Rebound of a rigid body falling on an elastic half-space

1969 ◽  
Vol 7 (5) ◽  
pp. 126-128 ◽  
Author(s):  
I. V. Simonov ◽  
L. M. Flitman
Keyword(s):  
Rigid Body ◽  
Half Space ◽  
Elastic Half Space

scholarly journals Contact Response Analysis of Vertical Impact between Elastic Sphere and Elastic Half Space

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yang Yang ◽  
Qingliang Zeng ◽  
Lirong Wan
Keyword(s):  
Rigid Body ◽  
Half Space ◽  
Contact Process ◽  
Elastic Half Space ◽  
Metal Plate ◽  
3D Simulation ◽  
Elastic Sphere ◽  
Research Results ◽  
Contact Response ◽  
Vertical Impact

At present, the contact problem between the particle and the plane plate is generally equivalent to the rigid sphere impacting the elastic half space or the elastic sphere impacting the rigid surface. However, in the actual contact process, there will be no rigid body, and both contact and contacted object will deform and absorb energy. The research results obtained from the equivalent of the contact material to the rigid body are less accurate. In order to obtain the accurate mechanical relation and contact response, we took the research of impact between particles and the metal plate as a breakthrough in which the particle is equivalent to an elastic sphere and the metal plate is equivalent to an elastic half space and established the theory of vertical impact contact between elastic sphere and elastic half space by the Hertz contact theory. Through the dynamic simulation of an elastic sphere which has similar properties with rock impacting target in elastic half space in LS-DYNA, the correctness of the established theory and the feasibility of the contact process simulated by LS-DYNA are verified. Based on the established theory and 3D simulation, we studied the influence law of material parameters on the contact response and analyzed the differences of the collision vibration signals caused by the different contact objects. From the above research results, we obtain that the theoretical model is more accurate to predict the maximum contact force and contact displacement in this paper than traditional Hertz theory. And the sphere radius and both contact objects’ elastic modulus have larger influence on the contact response than sphere density, while the Poisson’s ratio has the smallest influence on the contact response results. Different material properties will cause the different contact response. The conclusions of this paper provide a theoretical calculation method for contact and a 3D simulation method for elastic half space and provide theoretical guidance for the differences analysis of the vibration signal.

scholarly journals The use of modelling of impacts exerted by means of transport on the environment for ensuring safety

2018 ◽  
Vol 188 (2) ◽  
pp. 162-175
Author(s):  
Joanna Bril ◽  
Edward Rydygier
Keyword(s):  
Rigid Body ◽  
Half Space ◽  
Dynamic Properties ◽  
Elastic Half Space ◽  
Transport Systems ◽  
Concentrated Force ◽  
Foundation Soil ◽  
Infinite Mass ◽  
Model Research ◽  
Surface Rayleigh Wave

The article presents the model research on impacts exerted by means of transport on the structures. In modelling the dynamics of transport systems the dynamic properties of the ground forming the foundation soil for tracks or roadways have been taken into account. The ground has been modelled as an elastic half-space. The dynamics of an infinite mass band being in contact with an elastic half-space has been investigated. As part of the research on impacts exerted by means of transport on structures a model of a problem has been examined where an automotive vehicle, representing a concentrated force in motion, is in contact with a roadway described as a rigid body coupled with an elastic half-space. It has been demonstrated that a surface (Rayleigh) wave propagates in the ground, being a continuous (elastic) medium, and acts on a structure modelled as a rigid body. The research results have been presented in the form of vertical and horizontal transmittances of the ground for different frequencies of loading with different unit forces.

scholarly journals Two contact problems in anisotropic elasticity

1973 ◽  
Vol 15 (1) ◽  
pp. 35-41 ◽  
Author(s):  
D. L. Clements
Keyword(s):  
Rigid Body ◽  
Half Space ◽  
Early Stage ◽  
Contact Problems ◽  
Anisotropic Elasticity ◽  
Elastic Half Space ◽  
Restricted Class ◽  
General Anisotropy ◽  
Anisotropic Elastic ◽  
Fundamental Equations

In this paper we consider two contact problems for an anisotropic elastic half-space in which the stress is independent of one of the Cartesian co-ordinates. The results hold for the most general anisotropy in which no symmetry elements of the material are assumed. Problems of this type have been considered by Brilla [1], Clements [2], Galin [3], Green and Zerna [4] and Milne-Thomson [5], but the work of these authors is only applicable to a restricted class of anisotropic materials. We begin in section 1 by deriving some fundamental equations for the stress and displacement. It will be noted that at an early stage (equation (7)) the roots of a sextic polynomial are required. Since these cannot be obtained explicitly any application of the general theory must, of necessity, be numerical. However the calculation of the stress and displacement is simplified if certain symmetry elements of the material are assumed and the way in which these simplifications occur is indicated in section 2. In sections 3 and 4 we consider contact problems in which the elastic half-space is indented by a rigid body. For the problem considered in section 3, the rigid body is assumed to be able to move relative to the surface of the half-space, while for the problem considered in section 4 it is assumed to be linked to the half-space.

Impact of a Rigid Body on an Elastic Half Space

1977 ◽  
Vol 44 (2) ◽  
pp. 227-230 ◽  
Author(s):  
G. N. Bycroft
Keyword(s):  
Steady State ◽  
Rigid Body ◽  
Half Space ◽  
Frequency Factor ◽  
Elastic Half Space ◽  
Rigid Plate ◽  
Fourier Synthesis ◽  
Satisfactory Solution ◽  
Circular Area

A Fourier synthesis of the steady-state vibrations of a rigid plate on an elastic half space is used to determine the deceleration and penetration of a rigid body impacting an elastic half space over a flat circular area. In order to obtain a satisfactory solution, it is necessary to integrate to a large value of the frequency factor. The theoretical values are compared with some simple experiments on lead and Neoprene.

Continuous Bond Failure Due to a Moving Force

1973 ◽  
Vol 40 (2) ◽  
pp. 541-545 ◽  
Author(s):  
A. Jahanshahi
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Half Space ◽  
Stationary Solution ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Bond Failure ◽  
Moving Force ◽  
Line Force

Within the framework of the two-dimensional theory of elastodynamics a closed-form, quasi-stationary, solution is given to the problem of continuous failure of bond between an elastic half space and a rigid body. The bond failure is due to a line force moving at the interface.

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