The Impact of an Elastic Sphere on a Thin Elastic Plate Supported by a Winkler Foundation

1975 ◽  
Vol 42 (1) ◽  
pp. 133-135 ◽  
Author(s):  
H. D. Fisher
Keyword(s):  
Thin Plate ◽  
Contact Time ◽  
Viscoelastic Plate ◽  
Coefficient Of Restitution ◽  
Solution Technique ◽  
Rigid Sphere ◽  
Winkler Foundation ◽  
Thin Elastic Plate ◽  
Continuous Contact ◽  
The Impact

This paper investigates the elastic impact of a sphere on a thin plate which is in continuous contact with a foundation. The reaction pressure is considered to be proportional to the local deflection (Winkler hypothesis). A solution technique, which was originally developed to analyze the impact of a rigid sphere on a viscoelastic plate, is modified for application in the present study. The contact force, the coefficient of restitution, and the contact time are computed for a wide variation in the two dimensionless parameters which are required to describe a given problem. For the limiting cases of impact on a half space and impact on a thin plate supported by a rigid foundation, the contact time computed here is shown to correlate with the calculations of earlier investigators.

The Impact of the Conical Indenter on a Plate Laying on a Winkler Foundation

2018 ◽  
Vol 931 ◽  
pp. 84-90 ◽  
Author(s):  
Aleksey N. Beskopylny ◽  
Andrey A. Veremeenko ◽  
Elena E. Kadomtseva ◽  
Natalia I. Beskopylnaia
Keyword(s):  
Contact Time ◽  
Mechanical Characteristics ◽  
Strength Characteristics ◽  
Winkler Foundation ◽  
Building Structures ◽  
Dynamic Impact ◽  
Conical Indenter ◽  
Elastic Plastic ◽  
Plastic Indentation ◽  
The Impact

In the practice of civil engineering, the methods of impact diagnostics of materials find their application, allowing quickly and accurately measure the required strength characteristics at any point in the structure. Impact methods offer many advantages, for example, at smaller dimensions can be developed big the contact force, it can be recorded more information about the response of the material to dynamic impact and others. This approach is widely used in determining the hardness of materials and makes it possible to determine the complex mechanical characteristics: yield strength, ultimate strength, and elongation. In the paper we consider the axisymmetric problem of the impact of the conical indenter on the plate, laying on Winkler Foundation under elastic-plastic deformation. The solution is based on the phenomenological model of elastic-plastic indentation in a quasistatic formulation. The general deformations of the plate are considered elastic, and the local, in the contact zone, are elastoplastic. The main characteristics of the impact are determined: the force of the contact interaction, the local indentation, the contact time. The device and methods of determining the strength characteristics of plates under specified conditions of impact were developed on the basis of obtained solutions. The proposed method has been tested on many building structures: bridges, trusses, structural structures of artificial structures, reinforcement bars, welded joints.

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.

The Impact Between a Rigid Sphere and a Thin Layer

1970 ◽  
Vol 37 (1) ◽  
pp. 159-162 ◽  
Author(s):  
H. D. Conway ◽  
H. C. Lee ◽  
R. G. Bayer
Keyword(s):  
Thin Layer ◽  
Coefficient Of Restitution ◽  
Rigid Sphere ◽  
Approximate Analysis ◽  
Rigid Substrate ◽  
Perfectly Plastic ◽  
Major Loss ◽  
Elastic Perfectly Plastic ◽  
The Impact ◽  
Good Agreement

A simple model is presented for studying the impact between a rigid sphere and a thin layer of relatively soft material supported on a rigid substrate. By assuming that the major loss of energy during impact is due to the plastic deformation of the layer, an approximate analysis is made for computing the energy loss for layer materials which obey an elastic, perfectly plastic stress-strain law. An analytical expression for the coefficient of restitution is derived, and a parameter which controls the rebound characteristics is identified. Experimental results show generally good agreement with the analysis.

Experimental Investigations on the Coefficient of Restitution for Sphere–Thin Plate Elastoplastic Impact

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Deepak Patil ◽  
C. Fred Higgs
Keyword(s):  
Energy Dissipation ◽  
Thin Plate ◽  
Wall Thickness ◽  
Input Parameter ◽  
Contact Process ◽  
Infinite Plate ◽  
Coefficient Of Restitution ◽  
Experimental Investigations ◽  
Sphere Diameter ◽  
The Impact

In multiparticle simulations of industrial granular systems such as hoppers, tumblers, and mixers, the particle energy dissipation is governed by an important input parameter called the coefficient of restitution (COR). Oftentimes, the wall thickness in these systems is on the order of a particles diameter or less. However, the COR value implemented in event-driven simulations is either constant or a monotonically decreasing function of the impact velocity. The present work experimentally investigates the effect of wall thickness on the COR through sphere–thin plate elastoplastic impacts and elucidates the underlying impact phenomena. Experiments were performed on 0.635 cm and 0.476 cm diameter (d) spheres of various materials impacting aluminum 6061 plates of different thicknesses (t) with the low impact velocities up to 3.1 m/s. Besides COR, indentation measurements and numerical simulations are performed to gain a detailed understanding of the contact process and energy dissipation mechanism. As the “t/d” ratio decreases, a considerable amount of energy is dissipated into flexural vibrations leading to a significantly lower COR value. Based on the results, it can be concluded that using a constant COR input value in particle simulations may not always be an appropriate choice, especially, in the case of thin plates. However, these new COR results validate that when the wall thickness is more than twice the sphere diameter (i.e., t/d > 2), a constant COR value obtained for an impact with semi-infinite plate can be reasonably used.

Modelling of tennis ball impacts on a rigid surface

2004 ◽  
Vol 218 (10) ◽  
pp. 1139-1153 ◽  
Author(s):  
S R Goodwill ◽  
S J Haake
Keyword(s):  
Contact Time ◽  
Momentum Flux ◽  
Viscoelastic Model ◽  
Coefficient Of Restitution ◽  
Model Parameters ◽  
Total Force ◽  
Tennis Ball ◽  
Rigid Surface ◽  
Ball Impact ◽  
The Impact

A viscoelastic model of a tennis ball impact at normal incidence on a rigid surface is presented in this study. The ball model has three discrete elements that account for the structural stiffness, material damping and momentum flux loading. Experiments using a force platform are performed to determine the force that acts on the ball during impact, for a range of ball inbound velocities. The inbound and rebound velocities of the ball are measured using speed gates. The contact time and coefficient of restitution for the impact are also determined in these experiments. The model parameters are determined such that the values of the coefficient of restitution and contact time that are calculated by the model are consistent with those values determined experimentally. The model can be used to calculate the force that acts on the ball during impact. Generally, the force-time plots calculated by the model were consistent with those determined experimentally. Furthermore, the model can be used to calculate the three components of the force that acts on the ball during impact. It is shown that the main component of the force during the first 0.6 ms of impact is that due to momentum flux loading. This is approximately equal in magnitude for each ball type and explains why the total force acting on each ball is very similar during this period.

Impact of Particulate Matter on Distribution System Disinfection Efficacy

2008 ◽  
Vol 43 (1) ◽  
pp. 55-62 ◽  
Author(s):  
Linda Wojcicka ◽  
Carole Baxter ◽  
Ron Hofmann
Keyword(s):  
Helicobacter Pylori ◽  
Particulate Matter ◽  
Distribution System ◽  
Contact Time ◽  
Water Disinfection ◽  
Sphingomonas Paucimobilis ◽  
Soil Corrosion ◽  
Log Reduction ◽  
Drinking Water Disinfection ◽  
The Impact

Abstract Microorganisms have been shown to survive drinking water disinfection and remain viable in disinfected waters despite the presence of disinfectant residuals. This may be partially attributed to protection by particulate matter. The aim of this study was to determine the effects of the presence of particulate matter on disinfection kinetics. Sphingomonas paucimobilis ATCC 10829 and Helicobacter pylori ATCC 43504 were used in inactivation experiments in the presence and absence of soil, corrosion, and wastewater particles. The results showed that the presence of such particles tended to inhibit chlorine and monochloramine inactivation, although the magnitude of the impact under the conditions tested was small (e.g., 1-log reduction in inactivation for several minutes of contact time in the presence of less than 1 mg/L of disinfectant).

Ferro-nanofluid squeeze film lubrication with heat transfer

2021 ◽  
pp. 135065012110276
Author(s):  
Manimegalai Kavarthalai ◽  
Vimala Ponnuswamy
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Contact Time ◽  
Transfer Rate ◽  
Fluid Layer ◽  
Darcy Law ◽  
Squeeze Film ◽  
Mean Temperature ◽  
Special Cases ◽  
The Impact

A theoretical study of a squeezing ferro-nanofluid flow including thermal effects is carried out with application to bearings and articular cartilages. A representational geometry of the thin layer of a ferro-nanofluid squeezed between a flat rigid disk and a thin porous bed is considered. The flow behaviours and heat transfer in the fluid and porous regions are investigated. The mathematical problem is formulated based on the Neuringer–Rosensweig model for ferro-nanofluids in the fluid region including an external magnetic field, Darcy law for the porous region and Beavers–Joseph slip condition at the fluid–porous interface. The expressions for velocity, fluid film thickness, contact time, fluid flux, streamlines, pathlines, mean temperature and heat transfer rate in the fluid and porous regions are obtained by using a perturbation method. An asymptotic solution for the fluid layer thickness is also presented. The problem is also solved by a numerical method and the results by asymptotic analysis, perturbation and numerical methods are obtained assuming a constant force squeezing state and are compared. It is shown that the results obtained by all the methods agree well with each other. The effects of various parameters such as Darcy number, Beavers–Joseph constant and magnetization parameter on the flow behaviours, contact time, mean temperature and heat transfer rate are investigated. The novel results showing the impact of using ferro-nanofluids in the two applications under consideration are presented. The results under special cases are further compared with the existing results in the literature and are found to agree well.

scholarly journals Dynamics of Multibody Systems With Spherical Clearance Joints

2005 ◽  
Author(s):  
P. Flores ◽  
J. Ambro´sio ◽  
J. C. P. Claro ◽  
H. M. Lankarani
Keyword(s):  
Contact Force ◽  
Multibody Systems ◽  
Contact Forces ◽  
Force Model ◽  
Clearance Joints ◽  
Continuous Contact ◽  
Clearance Joint ◽  
Contact Force Model ◽  
Dynamics Of Multibody Systems ◽  
The Impact

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, being the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four bar mechanism is used as an illustrative example and some numerical results are presented, being the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

Study on Grinding Force in Two-Dimensional Ultrasonic Grinding Nano-Ceramics

2010 ◽  
Vol 42 ◽  
pp. 204-208 ◽  
Author(s):  
Xiang Dong Li ◽  
Quan Cai Wang
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Vibration ◽  
Contact Time ◽  
Reaction Force ◽  
Grinding Force ◽  
Two Dimensional ◽  
Indentation Fracture ◽  
Ultrasonic Grinding ◽  
The Impact ◽  
Ultrasonic Vibration Assisted Grinding

In this paper, the characteristic of grinding force in two-dimensional ultrasonic vibration assisted grinding nano-ceramic was studied by experiment based on indentation fracture mechanics, and mathematical model of grinding force was established. The study shows that grinding force mainly result from the impact of the grains on the workpiece in ultrasonic grinding, and the pulse power is much larger than normal grinding force. The ultrasonic vibration frequency is so high and the contact time of grains with the workpiece is so short that the pulse force will be balanced by reaction force from workpiece. In grinding workpiece was loaded by the periodical stress field, which accelerates the fatigue fracture.

scholarly journals Drops bouncing off macro-textured superhydrophobic surfaces

2017 ◽  
Vol 824 ◽  
pp. 866-885 ◽  
Author(s):  
Ali Mazloomi Moqaddam ◽  
Shyam S. Chikatamarla ◽  
Iliya V. Karlin
Keyword(s):  
Contact Time ◽  
Numerical Study ◽  
Three Dimensional ◽  
Superhydrophobic Surfaces ◽  
Nonlinear Behaviour ◽  
Textured Surfaces ◽  
Texture Density ◽  
Wide Range ◽  
Quantitative Manner ◽  
The Impact

Recent experiments with droplets impacting macro-textured superhydrophobic surfaces revealed new regimes of bouncing with a remarkable reduction of the contact time. Here we present a comprehensive numerical study that reveals the physics behind these new bouncing regimes and quantifies the roles played by various external and internal forces. For the first time, accurate three-dimensional simulations involving realistic macro-textured surfaces are performed. After demonstrating that simulations reproduce experiments in a quantitative manner, the study is focused on analysing the flow situations beyond current experiments. We show that the experimentally observed reduction of contact time extends to higher Weber numbers, and analyse the role played by the texture density. Moreover, we report a nonlinear behaviour of the contact time with the increase of the Weber number for imperfectly coated textures, and study the impact on tilted surfaces in a wide range of Weber numbers. Finally, we present novel energy analysis techniques that elaborate and quantify the interplay between the kinetic and surface energy, and the role played by the dissipation for various Weber numbers.

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