MOVING LOAD ON AN ELASTIC HALF-SPACE COATED WITH A THIN VERTICALLY INHOMOGENEOUS LAYER

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.

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Moving Load on a Plate Resting on an Elastic Half Space

Journal of Applied Mechanics ◽

10.1115/1.3607855 ◽

1967 ◽

Vol 34 (4) ◽

pp. 910-914 ◽

Cited By ~ 52

Author(s):

J. D. Achenbach ◽

S. P. Keshava ◽

G. Herrmann

Keyword(s):

Half Space ◽

Moving Load ◽

Elastic Half Space ◽

Winkler Foundation ◽

Bending Moments ◽

Line Load ◽

Resonance Effects ◽

Small Load ◽

Smooth Contact ◽

Time Invariant

An elastic plate supported by a semi-infinite elastic continuum is subjected to a moving line load. Both welded and smooth contact between plate and foundation are considered. Dynamic solutions for the bending moments in the plate are presented that are time-invariant relative to a coordinate system moving with the load. Resonance effects at certain critical velocities are discussed. The response of the system depends significantly on the relative stiffness of plate and half space and on the type of contact. For the relatively stiff plate certain resonances occur for smooth contact but not for welded contact. For subcritical load velocities the bending moments are calculated and compared with corresponding bending moments for a plate on a Winkler foundation. The Winkler foundation is adequate for smooth contact and small load velocities.

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Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

Acta Mechanica et Automatica ◽

10.2478/ama-2021-0005 ◽

2021 ◽

Vol 15 (1) ◽

pp. 30-36

Author(s):

Askar Kudaibergenov ◽

Askat Kudaibergenov ◽

Danila Prikazchikov

Keyword(s):

Surface Wave ◽

Half Space ◽

Moving Load ◽

Elastic Half Space ◽

Elementary Functions ◽

Material Models ◽

Line Load ◽

Transient Regimes ◽

Surface Wave Field ◽

Asymptotic Formulation

Abstract 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.

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Reduced model for the surface dynamics of a generally anisotropic elastic half-space

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0590 ◽

2020 ◽

Vol 476 (2234) ◽

pp. 20190590 ◽

Cited By ~ 4

Author(s):

Yibin Fu ◽

Julius Kaplunov ◽

Danila Prikazchikov

Keyword(s):

Surface Wave ◽

Half Space ◽

Travelling Waves ◽

Moving Load ◽

Multiple Scale ◽

Elastic Half Space ◽

Surface Dynamics ◽

Near Surface ◽

Surface Resonance ◽

Anisotropic Elastic

Near-surface resonance phenomena often arise in semi-infinite solids. For instance, when a moving load with a speed v close to the surface wave speed v R is applied to the surface of an elastic half-space, it will give rise to a large-amplitude disturbance inversely proportional to v − v R . The latter can be determined by a multiple-scale approach using an extra slow time variable. It has also been shown for isotropic elastic half-spaces that the reduced governing equation thus derived is capable of describing the surface wave contribution even for arbitrary dynamic loading. In this paper, we first derive the analogous evolution equation for a generally anisotropic elastic half-space, and then assess its applicability in the study of travelling waves in a half-space that is coated with a continuous array of spring-like vertical resonators or bonded to an elastic layer of different properties. Our results are validated by comparison with previously known results, and illustrative calculations are carried out for a fibre-reinforced half-space and a coated half-space that is subjected to a finite deformation.

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