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1

Near-resonant regimes of a moving load on a pre-stressed incompressible elastic half-space

Kudaibergenov Askar, Kudaibergenov Askat, Prikazchikov Danila

Acta Mechanica et Automatica

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2021

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Vol. 15, no. 1

30--36

EN

The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

2

Extremes of order statistics of stationary Gaussian processes

Zhao C.

Probability and Mathematical Statistics

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2018

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Vol. 38, Fasc. 1

61--75

EN

Let {Xi(t), t ≥ 0}, 1 ≤ i ≤ n, be mutually independent and identically distributed centered stationary Gaussian processes. Under some mild assumptions on the covariance function, we derive an asymptotic expansion of P [formula] ]X(r) (t) ≤ u) as u → ∞, where mr(u) = (P([formula] X(r) (t) > u))−1 (1 + o(1)), and {X(r) (t), t ≥ 0} is the rth order statistic process of {Xi(t), t ≥ 0}, 1 ≤ i, r ≤ n. As an application of the derived result, we analyze the asymptotics of supremum of the order statistic process of stationary Gaussian processes over random intervals.

3

Asymptotic analysis of the clamped-pinned elastica

Singh P., Goss V. G. A.

Archives of Mechanics

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2018

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Vol. 70, nr 4

317--336

EN

Asymptotic solutions for the clamped-pinned elastica when the displacement of the pinned end is small (immediately after buckling) and when it approaches its limiting displacement (when the force in the rod tends to infinity) are presented. Simple leading order relationships describing the force as a function of the pinned end’s displacement are derived. Those approximate the force-displacement behaviour of the clamped-pinned elastica for small and limiting end displacements. All our results are valid for the clamped-pinned elastica in any mode.

4

Two-parametric analysis of anti-plane shear deformation of a coated elastic half-space

Sultanova L.

Acta Mechanica et Automatica

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2018

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Vol. 12, no. 4

270--275

EN

The anti-plane shear deformation problem of a half-space coated by a soft or a stiff thin layer is considered. The two-term asymptotic analysis is developed motivated by the scaling for the displacement and stress components obtained from the exact solution of a model problem for a shear harmonic load. It is shown that for a rather high contrast in stiffness of the layer and the half-space Winklertype behaviour appears for a relatively soft coating, while for a relatively stiff one, the equations of plate shear are valid. For low contrast, an alternative approximation is suggested based on the reduced continuity conditions and the fact that the applied load may be transmitted to the interface. In case of a stiff layer, a simpler problem for a homogeneous half-space with effective boundary condition is also formulated, modelling the effect of the coating, while for a relatively soft layer a uniformly valid approximate formula is introduced.

5

Investigation of the dynamics of singular protected systems

Naumeyko I., Alja'afreh M.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

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2016

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Vol. 5, No 4

37--42

EN

The analysis of asymptotic representations of the systems protected from harmful influences is carried out. Various types of general models of the "manmachineenvironment" with protection are considered. Each of them adequately describes some of the practically important qualities of the object, and they all together describe the object in terms of its safe operation. The dynamic properties of complex ergonomic systems, presented in the form of systems of differential equations with a small parameter at the derivative are investigated The methods of reducing the impact on the person of harmful factors are theoretically substantiated. The dynamic protection response speed is considered to be significantly greater than the harmful factor production rate. Numerical solution of the general problem and the analytical solution for autonomous case is obtained for harmful effects. By using asymptotic the system of equations has been solved in closed form not only for autonomous case, but also for parameters smoothly changing in time. The estimates of the cost of protection was obtained for the various cost-functionals and for different functions in the right-hand side of the equation describing the dynamics of protection. To assess the accuracy of model calculations and for graphic representation of the results mathematical package MAXIMA is used.

6

Application of perturbed semi-Markov processes in reliability

Grabski F.

Journal of Polish Safety and Reliability Association

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2013

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Vol. 4, No. 2

179--188

EN

The paper is concerned with the application of perturbed semi-Markov (SM) processes in reliability problems. There are two kinds of perturbed SM processes presented in the paper. First of them was defined by Shpak and the second one was introduced by Pavlov and Ushakov. Shpak’s concept of perturbed SM is applied for calculating the approximate reliability function of many tasks operation process and Pavlov and Ushakov concept of that one is used to obtain the approximate reliability function of a repairable cold standby system with a switch.