Interaction of the Crack and Thin Elastic Layer in the Solid Under Time-Harmonic Loading

The problem of bonded contact between a uniform finite Timoshenko beam and an orthotropic half-plane via a thin elastic layer is considered in this paper. The beam is loaded by distributions of normal and tangential forces, and a uniaxial stress load is applied to the half-plane. The Timoshenko beam theory is extended in such a way that the tangential load is included when the shear contribution to the beam central line deflection is calculated. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated and numerically solved for the unknown interface stresses. A comparison with a corresponding FE-model is also performed.

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A NOTE ON THE VIBRO-ACOUSTIC RESPONSE OF A PERIODICALLY SUPPORTED BEAM SUBJECTED TO A TRAVELLING, TIME-HARMONIC LOADING

Journal of Sound and Vibration ◽

10.1006/jsvi.2000.3163 ◽

2001 ◽

Vol 239 (3) ◽

pp. 531-544 ◽

Cited By ~ 3

Author(s):

C.-C. CHENG ◽

C.-P. KUO ◽

J.-W. YANG

Keyword(s):

Harmonic Loading ◽

Acoustic Response ◽

Time Harmonic ◽

Travelling Time

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Multiply Loaded Rigid Punch on a Stressed Orthotopic Half-Plane via a Thin Elastic Layer

Journal of Applied Mechanics ◽

10.1115/1.2899475 ◽

1992 ◽

Vol 59 (2S) ◽

pp. S115-S122 ◽

Cited By ~ 3

Author(s):

Hans L. Bjarnehed

Keyword(s):

Half Plane ◽

Elastic Layer ◽

Singular Integral Equations ◽

Free Edge ◽

Shear Stresses ◽

Rigid Punch ◽

Fem Model ◽

Frictionless Contact ◽

Thin Elastic Layer ◽

Elastic Cushion

A uniaxially stressed orthotropic half-plane indented on the free edge by a multiply loaded rigid punch via a thin elastic layer is considered. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated for the unknown interface stresses between the cushion and the half-plane. Two kinds of friction conditions between the cushion and half-plane are treated, viz. completely adhesive and frictionless contact. An analytical solution for contact with a rigid cushion and a numerical solution with an elastic cushion are presented. Also, a comparison with a corresponding FEM model is performed. For frictionless contact, some analytical results concerning optimum design of the elastic cushion are given.

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Evolution of localized folding for a thin elastic layer in a softening visco-elastic medium

Pure and Applied Geophysics ◽

10.1007/bf00876491 ◽

1996 ◽

Vol 146 (2) ◽

pp. 229-252 ◽

Cited By ~ 26

Author(s):

G. W. Hunt ◽

H-B. M�hlhaus ◽

A. I. M. Whiting

Keyword(s):

Elastic Medium ◽

Elastic Layer ◽

Thin Elastic Layer

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Approximate formula for the H/V ratio of Rayleigh waves in incompressible orthotropic half-spaces coated by a thin elastic layer

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/10033 ◽

2017 ◽

Vol 39 (4) ◽

pp. 365-374

Author(s):

Pham Chi Vinh ◽

Tran Thanh Tuan ◽

Le Thi Hue

Keyword(s):

Free Surface ◽

Rayleigh Wave ◽

Half Space ◽

Rayleigh Waves ◽

Elastic Layer ◽

Approximate Formula ◽

Elastic Half Space ◽

Displacement Amplitude ◽

Vertical Displacements ◽

Thin Elastic Layer

This paper is concerned with the propagation of Rayleigh waves in an incompressible orthotropic elastic half-space coated with a thin incompressible orthotropic elastic layer. The main purpose of the paper is to establish an approximate formula for the Rayleigh wave H/V ratio (the ratio between the amplitudes of the horizontal and vertical displacements of Rayleigh waves at the traction-free surface of the layer). First, the relations between the traction amplitude vector and the displacement amplitude vector of Rayleigh waves at two sides of the interface between the layer and the half-space are created using the Stroh formalism and the effective boundary condition method. Then, an approximate formula for the Rayleigh wave H/V ratio of third-order in terms of dimensionless thickness of the layer has been derived by using these relations along with the Taylor expansion of the displacement amplitude vector of the thin layer at its traction-free surface. It is shown numerically that the obtained formula is a good approximate one. It can be used for extracting mechanical properties of thin films from measured values of the Rayleigh wave H/V ratio.

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