Modelling One-Dimensional Fractional Impact Using Basic Fractional Viscoelastic Models

2016 ◽  
Author(s):  
Arman Dabiri ◽  
Eric A. Butcher ◽  
Morad Nazari
Keyword(s):  
Maxwell Model ◽  
Viscoelastic Materials ◽  
One Dimensional ◽  
Viscoelastic Models ◽  
Depth Separation ◽  
Voigt Model ◽  
Impact Problems ◽  
Force Displacement ◽  
Enormous Number ◽  
Impact Models

Viscoelastic materials can be mathematically represented using integer- or order models. It has been shown in different studies that modeling a viscoelastic material usually requires an enormous number of parameters. Fractional viscoelastic models have been shown to be advantageous over integer viscoelastic models in the representation of viscoelastic materials, specifically when the system has memory or hereditary property. However, to the authors’ knowledge, no study has yet been done about fractional impact models. Thus, in this paper, fractional modified Kelvin-Voigt model and fractional Maxwell model are introduced as one-dimensional fractional impact models for basic fractional viscoelastic materials. The force-displacement hysteresis curves are obtained by using the fractional Chebyshev collocation method and the gradient of impact force, penetration depth, separation depth, and the coefficient of restitution are studies. It is shown numerically that fractional viscoelastic models behave more realistic than their integer counterparts in one-dimensional impact problems.

Characterizing Damping and Restitution in Compliant Impacts via Linear Viscoelastic Models

1999 ◽  
Author(s):  
Eric A. Butcher ◽  
Daniel J. Segalman
Keyword(s):  
Linear Models ◽  
Energy Losses ◽  
Displacement Boundary ◽  
Viscoelastic Models ◽  
Viscoelastic Parameters ◽  
Linear Viscoelastic ◽  
Standard Linear ◽  
Linear Damping ◽  
Voigt Model ◽  
Force Displacement

Abstract Strategies for characterizing damping and restitution in compliant impacts while eliminating the force discontinuities associated with the standard Kelvin-Voigt model are examined within the framework of linear viscoelasticity. A modification of the Kelvin-Voigt model as well as higher-order (Maxwell and standard linear) models are studied in an effort to satisfy the expected force-displacement boundary conditions. The restitution coefficients, energy losses per cycle, and equivalent linear damping ratios are then obtained analytically as functions of the dimensionless viscoelastic parameters which may be easily related to and obtained from experimentally measured restitution coefficients.

Contact Mechanics of a Hard Cylinder on a Viscoelastic Layer

Tribology ◽  
2006 ◽  
Author(s):  
Steven R. H. Barrett ◽  
Alexander H. Slocum
Keyword(s):  
Pressure Distribution ◽  
Contact Mechanics ◽  
Normal Force ◽  
Maxwell Model ◽  
Sliding Contact ◽  
Viscoelastic Layer ◽  
Tractive Force ◽  
Rolling Velocity ◽  
One Dimensional ◽  
The One

The rolling/sliding contact of a hard cylinder on a viscoelastic layer is re-examined. The one-dimensional Maxwell model, with the addition of a parallel spring, is used to model the normal stiffness of the viscoelastic layer A solution for the pressure distribution is presented. It is shown that the maximum tractive force that the cylinder can sustain before complete sliding is a function of the sense and magnitude of the rolling velocity. Two regimes of loading are considered - constant cylinder normal force and constant cylinder indentation.

The Effects of Small Sinusoidal Load Variations in Elastohydrodynamic Line Contacts

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
C. J. Hooke ◽  
G. E. Morales-Espejel
Keyword(s):  
Pressure Distribution ◽  
Maxwell Model ◽  
Total System ◽  
Low Frequencies ◽  
Load Variations ◽  
Entrainment Velocity ◽  
Line Contacts ◽  
Sinusoidal Load ◽  
Voigt Model ◽  
Low Amplitude

A method of determining the response of elastohydrodynamic line contacts to low amplitude, sinusoidal variations in load is presented. It is shown that the load variations alter the Hertz width, cyclically increasing and reducing the effective entrainment velocity. This produces clearance variations in the inlet, which are transported through the conjunction altering the pressure distribution as they pass. The resulting pressure and clearance changes can be many times greater than when the load changes slowly. The results are used to determine the flexibility and damping of the conjunctions. These vary depending on the number of transported waves inside the contact. It is shown that a Maxwell model rather than the usual Voigt model is required to define the contact's behavior. While the Voigt model may be used at low frequencies, it has a damping coefficient that is not unique to the contact but depends on the total system stiffness.

Comparison of 2-D numerical viscoelastic waveform modeling with ultrasonic physical modeling

Geophysics ◽  
1996 ◽  
Vol 61 (3) ◽  
pp. 862-871 ◽  
Author(s):  
Genmeng Chen
Keyword(s):  
Physical Model ◽  
Physical Modeling ◽  
Wave Attenuation ◽  
Numerical Study ◽  
Solid Model ◽  
Viscoelastic Materials ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Voigt Model

The objective of the study is to test the validity of theoretical models of wave attenuation by comparing their predictions of attenuation against physical model results. The study is confined to a 2-D geometry, and the viscoelastic materials used in physical modeling are those commonly used in the experiment. The physical modeling data of homogeneous media are compared with the numerical results in the frequency domain. The time‐domain comparisons between numerical modeling and physical modeling are also shown by three examples. The theoretical viscoelastic models used in the numerical study are the Kelvin‐Voigt model, the standard linear solid model, and the standard linear solid model with a continuous spectrum of relaxation time. On the comparison of a single model, all the models simulate the physical model fairly well, but the standard linear solid model gives the best result among them. The Kelvin‐Voigt model is easy to use as a quick first‐order simulation of the viscoelastic materials because it has fewer viscosity parameters than the other two models. The disadvantage of the Kelvin‐Voigt model is that it predicts too much attenuation of the high‐frequency components. It is also shown that neglecting the viscosity of some materials like polyvinylcloride plastic (PVC), which has high viscosity, will produce incorrect results in synthetic seismograms.

Analytical Solution of 1-D Viscoelastic Consolidation of Soft Soils with Fractional Maxwell Model

2012 ◽  
Vol 157-158 ◽  
pp. 419-423
Author(s):  
Ya Peng Zhang ◽  
Feng Gao
Keyword(s):  
Analytical Solution ◽  
Soft Soil ◽  
Soil Layer ◽  
Viscoelastic Model ◽  
Integral Form ◽  
Maxwell Model ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Fractional Maxwell Model ◽  
The One

Considering the rheological characteristics of soil, think the fractional maxwell with viscoelastic model can be described, the fractional maxwell model into integral form of saturated soft soil layer, the one dimensional compression, through the Laplace transform problems get instantaneous loading and single stage, the analytical solution of the loading conditions.

Improved nonlinear model of a yaw damper for simulating the dynamics of a high-speed train

2018 ◽  
Vol 233 (7) ◽  
pp. 651-665 ◽  
Author(s):  
Wanxiu Teng ◽  
Huailong Shi ◽  
Ren Luo ◽  
Jing Zeng ◽  
Caihong Huang
Keyword(s):  
Nonlinear Model ◽  
High Speed ◽  
Piecewise Linear ◽  
Excitation Frequency ◽  
Maxwell Model ◽  
Railway Vehicle ◽  
High Speed Train ◽  
Force Velocity ◽  
Linear Force ◽  
Force Displacement

The aim of this paper is to establish a simple and accurate nonlinear model of a yaw damper for the dynamic numerical simulation of high-speed trains. An improved nonlinear yaw damper model is proposed based on the traditional Maxwell model. It comprises a piecewise linear force–displacement spring and a piecewise linear force–velocity damper in series. These nonlinear inputs for the model are retrieved from the dynamic performance tests of the damper, and the force–displacement and force–velocity curves are further modified to improve the modelling accuracy according to the test results. The proposed model can accurately simulate the damper's dynamic stiffness and dynamic damping characteristics with respect to the excitation frequency or displacement, which cannot be reproduced when using the traditional Maxwell model. Both the traditional Maxwell model and the improved nonlinear model presented in this work are integrated into a multibody dynamics railway vehicle model to simulate the typical dynamic problems of a high-speed train operating at 250 km/h in northeast China. Through comparative analysis, it was found that the numerical simulations are consistent with the field measurements. It can be concluded that the proposed nonlinear damper model is more suitable for studying railway vehicle system dynamics under various operating cases. By contrast, the input parameters of the traditional Maxwell model must be modified artificially according to the vehicle responses and the dynamic characteristics of the yaw damper.

scholarly journals Study on the Generalized Formulations with the Aim to Reproduce the Viscoelastic Dynamic Behavior of Polymers

2020 ◽  
Vol 10 (7) ◽  
pp. 2321
Author(s):  
Andrea Genovese ◽  
Francesco Carputo ◽  
Antonio Maiorano ◽  
Francesco Timpone ◽  
Flavio Farroni ◽  
...  
Keyword(s):  
Experimental Data ◽  
Low Frequency ◽  
Maxwell Model ◽  
Wide Frequency Range ◽  
Material Behavior ◽  
Viscoelastic Materials ◽  
Optimum Parameters ◽  
Generalized Maxwell Model ◽  
Minimum Number ◽  
Real Behavior

Appropriate modelling of the real behavior of viscoelastic materials is of fundamental importance for correct studies and analyses of structures and components where such materials are employed. In this paper, the potential to employ a generalized Maxwell model and the relative fraction derivative model is studied with the aim to reproduce the experimental behavior of viscoelastic materials. For both models, the advantage of using the pole-zero formulation is demonstrated and a specifically constrained identification procedure to obtain the optimum parameters set is illustrated. Particular emphasis is given on the ability of the models to adequately fit the experimental data with a minimum number of parameters, addressing the possible computational issues. The question arises about the minimum number of experimental data necessary to estimate the material behavior in a wide frequency range, demonstrating that accurate results can be obtained by knowing only the data of the upper and low frequency plateaus plus the ones at the loss tangent peak.

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