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Effective boundary condition method and Rayleigh waves in orthotropic half-spaces coated by a thin layer with sliding contact

Vinh P. C., Anh V. T.

Archives of Mechanics

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2015

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Vol. 67, nr 6

477--498

EN

This paper studies the propagation of Rayleigh waves in an orthotropic elastic half-space coated by a thin orthotropic elastic layer. The half-space and the layer are assumed to be either compressible or incompressible and they are in sliding contact with each other. The main aim of the paper is to establish approximate secular equations of the wave for all (four) possibilities of a compressible or incompressible half-space covered with a compressible or incompressible thin layer, except the case of a compressible half-space coated by a compressible layer that has been considered [19]. In order to do that, the effective boundary condition method is employed and the approximate third-order secular equations regarding the dimensionless thickness of the layer are derived. It is shown that these approximate secular equations have a high accuracy. Based on the obtained secular equations, the effect of incompressibility on the Raleigh wave propagation is considered through some numerical examples. It is shown that incompressibility strongly affects the Raleigh wave velocity and the effect becomes stronger when the coating is incompressible.

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Rayleigh waves in an incompressible orthotropic half-space coated by a thin elastic layer

Vinh P. C., Linh N. T., Anh V. T.

Archives of Mechanics

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2014

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Vol. 66, nr 3

173--184

EN

The present paper is concerned with the propagation of Rayleigh waves in an orthotropic elastic half-space coated with a thin orthotropic elastic layer. The halfspace and the layer are both incompressible and they are in welded contact to each other. The main purpose of the paper is to establish an approximate secular equation of the wave. By using the effective boundary condition method an approximate secular equation of third-order in terms of the dimensionless thickness of the layer is derived. It is shown that this approximate secular equation has high accuracy. From it an approximate formula of third-order for the velocity of Rayleigh waves is obtained and it is a good approximation. The obtained approximate secular equation and formula for the velocity will be useful in practical applications.

3

Explicit homogenized equation of a boundary-value problem in two-dimensional domains separated by an interface highly oscillating between two concentric ellipses

Vinh P. C., Tung D. X.

Archives of Mechanics

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2012

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Vol. 64, nr 5

461-476

EN

The main purpose of this paper is to find the homogenized equation and the associate continuity condition in the explicit form of a boundary-value problem in two-dimensional domains separated by an interface oscillating rapidly between two concentric ellipses. This boundary-value problem originates from various mechanical problems. By the homogenization method and following the techniques presented recently by these authors the homogenized equation and the associate continuity condition in the explicit form are derived. Since the obtained homogenized equation is totally explicit it is convenient to use.