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.

Non-linear viscoelastic models predict fingertip pulp force-displacement characteristics during voluntary tapping

2003 ◽  
Vol 36 (4) ◽  
pp. 497-503 ◽  
Author(s):  
Devin L. Jindrich ◽  
Yanhong Zhou ◽  
Theodore Becker ◽  
Jack Tigh Dennerlein
Keyword(s):  
Viscoelastic Models ◽  
Non Linear ◽  
Linear Viscoelastic ◽  
Force Displacement

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.

Application of non-linear turbulence models in an engine-type flow configuration

2007 ◽  
Vol 8 (5) ◽  
pp. 449-464 ◽  
Author(s):  
C. H. Son ◽  
T. A. Shethaji ◽  
C. J. Rutland ◽  
H Barths ◽  
A Lippert ◽  
...  
Keyword(s):  
Experimental Data ◽  
Renormalization Group ◽  
Linear Models ◽  
Combustion Engine ◽  
Mean Flow ◽  
Modest Improvement ◽  
Non Linear ◽  
Standard Linear ◽  
Simple Flows ◽  
Engine Type

Three non-linear k-ε models were implemented into the multi-dimensional computational fluid dynamics code GMTEC with the purpose of comparing them with existing linear k-ε models including renormalization group variations. The primary focus of the present study is to evaluate the potential of these non-linear models in engineering applications such as the internal combustion engine. The square duct flow and the backwards-facing step flow were two simple test cases chosen for which experimental data are available for comparison. Successful simulations for these cases were followed by simulations of an engine-type intake flow to evaluate the performance of the non-linear models in comparison with experimental data and the standard linear k-ε models as well as two renormalization group types. All the non-linear models are found to be an improvement over the standard linear model, but mostly in simple flows. For more complex flows, such as the engine-type case, only the cubic non-linear models appear to make a modest improvement in the mean flow but without any improvement in the root-mean-square values. These improvements are overshadowed by the stiffness of the cubic models and the requirements for smaller time steps. The contributions of each non-linear term to the Reynolds stress tensor are analysed in detail in order to identify the different characteristics of the different non-linear models for engine intake flows.

Linear viscoelastic models

2009 ◽  
Vol 156 (1-2) ◽  
pp. 129-138 ◽  
Author(s):  
Tommi Borg ◽  
Esko J. Pääkkönen
Keyword(s):  
Viscoelastic Models ◽  
Linear Viscoelastic

Evaluation of molecular linear viscoelastic models for polydisperse H polybutadienes

2011 ◽  
Vol 55 (6) ◽  
pp. 1341-1373 ◽  
Author(s):  
Si Wan Li ◽  
Heon E. Park ◽  
John M. Dealy
Keyword(s):  
Viscoelastic Models ◽  
Linear Viscoelastic

scholarly journals Influence of cheese ripening on the viscoelastic behaviour of edam cheese

2013 ◽  
Vol 19 (No. 1) ◽  
pp. 1-7 ◽  
Author(s):  
J. Buchar ◽  
I. Kubiš ◽  
S. Gajdůšek ◽  
I. Křivánek
Keyword(s):  
Viscoelastic Properties ◽  
Rheological Model ◽  
Deformation Behaviour ◽  
Viscoelastic Body ◽  
Original Method ◽  
Cheese Ripening ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Pressure Bar

The paper deals with the study of the effect of cheese ripening on parameters of a rheological model of cheese mechanical behaviour. The Edam cheese has been tested by the method of the Hopkinson Split Pressure Bar. The original method of the evaluation of viscoelastic properties has been used. The rheological model of the three element linear viscoelastic body, so called “standard linear solid” has been used. This model successfully describes the experimentally observed deformation behaviour of cheese specimens. The effect of the time of cheese ripening on the parameters of the rheological model has been demonstrated.

On the Consistent Path Problem

2020 ◽  
Vol 68 (6) ◽  
pp. 1913-1931
Author(s):  
Leonardo Lozano ◽  
David Bergman ◽  
J. Cole Smith
Keyword(s):  
Linear Models ◽  
Linear Inequalities ◽  
Branch And Cut ◽  
Decision Diagrams ◽  
Decomposition Approach ◽  
Decomposition Scheme ◽  
Complexity Results ◽  
Standard Linear ◽  
Linear Relaxations

This paper studies a novel decomposition scheme, utilizing decision diagrams for modeling elements of a problem where typical linear relaxations fail to provide sufficiently tight bounds. Given a collection of decision diagrams, each representing a portion of the problem, together with linear inequalities modeling other portions of the problem, how can one efficiently optimize over such a representation? In this paper, we model the problem as a consistent path problem, where a path in each diagram has to be identified, all of which agree on the value assignments to variables. We establish complexity results and propose a branch-and-cut framework for solving the decomposition. Through application to binary cubic optimization and a variant of the market split problem, we show that the decomposition approach provides significant improvement gains over standard linear models.

scholarly journals Viscoelastic Characterization of Long-Eared Owl Flight Feather Shaft and the Damping Ability Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jia-li Gao ◽  
Jin-kui Chu ◽  
Le Guan ◽  
Hai-xin Shang ◽  
Zhen-kun Lei
Keyword(s):  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Golden Eagle ◽  
Flight Feather ◽  
Column Material ◽  
Significant Difference ◽  
Single Column ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear

Flight feather shaft of long-eared owl is characterized by a three-parameter model for linear viscoelastic solids to reveal its damping ability. Uniaxial tensile tests of the long-eared owl, pigeon, and golden eagle flight feather shaft specimens were carried out based on Instron 3345 single column material testing system, respectively, and viscoelastic response of their stress and strain was described by the standard linear solid model. Parameter fitting result obtained from the tensile tests shows that there is no significant difference in instantaneous elastic modulus for the three birds’ feather shafts, but the owl shaft has the highest viscosity, implying more obvious viscoelastic performance. Dynamic mechanical property was characterized based on the tensile testing results. Loss factor (tanδ) of the owl flight feather shaft was calculated to be 1.609 ± 0.238, far greater than those of the pigeon (0.896 ± 0.082) and golden eagle (1.087 ± 0.074). It is concluded that the long-eared owl flight feather has more outstanding damping ability compared to the pigeon and golden eagle flight feather shaft. Consequently, the long-eared owl flight feathers can dissipate the vibration energy more effectively during the flying process based on the principle of damping mechanism, for the purpose of vibration attenuation and structure radiated noise reduction.

Viscoelastic Properties of Soft Tissue by Discrete Model Characterization

1968 ◽  
Vol 90 (2) ◽  
pp. 239-247 ◽  
Author(s):  
C. E. Jamison ◽  
R. D. Marangoni ◽  
A. A. Glaser
Keyword(s):  
Experimental Technique ◽  
Human Body ◽  
Biological Tissues ◽  
Viscoelastic Models ◽  
Pig Skin ◽  
Viscoelastic Parameters ◽  
Body Tissues ◽  
Mathematical Equations ◽  
Viscoelastic Modeling ◽  
Injury Research

In order to study the response of the human body to acceleration and force, it is necessary to be able to relate force to deformation in various body tissues. Problems wherein this becomes essential include aerospace travel, crash injury research, and shock/vibration environments produced by mechanical systems. Since the tissues within the human body are viscoelastic in nature, it is important to apply proper viscoelastic relations when investigating the mechanics of deformation. This paper discusses on experimental technique for obtaining discrete viscoelastic models of soft biological tissues. The application of this experimental technique, using guinea pig skin as an example, is presented along with numerical results for the various viscoelastic parameters. A discussion of discrete viscoelastic modeling and the necessary mathematical equations for relating deformation to force is also included.

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