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 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 Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

scholarly journals Dynamics of inhomogeneous elastic half-space under moving load

2019 ◽  
Vol 97 ◽  
pp. 05048
Author(s):  
Bakhtiyor Yuldashev ◽  
Sagdulla Abdukadirov
Keyword(s):  
Half Space ◽  
Numerical Solutions ◽  
Moving Load ◽  
Elastic Base ◽  
Elastic Half Space ◽  
Thin Elastic Plate ◽  
Wave Processes ◽  
Load Effect ◽  
Time Period ◽  
Resonant Processes

Wave processes in an elastic half-space covered with an elastic layer and (or) a thin elastic plate are considered in the paper. External load moves along the free surface. In the stationary statement, the waveguide properties of the system are determined. The multiple roots of the dispersion equations are revealed and the critical load velocities, leading to the initiation of resonant processes, are determined. In the case when the load moves with the velocity of the Rayleigh wave, additional resonances determined by the structure can be realized in the structure under consideration. It is revealed that Rayleigh resonance exists for long waves only. Numerical solutions are obtained that make it possible to trace the development of resonant excitations. The models of simple structures that have dispersive properties in the medium wave zone are analyzed, such as a thin plate on an elastic base; a model with an attached inertial medium. Analytical solutions have been obtained for these models. Computer simulations conducted simultaneously allow us to analyze the quantitative features of process throughout the entire time period of the load effect. The numerical and asymptotic solutions are compared.

scholarly journals Fixed-Point Results for Generalized α -Admissible Hardy-Rogers’ Contractions in Cone b 2 -Metric Spaces over Banach’s Algebras with Application

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziaul Islam ◽  
Muhammad Sarwar ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Infinite System ◽  
Metric Spaces ◽  
Existence Of A Solution ◽  
System Of Integral Equations

In the current manuscript, the notion of a cone b 2 -metric space over Banach’s algebra with parameter b ≻ ¯ e is introduced. Furthermore, using α -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

scholarly journals Symmetry and Nonexistence of Positive Solutions for Weighted HLS System of Integral Equations on a Half Space

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Linfen Cao ◽  
Zhaohui Dai
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Positive Solutions ◽  
Type Theorem ◽  
Integral Form ◽  
System Of Integral Equations ◽  
Method Of Moving Planes ◽  
Rotationally Symmetric ◽  
Moving Planes ◽  
Pohozaev Type Identity

We consider system of integral equations related to the weighted Hardy-Littlewood-Sobolev (HLS) inequality in a half space. By the Pohozaev type identity in integral form, we present a Liouville type theorem when the system is in both supercritical and subcritical cases under some integrability conditions. Ruling out these nonexistence results, we also discuss the positive solutions of the integral system in critical case. By the method of moving planes, we show that a pair of positive solutions to such system is rotationally symmetric aboutxn-axis, which is much more general than the main result of Zhuo and Li, 2011.

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