Equivalent Viscoelastic Model Research Articles

Compliant joint to reduce docking loads between CubeSats

This paper presents the design, modelling and experimental verification of a damping joint for application to miniature space docking mechanisms. The joint design is based on deformable elastomeric elements, thus avoiding any sliding or contact between moving components. Numerical FEM simulations have been conducted in order to quantify the joint mechanical characteristics (rigidity and damping coefficient) as a function of the main design parameters (geometry, material, assembly). The obtained parametric relations provide an estimate of the joint characteristics based on the selected design. An equivalent visco-elastic model is developed and implemented in dynamic simulations. The results of the experimental evaluation of the joint design provide a validation of the developed models and prove the advantage of adopting damping joints in docking applications between small satellites, like reduced contact loads and enhanced damping.

Analysis of restoring characteristic in buried pipe and proposal of equivalent viscoelastic model

Analysis of restoring characteristic in buried pipe and proposal of equivalent viscoelastic model

Viscoelastic characteristics of low-frequency seismic wave attenuation in porous media

Mesoscopic fluid flow is the major cause of wave attenuation and velocity dispersion at seismic frequencies in porous rocks. The Johnson model provides solutions for the frequency-dependent quality factor and phase velocity in partially saturated porous media with pore patches of arbitrary shapes. We use the Johnson model to derive approximations for the quality factor Q at the high and low frequency limit, and obtain the approximate equation for Qmin based on geophysical and geometric parameters. A more accurate equation for Qmin is obtained after correcting for the linear errors between the exact and approximate Q values. The complexity of the pore patch shape affects the maximum attenuation of Qmin and the transition frequency ftr; furthermore, the effect on ftr is stronger than that on Qmin. Numerical solutions to Biot’s equation are computationally intensive; thus, we build an equivalent viscoelastic model on the basis of the Zener model, which well approximates the wave attenuation and dispersion in porous rocks in the seismic band.

Modelling and identification of structures with rate-independent linear damping

In the present paper, a linear model for multi-degree-of-freedom systems with rate-independent damping is proposed to the purposes of dynamic response prediction and identification. A viscoelastic model with memory, equivalent to the ideal hysteretic model as for the energy dissipation properties, but causal and physically consistent in both the time and the frequency domain, is developed by adopting the Maxwell–Wiechert kernel function and by requiring the loss modulus to be substantially independent of frequency in a specified range of interest. The finite element model of the equivalent viscoelastic system is constructed and its equations of motion are shown to be uncoupled, in terms of modal coordinates, by the real-valued eigenvectors of the conservative system. An augmented state-space formulation, which encompasses, besides the customary displacements and velocites, a number of internal variables devoted to represent the viscoelastic memory, is then provided for the sake of system identification. Mechanical and modal properties of the equivalent viscoelastic model are finally illustrated by means of numerical examples.

Constitutive model of saturated soft clay with cyclic loads under unconsolidated undrained condition

An equivalent visco-elastic model of saturated soft clay was studied under unconsolidated undrained (UU) condition, which can be used to evaluate the stability of ocean foundation. Cyclic triaxial compression and extension tests were conducted to study the parameters of the model. Results showed that the relationships of the damping ratio and the octahedral shear modulus with the octahedral cyclic shear strain were nearly unique, when the initial octahedral shear stress ratios of specimens were equal to 0.3, 0.5 and 0.7. The relationships of the damping ratio and the octahedral shear modulus with the octahedral cyclic shear strain determined from the cyclic triaxial compression tests were basically the same as those determined from the cyclic triaxial extension tests. Furthermore, the relationships were not related to the initial stress condition, the test stress state and the octahedral cyclic shear stress ratio. The relationships determined from the cyclic triaxial tests under no deviatoric stress were basically the same as those determined from the cyclic triaxial tests under deviatoric stress. The change of the octahedral cyclic accumulative strain with the number of cycles was unique under different tests stress states. An equivalent visco-elastic constitutive model of saturated soft clay under UU condition was initially established.

Algoritmo para determinação do amortecimento de materiais cerâmicos pela técnica das freqüências naturais de vibração via excitação por impulso

O amortecimento ou atrito interno é uma das propriedades mais sensíveis de materiais e estruturas tanto em escala macro como microscópica e um bom indicador para a caracterização de danos estruturais, sendo particularmente sensível à presença de trincas e micro-trincas. O objetivo deste trabalho foi desenvolver um algoritmo que permitisse incorporar a caracterização do amortecimento à técnica das freqüências naturais de vibração via excitação por impulso, já bem estabelecida pela norma ASTM E1876 e amplamente empregada na determinação não-destrutiva dos módulos elásticos de materiais cerâmicos. Foi desenvolvido um algoritmo para a determinação do amortecimento fundamentado na análise de sinal no domínio de tempo-freqüência, no método do decremento logarítmico e no modelo viscoelástico equivalente. O algoritmo foi validado empregando um gerador de ondas de formato arbitrário e aplicado na caracterização de dois materiais, sendo um concreto refratário de alta alumina, com e sem dano por choque térmico, e um aço SAE 1020. O algoritmo foi eficiente ao determinar a frequência e o amortecimento de sinais arbitrários e dos corpos de prova, e em limitar a análise ao modo de vibração de interesse, minimizando assim a interferência de outros modos. O algoritmo permitiu integrar com eficiência o cálculo do amortecimento à técnica de excitação por impulso.

Considering amplitude dependence during cyclic loading of elastomers using an equivalent viscoelastic approach

Although it is well known that the dynamic properties of rubber depend on both frequency and amplitude, there are few commercially available finite element codes that take account of these effects. This paper outlines a simplified procedure to extend the usability of the commercially available frequency dependent viscoelastic finite element models to also take account of the amplitude dependence. By first calculating the load level at each element it is possible to obtain an equivalent viscoelastic model for a cyclic load. Using this approach, two different frequency dependent models are treated; one frequency and one time domain viscoelastic model. Both models are verified against experimental data with good results.

An equivalent viscoelastic model for rock mass with parallel joints

An equivalent viscoelastic medium model is proposed for rock mass with parallel joints. A concept of “virtual wave source (VWS)” is proposed to take into account the wave reflections between the joints. The equivalent model can be effectively applied to analyze longitudinal wave propagation through discontinuous media with parallel joints. Parameters in the equivalent viscoelastic model are derived analytically based on longitudinal wave propagation across a single rock joint. The proposed model is then verified by applying identical incident waves to the discontinuous and equivalent viscoelastic media at one end to compare the output waves at the other end. When the wavelength of the incident wave is sufficiently long compared to the joint spacing, the effect of the VWS on wave propagation in rock mass is prominent. The results from the equivalent viscoelastic medium model are very similar to those determined from the displacement discontinuity method. Frequency dependence and joint spacing effect on the equivalent viscoelastic model and the VWS method are discussed.