Modelling Damping in Computer Simulations: Is All Damping Viscous?

2011 ◽  
Author(s):  
Hugh Goyder
Keyword(s):  
Computer Simulations ◽  
First Principles ◽  
Damping Force ◽  
Lagrange’S Equation ◽  
Starting Point ◽  
Air Resistance ◽  
Viscoelastic Effects ◽  
Dissipation Model ◽  
Dynamic Components ◽  
Damping Model

The standard damping model is the viscous dashpot for which the damping force is proportional to velocity. However, this simple model seems not to reflect real conditions where there may be viscoelastic effects, friction or air resistance. No general models for damping are available that can be developed from first principles and used in computer simulations. To help with this difficulty the fundamental theory that should underpin any general damping model is assembled here. The only available formulation for damping in mechanics is the Rayleigh dissipation model that can be used with Lagrange’s equation. This model is strictly viscous and linear. The possibility of using this model for all damping circumstances is examined. A starting point for the development of a theory is the need for causality. This need is used to formulate the concept of a pure dashpot (i.e. not mixed with other dynamic components) which is shown to be viscous. Furthermore in order to represent damping in general it is necessary to embed the viscous dashpot with other mechanical components which are not dissipative and are either linear or nonlinear. It appears that even for non-linear systems the only form of damper that is possible is the linear viscous dashpot.

scholarly journals Equation of state of hot, dense magnesium derived with first-principles computer simulations

2020 ◽  
Vol 27 (9) ◽  
pp. 092706 ◽  
Author(s):  
Felipe González-Cataldo ◽  
François Soubiran ◽  
Burkhard Militzer
Keyword(s):  
Equation Of State ◽  
Computer Simulations ◽  
First Principles

A Nonlinear Leg Damping Model for the Prediction of Running Forces and Stability

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Ian Abraham ◽  
ZhuoHua Shen ◽  
Justin Seipel
Keyword(s):  
Ground Reaction Force ◽  
Reaction Force ◽  
Energetic Cost ◽  
Ground Reaction Forces ◽  
Slip Model ◽  
Damping Force ◽  
Reaction Forces ◽  
Linear Damping ◽  
The Stability ◽  
Damping Model

Despite the neuromechanical complexity underlying animal locomotion, the steady-state center-of-mass motions and ground reaction forces of animal running can be predicted by simple spring-mass models such as the canonical spring-loaded inverted pendulum (SLIP) model. Such SLIP models have been useful for the fields of biomechanics and robotics in part because ground reaction forces are commonly measured and readily available for comparing with model predictions. To better predict the stability of running, beyond the canonical conservative SLIP model, more recent extensions have been proposed and investigated with hip actuation and linear leg damping (e.g., hip-actuated SLIP). So far, these attempts have gained improved prediction of the stability of locomotion but have led to a loss of the ability to accurately predict ground reaction forces. Unfortunately, the linear damping utilized in current models leads to an unrealistic prediction of damping force and ground reaction force with a large nonzero magnitude at touchdown (TD). Here, we develop a leg damping model that is bilinear in leg length and velocity in order to yield improved damping force and ground reaction force prediction. We compare the running ground reaction forces, small and large perturbation stability, parameter sensitivity, and energetic cost resulting from both the linear and bilinear damping models. We found that bilinear damping helps to produce more realistic, smooth vertical ground reaction forces, thus fixing the current problem with the linear damping model. Despite large changes in the damping force and power loss profile during the stance phase, the overall dynamics and energetics on a stride-to-stride basis of the two models are largely the same, implying that the integrated effect of damping over a stride is what matters most to the stability and energetics of running. Overall, this new model, an actuated SLIP model with bilinear damping, can provide significantly improved prediction of ground reaction forces as well as stability and energetics of locomotion.

A New Damping Model for Non-Linear Stiffness Systems With Variable Preload Displacements and Constant Amplitude Decay Ratios

1992 ◽  
Author(s):  
T. Xu ◽  
G. G. Lowen
Keyword(s):  
Energy Loss ◽  
Mathematical Description ◽  
Damping Coefficient ◽  
Constant Amplitude ◽  
Damping Force ◽  
Non Linear ◽  
Linear Damping ◽  
Damping Model ◽  
Good Agreement

Abstract This study of the behavior of non-linear stiffness systems with variable preload displacements and constant amplitude decay ratios showed that the energy loss per cycle is dependent on these preload displacements. By introducing a non-linear damping force, which is a function of both displacement and velocity, the associated work per cycle can be made approximately the same function of the preload displacement as is the case for the energy loss. In this manner, it becomes possible to make the resulting damping coefficient essentially independent of the preload displacement. This new damping model was incorporated into the mathematical description of an over-running sprag clutch. Confirming experimentation showed very good agreement with computed results.

scholarly journals Theoretical Analysis and Experimental Verification of Particle Damper-Based Energy Dissipation with Applications to Reduce Structural Vibration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Wangqiang Xiao ◽  
Lina Jin ◽  
Binqiang Chen
Keyword(s):  
Energy Dissipation ◽  
Simulation Model ◽  
Particle Density ◽  
Structural Vibration ◽  
Practical Application ◽  
Air Resistance ◽  
Optimal Damping ◽  
Particle Damping ◽  
Dissipation Model ◽  
Particle Parameters

Particle damping technology can greatly reduce vibration of equipment and structure through friction and inelastic collisions of particles. An energy dissipation model for particle damper has been presented based on the powder mechanics and the collision theory. The energy dissipation equations of friction and collision motion are developed for the particle damper. The rationality of energy dissipation model has been verified by the experiment and the distributions for the energy dissipation of particles versus acceleration are nonlinear. As the experiment process includes lots of factors of energy dissipation, such as the noise and the air resistance, the experimental value is about 7% more than the simulation value. The simulation model can provide an effective method for the design of particle damper. And the particle parameters for damper have been investigated. The results have shown that choosing an appropriate particle density, particle size, and particle filling rate determined based on the simulation model will provide the optimal damping effect for the practical application of particle damping technology.

Experimental Validation of Two Damping Force Models for the ANCF

2007 ◽  
Author(s):  
Hyun-Woo Kim ◽  
Wan-Suk Yoo ◽  
Jeong-Hyun Sohn
Keyword(s):  
Computer Simulations ◽  
Experimental Validation ◽  
Large Deformations ◽  
Absolute Nodal Coordinate Formulation ◽  
Experimental Measurements ◽  
Damping Force ◽  
Absolute Nodal Coordinate ◽  
Elastic Bodies ◽  
Physical Experiments ◽  
Quadratic Damping

Many researchers have studied computer-aided simulations of elastic bodies undergoing large deflections and large deformations. But there have been few attempts to validate the numerical formulations used in these studies. The main aim of this paper is to validate the absolute nodal coordinate formulation (ANCF) by comparing the results to experimental measurements on beams. Physical experiments with a highspeed camera were carried out to capture the large displacement of the beam and to verify the results of computer simulations. To consider the damping forces, Rayleigh’s damping and quadratic damping are employed and compared to the experimental results. Numerical results obtained from computer simulations were compared with the results from the physical experiments according to the 1st mode and the 2nd mode of the beam, respectively.

Modal Analysis of Nonviscously Damped Beams

2006 ◽  
Vol 74 (5) ◽  
pp. 1026-1030 ◽  
Author(s):  
S. Adhikari ◽  
M. I. Friswell ◽  
Y. Lei
Keyword(s):  
Natural Frequencies ◽  
Past History ◽  
Kernel Functions ◽  
Mode Shapes ◽  
Damping Force ◽  
The Past ◽  
Convolution Integrals ◽  
Special Cases ◽  
History Of ◽  
Damping Model

Linear dynamics of Euler–Bernoulli beams with nonviscous nonlocal damping is considered. It is assumed that the damping force at a given point in the beam depends on the past history of velocities at different points via convolution integrals over exponentially decaying kernel functions. Conventional viscous and viscoelastic damping models can be obtained as special cases of this general damping model. The equation of motion of the beam with such a general damping model results in a linear partial integro-differential equation. Exact closed-form equations of the natural frequencies and mode shapes of the beam are derived. Numerical examples are provided to illustrate the new results.

scholarly journals Nonideal mixing effects in warm dense matter studied with first-principles computer simulations

2020 ◽  
Vol 153 (18) ◽  
pp. 184101
Author(s):  
Burkhard Militzer ◽  
Felipe González-Cataldo ◽  
Shuai Zhang ◽  
Heather D. Whitley ◽  
Damian C. Swift ◽  
...  
Keyword(s):  
Computer Simulations ◽  
First Principles ◽  
Dense Matter ◽  
Warm Dense Matter ◽  
Mixing Effects
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