Planar problem of the impact of a shell on an elastic half-space

1995 ◽  
Vol 31 (6) ◽  
pp. 483-490 ◽  
Author(s):  
V. D. Kubenko ◽  
V. R. Bogdanov
Keyword(s):  
Half Space ◽  
Elastic Half Space ◽  
Planar Problem ◽  
The Impact

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

scholarly journals One approach to the axisymmetric problem of impact of fine shells of the S.P. Timoshenko type on elastic half-space

2021 ◽  
pp. 77-89
Author(s):  
Vladislav Bogdanov
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Axisymmetric Problem ◽  
Infinite System ◽  
Elastic Half Space ◽  
Wave Processes ◽  
System Of Integral Equations ◽  
Timoshenko Type ◽  
Dynamics Problems ◽  
The Impact

Refined model of S.P. Timoshenko makes it possible to consider the shear and the inertia rotation of the transverse section of the shell. Disturbances spread in the shells of S.P. Timoshenko type with finite speed. Therefore, to study the dynamics of propagation of wave processes in the fine shells of S.P. Timoshenko type is an important aspect as well as it is important to investigate a wave processes of the impact, shock in elastic foundation in which a striker is penetrating. The method of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind and the convergence of this solution are well studied. Such approach has been successfully used for cases of the investigation of problems of the impact a hard bodies and an elastic fine shells of the Kirchhoff-Love type on elastic a half-space and a layer. In this paper an attempt is made to solve the axisymmetric problem of the impact of an elastic fine spheric shell of the S.P. Timoshenko type on an elastic half-space using the method of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind. It is shown that this approach is not acceptable for investigated in this paper axisymmetric problem. The discretization using the Gregory methods for numerical integration and Adams for solving the Cauchy problem of the reduced infinite system of Volterra equations of the second kind results in a poorly defined system of linear algebraic equations: as the size of reduction increases the determinant of such a system to aim at infinity. This technique does not allow to solve plane and axisymmetric problems of dynamics for fine shells of the S.P. Timoshenko type and elastic bodies. This shows the limitations of this approach and leads to the feasibility of developing other mathematical approaches and models. It should be noted that to calibrate the computational process in the elastoplastic formulation at the elastic stage, it is convenient and expedient to use the technique of the outcoming dynamics problems to solve an infinite system of integral equations Volterra of the second kind.

The Normal Impact on an Elastic Half Space of an Elastic Rod-Mass System

1987 ◽  
Vol 54 (2) ◽  
pp. 359-366 ◽  
Author(s):  
H. A. Downey ◽  
D. B. Bogy
Keyword(s):  
Integral Equation ◽  
Closed Form ◽  
Half Space ◽  
Contact Stress ◽  
Elastic Half Space ◽  
Elastic Rod ◽  
Lumped Mass ◽  
Normal Impact ◽  
Mass System ◽  
The Impact

The normal impact problem of a one-dimensional elastic rod with a lumped mass on the trailing end onto an elastic half space is solved for the time-dependent interface displacement and stress. This problem is reduced to an integral equation, whose kernel is the solution of a simpler auxiliary problem, which is solved in closed form. After examining the graph of the kernel it is found that a simple linear expression adequately represents its half space contribution. This approximation allows the integral equation to be solved in closed form and provides insight into its solution. Numerical results are presented, which display the impact and rebound of the rod, and illustrate the presence of major effects from the Rayleigh wave in the half space and the reflected wave from the trailing end of the rod. Results are presented for various half-space materials, rod lengths, and masses. It is found that in the absence of the mass the maximum contact stress depends entirely on the rod material, but with the lumped mass added the contact stress can become much greater and depends on the rod, the half space, and the mass.

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