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1

Love waves in fiber-reinforced layer imperfectly bonded to microstructural couple stress substrate

Sharma Vishal, Sharma Vikas

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 1

221--232

EN

Interior of the Earth is quite complex and it shows many heterogeneities in the form of microstructures. It is difficult to model the Earth in mathematical formulation of a problem, yet it is always desirable that the proposed model should be the nearest approximation of the Earth. In this paper, Love waves are investigated, using a new geometrical configuration which consists of a finite thicker fiber-reinforced layer lying over a couple stress half-space having internal microstructures. The two media are assumed to be imperfectly bonded to each other at the interface. Dispersion and damping equations are derived for the propagation of Love waves in the considered model. The impact of various parameters like imperfectness at the interfacial surface, thickness of the layer, characteristic length parameter of the halfspace, direction of reinforcement are studied on the phase and damping velocities of Love waves.

2

Nonlinear surface elastic waves in materials

Rushchitsky J.

Vibrations in Physical Systems

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2014

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Vol. 26

33--40

EN

This paper is devoted to analysis of the surface nonlinear elastic harmonic waves of four types (Rayleigh and Stoneley harmonic waves within the framework of plane strain state; Love and Mozhaev harmonic wave within the framework of anti-plane strain state). The nonlinear model is based on introducing the Murnaghan elastic potential, which includes both geometrical and physical nonlinearities. Each type of surface waves is discussed in four steps: statement of the problem, nonlinear wave equations, approximate solution (first two approximations), so-me conclusions. A nonlinear analysis of waves required many novelties: new variants of the Murnaghan potential, new nonlinear wave equations and new nonlinear boundary conditions. The nonlinear wave equations were solved by the method of successive approximations. A new approach to analyze the boundary conditions is offered. Some new nonlinear wave effects are observed theoretically: a wave picture is reached by the 2nd harmonic and becomes changing in time of propagation, the wave numbers become depending on the initial amplitude.

3

Shear velocity inversion procedure for love waves

Zaman F. D., Masod K.

Journal of Technical Physics

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2003

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Vol. 44, no 3

295-301

EN

An inverse solution is presented to the seismic inverse problem for one-dimensional shear velocity variations. The Love waves, travelling in a layer overlying a half-space incident upon delta-function potential, are considered. The equation of motion for Love waves is transformed to the Schrodinger equation and then the potential is recovered by applying Gelfand-Levitan and Marchenko procedure.

4

Love wave-induced liquefaction in a saturated sand layer

Staroszczyk R.

Journal of Theoretical and Applied Mechanics

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1998

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nr 3

723-744

EN

The paper is concerned with the plane strain problem of Love wave propagation through a water-saturated sand layer overlaying an elastic half-space. Dynamic loads, induced by the wave passage, generate irreversible strains in the soil matrix, giving rise to the development of excess pore water pressures and subsequent reduction of soil liquefaction. The process of pore pressure generation is analysed within the framework of compaction theory of saturated granular media. Results of numerical calculations, carried out by means of the finite element method, illustrate the evolution of pore pressures and the development of liquefaction in the subsoil, as well as the changes in the free surface displacements.

PL

Praca poświęcona jest płaskiemu zagadnieniu propagacji fal Love'a w warstwie piasku nasyconego woda, znajdującej się na półprzestrzeni ośrodka sprężystego. Obciążenia dynamiczne spowodowane przejściem fali wywołują nieodwracalne odkształcenia w szkielecie gruntowym, które są przyczyną zwiększenia ciśnienia w wodzie wypełniającej pory ośrodka i tym samym zmniejszenia naprężeń efektywnych w gruncie, co w końcowym przypadku może prowadzić do upłynnienia podłoża. Proces generacji ciśnień porowych jest analizowany na bazie teorii zagęszczenia nawodnionych ośrodków granulowanych. Wyniki obliczeń numerycznych, przeprowadzonych w oparciu o metodę elementów skończonych, ilustrują ewolucję ciśnień porowych, rozwój strefy upłynnienia w podłożu oraz zmiany w czasie przemieszczeń powierzchni swobodnej warstwy.