Dashpot Model Research Articles

Influence of reclaimed asphalt pavement content on complex modulus of asphalt binder blends and corresponding mixes: experimental results and modelling

The objective of the presented study is to determine linear viscoelastic (LVE) properties of corresponding binders and mixes and to check how they change with reclaimed asphalt pavement (RAP) content. The investigation is part of a wider on-going research project, in the framework of a PhD thesis, in collaboration between Université de Lyon/École Nationale Travaux Publics de l’État (ENTPE), EIFFAGE Travaux Publics and Beyond Petroleum. Dynamic shear rheometer and tension/compression (using a Métravib device) complex modulus tests were performed on nine different bitumens, produced as blends of two different base bitumens and RAP-extracted bitumen in various proportions. LVE properties of six asphalt mixes, produced with the same materials and proportions of certain bitumen blends among the nine tested ones, were measured in tension/compression mode. 2 Springs, 2 Parabolic Elements, 1 Dashpot model was used to fit experimental data both for binders and mixes. Shift-Homothety-Shift in time-Shift transformation (developed at ENTPE) was applied to verify the correspondence of LVE behaviours of related binders and mixes.

A simplified model for coupled horizontal and rocking vibrations of embedded foundations

For a foundation–soil system undergoing coupled horizontal and rocking motions, a simplified mass–spring–dashpot model is proposed to simulate unbounded soil. Through three equivalent criteria, a group of equivalent models are established for the foundation–soil system. An optimal equivalent model is then determined to represent the best simplified model. The method proposed to develop the optimal equivalent model may be more efficient than lengthy optimization techniques used by most existing models. The dynamic responses of the foundation–soil system using the optimal equivalent model are compared with those obtained by the half-space theory and by the existing lumped-parameter models. A validation of the proposed model in time domain is also provided. Since the coupling of horizontal and rocking motions is adequately considered, the optimal equivalent model is found to have more accurate results than most existing models. It is also found that the rotational responses of embedded foundations subjected to a harmonic rocking moment may be significantly underestimated without considering the coupling behavior. This proposed method may be effectively applied to practical engineering problems.

On a fractional Zener elastic wave equation

Abstract This survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener stress-strain relation plus linearized conservation of mass and momentum. A connection between this four-parameter fractional wave equation and a physically well established multiple relaxation acoustical wave equation is reviewed. The fractional Zener wave equation implies three distinct attenuation power-law regimes and a continuous distribution of compressibility contributions which also has power-law regimes. Furthermore it is underlined that these wave equation considerations are tightly connected to the representation of the fractional Zener stress-strain relation, which includes the spring-pot viscoelastic element, and by a Maxwell-Wiechert model of conventional springs and dashpots. A purpose of the paper is to make available recently published results on fractional calculus modeling in the field of acoustics and elastography, with special focus on medical applications.

Compressive relaxation of the stress and resistance for carbon nanotube filled silicone rubber composite

The changes in the stress and the electrical resistance of carbon nanotube filled silicone rubber composite during compressive stress relaxation are researched quantitatively. The changing tendency of the electrical resistance is similar to that of the stress. The experimental data of the electrical resistance and the stress over time can be fitted by the spring–dashpot model based on the viscoelastic theory. Both the final relative resistance and the final relative stress increase with the increase of the loading speed and decrease with the increase of the carbon nanotube concentration. Both the resistance relaxation time and the stress relaxation time decrease with the increase of the loading speed. The similarity between the compressive resistance relaxation and the compressive stress relaxation is explained by analyzing the correlation between the changes in the conductive network and the disorientation of the polymer macromolecules.

Negative coefficient of normal restitution

This paper shows that negative coefficients of normal restitution occur inevitably when the interaction force between colliding particles is finite. We derive an explicit criterion showing that for any set of material properties there is always a collision geometry leading to negative restitution coefficients. While from a phenomenological point of view, negative coefficients of normal restitution appear rather artificial, this phenomenon is generic and implies an important overlooked limitation of the widely used hard sphere model. The criterion is explicitly applied to two paradigmatic situations: for the linear dashpot model and for viscoelastic particles. In addition, we show that for frictional particles the phenomenon is less pronounced than for smooth spheres.

Energy harvester for vehicle tires: Nonlinear dynamics and experimental outcomes

This article presents a very compact electromechanical wideband energy harvester optimized for tire applications. The device exploits an asymmetric magnetic spring to be adaptive and effective at almost any vehicle speed. The device has been simulated through an experimentally validated SIMULINK block-oriented model. The simulation takes into account nonlinear dynamic and adaptive resonant behavior of the seismic mass, electromagnetic, and magnetostatic coupling between floating magnetic mass and coils, and the transfer of the generated power to an external load by means of a nonlinear circuit interface. A particular focus on the pneumatic effect on the floating magnet has been made. A convenient choice of clearance between moving and fixed parts can be used to create an effective air brake preventing or softening shocks with end stops and to modify system dynamic. A nonlinear equivalent spring dashpot model of the pneumatic effect and a method to estimate its parameters from geometry have been proposed. An analysis of different nonlinearities of the system at different vehicle speed and a study on the combined effect of softening and hardening behavior of the device have been performed and discussed.

Thermo-mechanical analysis of packed beds for large-scale storage of high temperature heat

Thermal storage systems are central elements of various types of power plants operated using renewable and conventional energy sources. Where gaseous heat transfer media are used, a regenerator-type heat storage with a packed bed inventory is a particularly cost-effective solution. However, suitable design tools to analyse the thermo-mechanical aspects of large-scale storage of high temperature heat are currently still missing. As a basis for such a tool, this contribution presents a novel approach for the prediction of the thermo-mechanical behaviour of such storage under thermo-cyclic operation. The relevant relations are formulated on the basis of the discrete element method (DEM). Here, the forces interacting between spherical particles are calculated by spring, dashpot and friction models and the resulting translations and rotations are determined solving Newton’s equations of motion. Coupling these equations with a simplified thermal model that considers the heat resistance within the particles allows for investigation of the thermo-mechanical behaviours of a packed bed. For adequate implementation of this new approach and for reduced computational effort, a time-step control has been implemented and validated. Initial simulation results include the temporal and spatial displacements as well as the forces acting on the individual bodies for a thermo-cyclic operation.

Viscoelastic modelling of rotor—shaft systems using an operator-based approach

Damping exists in every material in varying degrees, so materials in general are viscoelastic in nature. Energy storage, as well as dissipation in varying degrees, accompanies every time-varying deformation, with the effect that stress and strain in a material get out of phase. This work presents the development of equations of motion of a rotor—shaft system with a viscoelastic rotor after discretizing the system into finite elements. Subsequently, these equations are used to study the dynamics of the rotor—shaft system in terms of stability limit of spin speed and time response of a disc as a result of unbalance. The primary inspiration for a viscoelastic model arises from the need to capture the influence of broad band spectral behaviour of rotor—shaft materials, primarily polymers and polymer composites, which are principally the materials of light rotors, on the dynamics of rotor—shaft system. For this, the material constitutive relationship has been represented by a differential time operator. Use of operators enables one to consider general linear viscoelastic behaviours, represented in the time domain by multi-element (three, four, or higher elements) spring—dashpot models or internal variable models, for which, in general, instantaneous stress and its derivatives are proportional to instantaneous strain and its derivatives. Again such representation is fairly generic, in a sense that the operator may be suitably chosen according to the material model to obtain the equations of motion of a rotor—shaft system. The equations so developed may be easily used to find the stability limit speed of a rotor—shaft system as well as the time response when the rotor—shaft system is subjected to any dynamic forcing function.

The 2S2P1D: An Excellent Linear Viscoelastic Model

An experimental campaign has been carried out on five different unaged and five aged penetration grade bitumens to determine the properties of the 2S2P1D (combinations of two springs, two parabolic elements and one dashpot) model. The dynamic oscillatory test was conducted in order to obtain the rheological data using the dynamic shear rheometer (DSR). Earlier, the samples were aged following the Rolling Thin Film Oven Test (RTOFT) test procedure. It was found that the 2S2P1D model which consists of seven parameters simulates in an excellent way the linear viscoelastic properties of aged and unaged penetration grade bitumens over a wide range of temperatures and frequencies. The goodness of fit statistical analysis showed that the model had a good correlation and comparable to the measured dynamic data.

An investigation of segregation and mixing in dense phase pneumatic conveying

Pneumatic conveying of bulk materials has become an important technology in many industries: from pharmaceuticals to petro-chemicals and power generation. Particulate segregation has been investigated in many solids handling processes. However, little work has been published on the segregation and mixing in pneumatic conveying pipelines, particularly in dense phase pneumatic conveying. Due to the character of dense phase flow, it is difficult to investigate the segregation in a flowing plug. A sampling device was designed and built to take samples from the pneumatic conveying pipeline after “catching a plug”. Several experiments were conducted over a range of gas–solids flow conditions with 3 mm nylon pellets and 3 mm ballotini as a segregating mixture. Experimental data combined with video footage were analysed to describe the segregation and mixing of solids plugs in pipes. This investigation provides initial research on establishing a segregation index in a flowing plug. A gas–solids two-dimensional mathematical model was developed for plug flow of a nylon-glass particulate mixture in a horizontal pipeline in dense phase pneumatic conveying. The model was developed based on the discrete element method (DEM). The model was used to simulate the motion of particles both in a homogeneous flow and as binary mixtures taking into account the various interactions between gas, particles and pipe wall. For the gas phase, the Navier Stokes equations were integrated by the semi-implicit method for pressure-linked equations (SIMPLE) using the scheme of Patankar employing the staggered grid system. For the particle motion the Newtonian equations of motion of individual particles were integrated, where repulsive and damping forces for particle collision, the gravity force, and the drag force were taken into account. For particle contact, a model with a simple non-linear spring and dash pot model for both normal and tangential components was used. This model employed a mixture of 3 mm pellets and ballotini as virtual materials with properties of nylon and glass. The results from the model are discussed and compared with experimental work and show qualitative agreement. Further modelling and experimental work in key areas is proposed.

Experimental evaluation of vertical response of rigid surface footing on layered soil

The study of the dynamic response of foundations is of significant importance in the machine foundation design and soil-foundation interaction problems, in general. This paper presents experimental investigations in the field studying the effect of layering of soil mass on the dynamic response of foundation under vertical mode of vibration. Model block vibration tests on a rigid surface footing were conducted on different layered soil systems. A concrete block of size 400×400×100 mm was used as the model block and a Lazan type mechanical oscillator was used for inducing vibration in vertical direction. In the investigation two different soils, namely, gravel and fly ash were used. In total 132 tests were conducted on different layered soil beds with different loading combinations. Dynamic response of foundation resting on layered soil system were also analyzed by two simple approximate methods namely, mass spring dashpot model and equivalent elastic half-space theory. Results obtained from the two methods were compared with that obtained from the experimental investigation. It was found from the comparisons that the simple mass-spring dashpot model was capable of predicting the resonance frequency and the resonance amplitude satisfactorily. Elastic half space theory with equivalent soil properties was found to underestimate the displacement amplitude.

A mechanical model for three-phase permanent deformation of asphalt mixture under repeated load

On basis of the Burgers model, a new model consisting of modified dashpot and Van Der Poel model was derived from rheological and viscoelastic theory. Subsequently, triaxial repeated load permanent deformation tests of AC16 asphalt mixtures were conducted to validate this new developed model. Parameters of new developed model were obtained by a nonlinear regression analysis of test data, and then permanent strains and flow number of each mixture were calculated. The experimental results prove that the new developed model can well describe three phases permanent deformation of asphalt mixture under repeated load and it can be used for pavement mechanical analysis and rutting prediction.

Synthesis, Characterization and Swelling Behaviour of Poly(sodium acrylate)/Palygorskite Superabsorbent Composites based on Palygorskite and Organo-palygorskite

Novel superabsorbent composites based on partially neutralized acrylic acid (SA) and palygorskite (PLG) were synthesized by aqueous solution polymerization. The effects of PLG, organo-PLG (O-PLG) and the content of PLG in the copolymeric gels on the water sorption and the initial swelling rate in deionized water and saline solution (0.2 wt% NaCl (aq) ) were studied. Experimental results indicate that the absorption in saline solution is smaller than that in deionized water. In comparison with a polymer prepared under clay-free conditions (415 gg -1 ), no considerable change in absorption is observed with incorporating 20.0 wt% PLG or 20.0 wt% O-PLG (368 gg -1 or 356 gg -1 ), which significantly reduces in the cost of preparing superabsorbents. Plots of swelling against time have been found to fit mathematical relationships which are based on spring and dashpot models and are applied in the polymer field to viscoelastic systems. The thermal stability of the composites was found to be increased, and this was associated with the addition of palygorskite. In addition, the XRD patterns of poly(SA)/PLG and poly(SA)/O-PLG indicate the formation of a traditional microcomposite.

A Viscoelastic Biomechanical Model of the Cornea Describing the Effect of Viscosity and Elasticity on Hysteresis

To develop a method for evaluating viscosity and elasticity of the cornea and to examine the effect that both properties have on hysteresis. A three-component spring and dashpot model was created in Simulink in Matlab to represent the purely elastic and viscoelastic behavior of the cornea during a measurement using device called an ocular response analyzer (ORA). Values for elasticity and viscosity were varied while sinusoidal stress was applied to the model. The simulated stresses were used to determine how hysteresis is affected by the individual components of elasticity, viscosity, and maximum stress. To validate the model, high-speed photography was used to measure induced strain in a corneal phantom during ORA measurement. This measured strain was compared with the strains simulated by the model. When the spring in the viscoelastic portion of the model was stiffened, hysteresis decreased. When the spring in the purely elastic element was stiffened, hysteresis increased. If both springs were stiffened together, hysteresis peaked strongly as a function of the viscosity of the viscoelastic element. Below the peak value, lower elasticity was associated with higher hysteresis. Above the peak value, higher elasticity was associated with higher hysteresis. In addition, hysteresis increased as the air maximum pressure was increased. Measurements from phantom corresponded to predictions from the model. A viscoelastic model is presented to illustrate how changing viscosity and elasticity may affect hysteresis. Low hysteresis can be associated with either high elasticity or low elasticity, depending on the viscosity, a finding consistent with clinical reports.

Energy dissipation in spacecraft structures incorporating bolted joints with viscoelastic layers

The energy dissipation capacity of bolted joints with viscoelastic layers in a spacecraft structure was investigated. Initially, a linear spring dashpot model was used to represent the bolts in a satellite structure. A relationship was developed between the model parameters (stiffness and damping coefficient) and the viscoelastic material and geometric properties (shear modulus, loss factor, operating area, and thickness) of the actual bolted joint. This model was then developed into the non-linear domain. Experiments on bolted joints with viscoelastic layers were carried out to provide information for the non-linear joint model. These models were incorporated into a simple spacecraft model to investigate the effect on the spacecraft response. Based on these numerical analysis, it was found that the joints can dissipate much energy and the response of the spacecraft structure to vibrations during launch can be decreased significantly.

Coefficient of tangential restitution for the linear dashpot model

The linear dashpot model for the inelastic normal force between colliding spheres leads to a constant coefficient of normal restitution, epsilonn=const, which makes this model very popular for the investigation of dilute and moderately dense granular systems. For two frequently used models for the tangential interaction force we determine the coefficient of tangential restitution, epsilont, both analytically and by numerical integration of Newton's equation. Although epsilonn=const for the linear-dashpot model, we obtain pronounced and characteristic dependences of the tangential coefficient on the impact velocity, epsilont=epsilont(g). The results may be used for event-driven simulations of granular systems of frictional particles.

Coefficient of restitution and linear–dashpot model revisited

With the assumption of a linear–dashpot interaction force, the coefficient of restitution, $$\varepsilon_d^0(k, \gamma)$$ , can be computed as a function of the elastic and dissipative material constants, k and γ by integrating Newton’s equation of motion for an isolated pair of colliding particles. If we require further that the particles interact exclusively repulsive, which is a common assumption in granular systems, we obtain an expression $$\varepsilon_d(k, \gamma)$$ which differs even qualitatively from the known result $$\varepsilon_d^0(k, \gamma)$$ . The expression $$\varepsilon_d(k, \gamma)$$ allows to relate Molecular Dynamics simulations to event-driven Molecular Dynamics for a widely used collision model.

Simulation of slowly dragging a cylinder through a confined pressurized bed of granular materials using the discrete element method

A nonlinear spring dash pot model to describe the interaction forces between confined granules under high pressures based on Hertz contact theory is proposed. The discrete element method (DEM) is used to simulate the movement and calculate the normal and tangential contact forces among the granules when a cylinder is dragged through a granular bed at low velocities. The time-dependent, total drag force required to pull the circular cylinder is also calculated and used to compare the effect of material and boundary conditions on flow behavior. Simulation results show that drag force increases with cylinder diameter, granular volume fraction, granular size, and the friction coefficient between granules. Drag force was found to be independent of the velocity of the cylinder at low speed, the friction coefficient between the granules and the cylinder, and the friction coefficient between the granules and the container walls.

Effect of Contact Force Models on Granular Flow Dynamics

The contact force model consisting of a linear spring dashpot with a frictional glider has been widely adapted to simulate granular flows. Real contact mechanics between two solid bodies is very complicated. Extensive theoretical and experimental studies exist for binary contacts. Very little work has been reported that addresses the effect of contact mechanics on the bulk behavior of granular materials. We first briefly summarize the difference of binary contacts between a linear spring–dashpot model and the Hertzian nonlinear spring with two nonlinear dashpot models. We then compare the constitutive behaviors of a granular material using a linear and a nonlinear model. The stress- and strain-rate relation in simple shear flow and the resulting coordination number are calculated using the discrete element method. It is found that although at the grain level binary contact between two particles depends on whether a linear or a nonlinear model is used, the bulk behavior of granular materials is qualitative...

Numerical simulation of particle motion in dense phase pneumatic conveying

A gas-solids two-dimensional mathematical model was developed for plug flow of cohesionless particles in a horizontal pipeline in dense phase pneumatic conveying. The model was developed based on the discrete element method (DEM). For the gas phase, the Navier-Stokes equations were integrated by the semi-implicit method for pressure-linked equations (SIMPLE) scheme of Patankar employing the staggered grid system. For the particle motion the Newtonian equations of motion of individual particles were integrated, where repulsive and damping forces for particle collision, the gravity force, and the drag force were taken into account. For particle contact, a nonlinear spring and dash pot model for both normal and tangential components was used. In order to get more realistic results, the model uses realistic pneumatic system and material values.