An example of stick–slip and stick–slip–separation waves

Moirot, Franck; Nguyen, Quoc Son; Oueslati, Abdelbacet

doi:10.1016/s0997-7538(02)00004-9

Cited by 24 publications

(19 citation statements)

References 14 publications

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“…Following results in literature [9,10,20], the stick-slip wave propagates from rear to front, i.e. from the right to the left in our problem.…”

Section: Formulation Of the Problemmentioning

confidence: 71%

“…Contrary to some authors who change the friction law and adopt generally a rate-and-state friction law to overcome this diculty, our future plans is to conserve the Coulomb friction law and to investigate at least many possible models in the future: (i) Model of stick-slip-separation (ii) Stickslip-separation-reverse slip waves as already worked out semi-analytically and numerically by Oueslati et al [28] and Nguyen et al [20] (iii) Model of stickslip with regular functions at a k and b k , for which the method outlined in this paper does not work.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

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Stick-slip waves between elastic and rigid half-spaces

Bui¹,

Oueslati²

2012

Journal of Applied Mathematics and Mechanics

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This paper is devoted to the construction of analytic solution of stick-slip waves crossing the interface between an elastic half-space and a rigid one under unilateral contact and Coulomb friction. The method of solution is based on the analytic continuation method of Radok's complex potentials within the framework of steady elastodynamical problems. The governing equations combined with the boundary conditions are reduced to a RiemannHilbert problem with discontinuous coecient and closed-form expressions of the solution are derived. It is found that the existence of solutions depends on the additional velocity V £ which is related to the longitudinal elongation. If V £ is ignored (V £ = 0) then there is no solution, if not (V £ 6 = 0) then it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone where the waves exhibit a crack-like behaviour.

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“…Following results in literature [9,10,20], the stick-slip wave propagates from rear to front, i.e. from the right to the left in our problem.…”

Section: Formulation Of the Problemmentioning

confidence: 71%

Section: Formulation Of the Problemmentioning

confidence: 99%

Stick-slip waves between elastic and rigid half-spaces

Bui¹,

Oueslati²

2012

Journal of Applied Mathematics and Mechanics

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“…Notice that, due to the change of variables (27), the variables of problem (28)-(30) belong to cones with a much simpler structure than the cones defined by (25,26). However, the matrices in (28) are no longer symmetric, as opposed to those in (23).…”

Section: Two Relevant Non-classical Eigenproblemsmentioning

confidence: 99%

Frictional instabilities in orthotropic hollow cylinders

Costa

Agwa

2009

Computers & Structures

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“…The authors showed that a possible regularization of the problem could be achieved by using a memory-dependent rateand-state friction law proposed by Prakash [44]. Nguyen et al [32,33,39,43] studied the sliding steady state for an elastic tube in frictional contact with a rigid and rotating shaft modeling a brake-like system. It is found that in frictionless contact, two harmonic waves propagating in opposite senses are obtained as in classical elasticity.…”

Section: Introductionmentioning

confidence: 99%

“…Nevertheless, these solutions are not physical and show a crack-like behavior because of the singularity of the normal contact stress. For bounded solids, to our knowledge, the only semi-analytic stick-slip and stick-slip-separation waves are derived in [32,33,43] in view of the study of two-dimensional brake-like system. Based upon a Galerkin expansion, elastodynamic equations involving contact and Coulomb friction constraints are bring to the boundary giving a set of reduced equations.…”

Section: Introductionmentioning

confidence: 99%

On the stick-slip waves under unilateral contact and Coulomb friction

Bui

Oueslati

2010

Ann. Solid Struct. Mech.

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International audienceIn this paper, the construction of analytic solution of stick-slip waves propagating along the interface between an elastic half-space and a moving rigid one is investigated. The contact between the solids is governed by unilateral constraints and Coulomb friction law and the deformable body is loaded by remote uniform stresses t*yy<0, t*xy>0. The method of solution is based on the continuation of Radok's complex potentials within the framework of steady state elastodynamical problems. The governing equation combined with the boundary conditions are reduced to a Riemann-Hilbert problem with discontinuous coefficient. This approach for the stick-slip study is novel and differs from those in the literature, namely the series method and the Weertmann's dislocation formulation. We present the closed form solution of the Riemann-Hilbert problem and show that the principal unknowns are of number two: the wave celerity and the ratio of the slip length by the stick one. The considered loading introduces an additional velocity V* related to the elongation e*xx due to the normal stress t*yy. We show that if V* vanishes there is no solution. When V* is taken into account, it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone at transition points: The shear stress is singular over a small zone and the normal stress exhibits a positive singularity over a very small zone in the slip region which implies a separation near the singular transition

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An example of stick–slip and stick–slip–separation waves

Cited by 24 publications

References 14 publications

Stick-slip waves between elastic and rigid half-spaces

Stick-slip waves between elastic and rigid half-spaces

Frictional instabilities in orthotropic hollow cylinders

On the stick-slip waves under unilateral contact and Coulomb friction

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