Models for Materials Damping, Loss Factor, and Coefficient of Restitution

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Hany A. Sherif ◽  
Fahad. A. Almufadi
Keyword(s):  
Loss Factor ◽  
Polymeric Materials ◽  
Theoretical Models ◽  
Coefficient Of Restitution ◽  
Complex Model ◽  
Damping Coefficient ◽  
Damping Factor ◽  
Simple Method ◽  
Adopted Model ◽  
The Impact

Common parameters between metallic and polymeric materials are the coefficient of restitution, the damping coefficient, and loss factor. Although the relationship between the coefficient of restitution and the loss factor is quite direct, their dependence on the damping coefficient is not so simple and mainly affected by the adopted model used to describe the material response under impact. In the present study, Kelvin–Voigt linear model and Hunt–Crossley complex model are analyzed to describe how the coefficient of restitution depends on the viscous damping coefficient of impact. The correlation between the theoretical models and the experimental data is also shown. A simple method to predict the impact damping factor of both polymeric and metallic materials from the measured temporal signal of the impact force is demonstrated.

Polymer Modulus of Elasticity and Hardness From Impact Data

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Hany A. Sherif ◽  
Fahad A. Almufadi
Keyword(s):  
Modulus Of Elasticity ◽  
Complex Modulus ◽  
Polymeric Materials ◽  
Time Duration ◽  
Simple Method ◽  
Normal Contact ◽  
Adopted Model ◽  
Force Time ◽  
Impact Data ◽  
The Impact

The present paper introduces a simple method to predict the modulus of elasticity and the hardness of polymeric materials that range from soft elastomers to hard plastics. Hertzian elastic impact model is used to define the relationship between the contact time duration and the maximum force of normal contact due to the impact of a hard sphere indenter with the tested polymer sample. It is shown that the adopted model and experimental method can be used as a tool for extracting the magnitude of the complex modulus of elasticity. Moreover, a new impact index is shown to be proportional to the polymer shore hardness. Theoretical and experimental results based on the force–time signals are consistent and show good correlation.

Dynamics and Performance of a Harmonically Excited Vertical Impact Damper

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Sanjiv Ramachandran ◽  
George Lesieutre
Keyword(s):  
Loss Factor ◽  
Vertical Direction ◽  
Theoretical Models ◽  
Coefficient Of Restitution ◽  
Numerical Continuation ◽  
Particle Impact ◽  
Impact Damper ◽  
High Loss ◽  
Wide Range ◽  
And Performance

Particle impact dampers (PIDs) have been shown to be effective in vibration damping. However, our understanding of such dampers is still limited, based on the theoretical models existing today. Predicting the performance of the PID is an important problem, which needs to be investigated more thoroughly. This research seeks to understand the dynamics of a PID as well as those parameters which govern its behavior. The system investigated is a particle impact damper with a ceiling, under the influence of gravity. The base is harmonically excited in the vertical direction. A two-dimensional discrete map is obtained, wherein the variables at one impact uniquely dictate the variables at the next impact. This map is solved using a numerical continuation procedure. Periodic impact motions and “irregular” motions are observed. The effects of various parameters such as the gap clearance, coefficient of restitution, and the base acceleration are analyzed. The dependence of the effective damping loss factor on these parameters is also studied. The loss factor results indicate peak damping for certain combinations of parameters. These combinations of parameters correspond to a region in parameter space where two-impacts-per-cycle motions are observed over a wide range of nondimensional base accelerations. The value of the nondimensional acceleration at which the onset of two-impacts-per-cycle solutions occurs depends on the nondimensional gap clearance and the coefficient of restitution. The range of nondimensional gap clearances over which two-impacts-per-cycle solutions are observed increases as the coefficient of restitution increases. In the regime of two-impacts-per-cycle solutions, the value of nondimensional base acceleration corresponding to onset of these solutions initially decreases and then increases with increasing nondimensional gap clearance. As the two-impacts-per-cycle solutions are associated with high loss factors that are relatively insensitive to changing conditions, they are of great interest to the designer.

scholarly journals Optimal damping coefficient for a class of continuous contact models

2020 ◽  
Vol 50 (2) ◽  
pp. 169-188
Author(s):  
Mohammad Poursina ◽  
Parviz E. Nikravesh
Keyword(s):  
Contact Force ◽  
Analytical Formula ◽  
Coefficient Of Restitution ◽  
Damping Coefficient ◽  
Optimization Strategy ◽  
Continuous Contact ◽  
Optimal Damping ◽  
Wide Range ◽  
Contact Models ◽  
The Impact

Abstract In this study, we develop an analytical formula to approximate the damping coefficient as a function of the coefficient of restitution for a class of continuous contact models. The contact force is generated by a logical point-to-point force element consisting of a linear damper connected in parallel to a spring with Hertz force–penetration characteristic, while the exponent of deformation of the Hertz spring can vary between one and two. In this nonlinear model, it is assumed that the bodies start to separate when the contact force becomes zero. After separation, either the restitution continues or a permanent penetration is achieved. Therefore, this model is capable of addressing a wide range of impact problems. Herein, we apply an optimization strategy on the solution of the equations governing the dynamics of the penetration, ensuring that the desired restitution is reproduced at the time of separation. Furthermore, based on the results of the optimization process along with analytical investigations, the resulting optimal damping coefficient is analytically expressed at the time of impact in terms of system properties such as the effective mass, penetration velocity just before the impact, coefficient of restitution, and the characteristics of the Hertz spring model.

Validation of Nonlinear Viscoelastic Contact Force Models for Low Speed Impact

2009 ◽  
Vol 76 (5) ◽  
Author(s):  
Yuning Zhang ◽  
Inna Sharf
Keyword(s):  
Contact Force ◽  
Nonlinear Damping ◽  
Coefficient Of Restitution ◽  
Contact Dynamics ◽  
Dynamics Simulation ◽  
Damping Coefficient ◽  
Force Model ◽  
Nonlinear Viscoelastic ◽  
The Impact ◽  
Viscoelastic Contact

Compliant contact force modeling has become a popular approach for contact and impact dynamics simulation of multibody systems. In this area, the nonlinear viscoelastic contact force model developed by Hunt and Crossley (1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42, pp. 440–445) over 2 decades ago has become a trademark with applications of the model ranging from intermittent dynamics of mechanisms to engagement dynamics of helicopter rotors and implementations in commercial multibody dynamics simulators. The distinguishing feature of this model is that it employs a nonlinear damping term to model the energy dissipation during contact, where the damping coefficient is related to the coefficient of restitution. Since its conception, the model prompted several investigations on how to evaluate the damping coefficient, in turn resulting in several variations on the original Hunt–Crossley model. In this paper, the authors aim to experimentally validate the Hunt–Crossley type of contact force models and furthermore to compare the experimental results to the model predictions obtained with different values of the damping coefficient. This paper reports our findings from the sphere to flat impact experiments, conducted for a range of initial impacting velocities using a pendulum test rig. The unique features of this investigation are that the impact forces are deduced from the acceleration measurements of the impacting body, and the experiments are conducted with specimens of different yield strengths. The experimental forces are compared with those predicted from the contact dynamics simulation of the experimental scenario. The experiments, in addition to generating novel impact measurements, provide a number of insights into both the study of impact and the impact response.

Shape and Frequency Composition of Pulses From an Impact Pair

1977 ◽  
Vol 99 (3) ◽  
pp. 513-518 ◽  
Author(s):  
R. G. Herbert ◽  
D. C. McWhannell
Keyword(s):  
Power Law ◽  
High Frequency ◽  
Coefficient Of Restitution ◽  
Damping Coefficient ◽  
Direct Solution ◽  
Impact Pulse ◽  
Surface Stiffness ◽  
Articulated Systems ◽  
Nonlinear Surface ◽  
The Impact

With the need to improve the reliability and noise emissions from real mechanisms, an impact in the classical impact pair configuration is investigated considering the impact pulse level and its frequency composition as possible sources of high-frequency energy in articulated systems. The analog representation of the impact pair uses a nonlinear surface stiffness together with a nonlinear surface damping. Developments of the Dubowsky model carried out by Crossley are further extended to allow the surface damping coefficient, as a function of the coefficient of restitution, to be calculated assuming energy is dissipated throughout the impact for any series power law representation of the surface stiffness. The practical system used by Veluswami is simulated, and the results for Dubowsky, Crossley, and the direct solution are compared to Veluswami’s practical data.

scholarly journals Design and development of a vortex ring generator to study the impact of the ring as a gust

2020 ◽  
Author(s):  
Dipendra Gupta ◽  
Sanjay P. Sane ◽  
Jaywant H. Arakeri
Keyword(s):  
Reynolds Number ◽  
Vortex Ring ◽  
Aquatic Plant ◽  
Theoretical Models ◽  
Flow Properties ◽  
Simple Method ◽  
Wing Chord ◽  
The Impact ◽  
Bead Method ◽  
Gust Response

ABSTRACTWe present a simple method to generate discrete aerodynamic gust under controlled laboratory condition in the form of a vortex ring which, unlike conventional methods of perturbation, is well studied and highly controllable. We characterized the flow properties of the vortex ring using flow visualization and novel light bead method. Reynolds number of the vortex ring, based on its average propagation velocity and nozzle exit diameter, was 16000. We demonstrate this method by studying the impact of head-on gust on freely flying soldier flies, Reynolds number of which, based on its wingtip velocity and mean wing chord, was 1100. We also present simple theoretical models to characterize the vortex ring based on generating conditions. The device can also be used to generate continuous gust in any direction and can be applied, in general, to study the gust response of natural fliers and swimmers, man-made micro aerial vehicles and aquatic plant lives.

The Effects of Employment Protection legislationon Personnel Policies: A Review of Theoretical Modelsand Empirical results

2014 ◽  
pp. 126-140
Author(s):  
O. Mironenko
Keyword(s):  
Personnel Selection ◽  
Selection Criteria ◽  
Theoretical Models ◽  
Employment Protection ◽  
Empirical Results ◽  
Protection Legislation ◽  
Labour Contracts ◽  
Hiring And Firing ◽  
The Impact ◽  
Personnel Policies

Employers incur costs while fulfilling the requirements of employment protection legislation. The article contains a review of the core theoretical models and empirical results concerning the impact of these costs on firms’ practices in hiring, firing, training and remuneration. Overall, if wages are flexible or enforcement is weak, employment protection does not significantly influence employers’ behavior. Otherwise, stringent employment protection results in the reduction of hiring and firing rates, changes in personnel selection criteria, types of labour contracts and dismissal procedures, and, in some cases, it may lead to the growth of wages and firms’ investments to human capital.

scholarly journals A Rational Numerical Method for Simulation of Drop-Impact Dynamics of Oleo-Pneumatic Landing Gear

2021 ◽  
Vol 11 (9) ◽  
pp. 4136
Author(s):  
Rosario Pecora
Keyword(s):  
Numerical Method ◽  
Initial Conditions ◽  
Impact Load ◽  
Numerical Models ◽  
Landing Gear ◽  
Design Stage ◽  
Impact Dynamics ◽  
State Variables ◽  
Adopted Model ◽  
The Impact

Oleo-pneumatic landing gear is a complex mechanical system conceived to efficiently absorb and dissipate an aircraft’s kinetic energy at touchdown, thus reducing the impact load and acceleration transmitted to the airframe. Due to its significant influence on ground loads, this system is generally designed in parallel with the main structural components of the aircraft, such as the fuselage and wings. Robust numerical models for simulating landing gear impact dynamics are essential from the preliminary design stage in order to properly assess aircraft configuration and structural arrangements. Finite element (FE) analysis is a viable solution for supporting the design. However, regarding the oleo-pneumatic struts, FE-based simulation may become unpractical, since detailed models are required to obtain reliable results. Moreover, FE models could not be very versatile for accommodating the many design updates that usually occur at the beginning of the landing gear project or during the layout optimization process. In this work, a numerical method for simulating oleo-pneumatic landing gear drop dynamics is presented. To effectively support both the preliminary and advanced design of landing gear units, the proposed simulation approach rationally balances the level of sophistication of the adopted model with the need for accurate results. Although based on a formulation assuming only four state variables for the description of landing gear dynamics, the approach successfully accounts for all the relevant forces that arise during the drop and their influence on landing gear motion. A set of intercommunicating routines was implemented in MATLAB® environment to integrate the dynamic impact equations, starting from user-defined initial conditions and general parameters related to the geometric and structural configuration of the landing gear. The tool was then used to simulate a drop test of a reference landing gear, and the obtained results were successfully validated against available experimental data.

scholarly journals Transport Properties of Natural and Artificial Smart Fabrics Impregnated by Graphite Nanomaterial Stacks

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 1018
Author(s):  
Carola Esposito Corcione ◽  
Francesca Ferrari ◽  
Raffaella Striani ◽  
Antonio Greco
Keyword(s):  
Electrical Conductivity ◽  
Transport Properties ◽  
Low Cost ◽  
Empirical Relationship ◽  
Theoretical Models ◽  
Expandable Graphite ◽  
Easy Method ◽  
Textile Materials ◽  
Fabric Materials ◽  
The Impact

In this work, we studied the transport properties (thermal and electrical conductivity) of smart fabric materials treated with graphite nanomaterial stacks–acetone suspensions. An innovative and easy method to produce graphite nanomaterial stacks–acetone-based formulations, starting from a low-cost expandable graphite, is proposed. An original, economical, fast, and easy method to increase the thermal and electrical conductivity of textile materials was also employed for the first time. The proposed method allows the impregnation of smart fabric materials, avoiding pre-coating of the fibers, thus reducing costs and processing time, while obtaining a great increase in the transport properties. Two kinds of textiles, cotton and Lycra®, were selected as they represent the most used natural and artificial fabrics, respectively. The impact of the dimensions of the produced graphite nanomaterial stacks–acetone-based suspensions on both the uniformity of the treatment and the transport properties of the selected textile materials was accurately evaluated using several experimental techniques. An empirical relationship between the two transport properties was also successfully identified. Finally, several theoretical models were applied to predict the transport properties of the developed smart fabric materials, evidencing a good agreement with the experimental data.

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