation, the constitutive representation and the numerical simulation of the amplitude dependence of filler-reinforced elastomers. A standard way to investigate the dynamic properties of viscoelastic materials is via the dynamic modulus which is obtained from stress signals due to harmonic strain excitations. Based on comprehensive experimental data, an amplitude-dependent constitutive model of finite viscoelasticity is developed. The model is based on a modified Maxwell chain with process-dependent viscosities which depend on additional internal state variables. The evaluation of this thermodynamically consistent model is possible in both the time domain, via stress-time signals, and in the frequency domain, via the dynamic modulus. This property is very profitable for the parameter identification process. The implementation of the constitutive model into the commercial finite element code ANSYS with the user-programmable feature (UPF) USERMAT for large deformations in updated Lagrange formulation is presented. This implementation allows simulating the time-dependent behaviour of rubber components under arbitrary transient loading histories. Due to physical and geometrical nonlinearities, these simulations are not possible in the frequency domain. But, transient FEM computations of large loading histories are sometimes not possible in an acceptable time. In the context of the parameter identification the fundamental ideas are presented, how this problem has been solved. Transient FEM simulations of real rubber components are also shown to visualize the properties of the model in the context of the transient material behaviour.

Measurement of Dynamic Properties of Viscoelastic Materials

An improved method to measure the dynamic viscoelastic properties of elastomers is proposed. The method is based on the analysis of forced oscillation of a cylindrical sample loaded with an inertial mass. No special equipment or instrumentation other than the ordinary vibration measurement apparatus is required. Upper and lower surfaces of the viscoelastic material sample were bonded to a load disc and a rigid base plate, respectively. The rigid base plate was subject to forced oscillations driven by a vibration exciter. Two accelerometers were attached to monitor the displacement of the base plate and the load disc. The recorded magnitude ratio and the phase difference between the load disc and the base plate vibrations represent the axial, dynamic deformation of the sample. The data are sufficient to obtain the dynamic properties of the sample, oscillation properties of vibration exciter, whereas the sensitivity of gauges having no effect on the calculation results. For accurate calculation of the properties, a two-dimensional numerical model of cylindrical sample deformation was used. Therefore, a form factor, which takes into account the sample sizes in one-dimensional models, is not required in this method. Typical measurement of the viscoelastic properties of a silicone rubber Silastic® S2 were measured over the frequency range from 10 Hz to 3 kHz under deformations (ratio of vibration magnitude to sample thickness) from 10−4% to 5%. It was shown that the modulus of elasticity and the loss tangent fall on a single curve when the ratio of load mass to sample mass changed from 1 to 20. When the sample diameter was varied from 8 to 40 mm, the modulus of elasticity fall on the same curve, but the loss tangent curves showed some degree of scatter. Studied temperature dependence and nonlinear behavior of viscoelastic properties is found not to be associated with this effect.

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.

Transverse vibration of prestressed beams: An experimental technique for the determination of dynamic viscoelastic material properties of tissue mimicking materials

An experimental dynamic material property identification technique is presented that is based on the theoretical formulations of a vibrating prestressed beam. The technique determines the viscoelastic material properties of tissue mimicking materials that govern their dynamic behavior. Results are presented for silicone‐based materials (Sylgard 184, Dow Corning, Midland, MI) that are formed in the lab using a range of mixing ratios and cast in the form of a thick string held between fixed supports under tensile pre‐stress. The specimens are excited through the transverse harmonic displacement of the boundary. Transverse vibration at an arbitrary location is measured and compared with theory to identify material viscoelastic moduli valid up to at least several hundred Hertz. The presented technique can aid in providing accurate viscoelastic parameter values for phantoms that are used in the development of a range of medical diagnostic techniques that attempt to identify pathology or tissue differentiation ...

Measurement of dynamic properties of viscoelastic materials

A new method for measurement of viscoelastic properties of materials, based on the exact solution of the problem of the forced oscillations of a flat sample loaded by inertial mass, is proposed. The device for these measurements is described. The elasticity modulus and loss tangent are measured within the frequency range from 100 Hz to 10 kHz at relative deformation of a sample below 1%. The approximate formulas for calculation of viscoelastic properties are derived, and the conditions of their applicability are determined. The methods for expansion of the frequency range and measurement of materials with extremely high loss tangent are proposed. The proposed method is compared with the current Standard. It is shown that the new method has the higher accuracy and expanded range of parameter measurements, and the construction of device is easy and reliable, since it does not require the knowledge on the oscillation properties of vibration source.

437 分数階微分で表される粘弾性体を用いた動吸振器

Dynamic vibration absorber is one of vibration control devices. It consists of a mass and a viscoelastic element. Several kinds of viscoelastic materials are employed for the viscoelastic element of the vibration absorber. The use of viscoelastic materials has possibility to simplify the constitution of the vibration absorber and make the device with low cost. In this paper, to express the dynamic properties of viscoelastic materials, a fractional dynamic model is employed, and the vibration absorber is optimized with respect to a parameter of shape factor of the viscoelastic element. As a result, it is found that optimal value is affected by dynamic properties of the viscoelastic material and the natural frequency of the main system.

A generalised fractional derivative approach to viscoelastic material properties measurement

Viscoelastic materials are largely used as a means to provide damping to structures, thus mitigating resonant vibration responses. Devices made with viscoelastic materials such as isolators, dynamic vibration neutralisers (also called dynamic vibration absorbers), sandwich panels and structural links can be designed for highly efficient vibration control. To properly devise a vibration control strategy with viscoelastic materials, two basic dynamic properties must be known: the material loss factor and the dynamic modulus of elasticity. In the past the rheological model for viscoelastic materials was based on the classical concept of derivative (with respect to time) of integer order. These constitutive equations contained too many parameters to be identified, which made it computationally impractical. In this paper a new approach to the identification of the dynamic properties of viscoelastic materials, based on the fractional derivative model, is presented. Numerical and experimental results are produced and discussed.

Single-cell elastography: probing for disease with the atomic force microscope.

The atomic force microscope (AFM) is emerging as a powerful tool in cell biology. Originally developed for high-resolution imaging purposes, the AFM also has unique capabilities as a nano-indenter to probe the dynamic viscoelastic material properties of living cells in culture. In particular, AFM elastography combines imaging and indentation modalities to map the spatial distribution of cell mechanical properties, which in turn reflect the structure and function of the underlying cytoskeleton. Such measurements have contributed to our understanding of cell mechanics and cell biology and appear to be sensitive to the presence of disease in individual cells. This chapter provides a background on the principles and practice of AFM elastography and reviews the literature comparing cell mechanics in normal and diseased states, making a case for the use of such measurements as disease markers. Emphasis is placed on the need for more comprehensive and detailed quantification of cell biomechanical properties beyond the current standard methods of analysis. A number of technical and practical hurdles have yet to be overcome before the method can be of clinical use. However, the future holds great promise for AFM elastography of living cells to provide novel biomechanical markers that will enhance the detection, diagnosis, and treatment of disease.

Homogenization Method for Dynamic Viscoelastic Analysis of Composite Materials.

In this paper we propose a new homogenization method for composite materials in order to predict effective dynamic viscoelastic material properties in the frequency domain. The loss tangent, which is the ratio of storage modulus to loss modulus, is an important design variable for products made of viscoelastic materials. The proposed procedure, by which it is possible to compute the effective loss tangent of composite materials with periodic structure, is implemented in a homogenization analysis system based on the general purpose finite element analysis code, ABAQUS. The results of the numerical analysis are very close to experimental results which are obtained by using a rubber composite containing a stiff rubber and a soft rubber.

Complex eigensensitivity-based characterization of structures with viscoelastic damping

Damping plays an important role in structural stability and vibration control and different methods have been developed to design structures with maximum possible damping capacity. The most effective measure to date is perhaps the viscoelastic damping treatment. However, the dynamic properties of viscoelastic materials are generally frequency and temperature dependent. This makes the dynamic characterization of viscoelastically damped structures a tremendously difficult task. Conventional approximate methods, such as the direct frequency response method and the modal strain energy method, become quite inaccurate when the damping of a structure to be analyzed becomes high. An iterative complex eigensolution algorithm, though it is exact, requires a tremendous amount of computational effort since, for each mode, repeated complex eigensolutions are required until converged results are obtained. In the present paper, a new iterative complex eigensensitivity-based characterization method is presented. Based on the real eigensolution performed using finite-element analysis, the proposed method successively updates the complex eigenvalues and eigenvectors until required accuracy is achieved. As compared with conventional methods, the new method improves considerably numerical accuracy while it maintains the computational efficiency required for practical applications. A multilayer sandwich beam structure is used to demonstrate the practicality of the proposed method and the results show that the method is numerically very accurate and computationally very efficient.

Homogenization Method for Analysis of Dynamic Viscoelastic Properties of Composite Materials.

In this paper, we propose a new homogenization method for composite materials in order to predict effective dynamic viscoelastic material properties in the frequency domain. The loss tangent, which is the ratio of storage modulus to loss modulus, is an important design variable for products made of viscoelastic materials. The proposed procedure, which makes it possible to compute the effective loss tangent of composite materials with periodic structure, is implemented in a homogenization analysis system based on the general purpose finite element analysis code, ABAQUS. The results of the numerical analysis are very close to experimental results obtained using rubber composite containing a stiff rubber and a soft rubber.

Wayne T. Reader: The Vector Research Company years, 1988–1994

After 30 years of distinguished government service Dr. Wayne T. Reader retired in 1988 and joined Vector Research Co., Inc. as principal research scientist. He continued his Navy‐sponsored anechoic materials research program. He recruited a talented research and development team and established a state‐of‐the‐art dynamic material evaluation laboratory. He developed unique experimental procedures for evaluating static and dynamic properties of viscoelastic materials, an extensive material properties database, and analytical computer programs to predict acoustic performance of layered media including anechoic lining systems. He continued to seek economical solutions to acoustic quieting and won a competitive Navy procurement to design and install an innovative lining system to a large anechoic test tank. While continuing his work with passive voided polymers, he began exploring the advantages of composites containing discrete and distributed piezoelectric particles in a polyurethane medium. In addition to his technical work, Wayne Reader established a working environment which met not only his interests but also the company’s and the Navy’s as well. He attracted and mentored several young scientists who continue to work in this field.

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.