scholarly journals Self-excited oscillations of a finite-thickness elastic layer sliding against a rigid surface with a constant coefficient of friction

2017 ◽  
Author(s):  
Karami Mohammadi
Keyword(s):  
Coefficient Of Friction ◽  
Constant Coefficient ◽  
Elastic Layer ◽  
Finite Thickness ◽  
Rigid Surface

Self-Excited Oscillations of a Finite-Thickness Elastic Layer Sliding Against a Rigid Surface With a Constant Coefficient of Friction

2017 ◽  
Vol 85 (2) ◽  
Author(s):  
Neda Karami Mohammadi ◽  
George G. Adams
Keyword(s):  
Friction Coefficient ◽  
Coefficient Of Friction ◽  
Elastic Layer ◽  
Sliding Friction ◽  
Finite Thickness ◽  
Elastic Solid ◽  
Constant Speed ◽  
Bottom Surface ◽  
Rigid Surface ◽  
Positive Real

This investigation considers the dynamic stability of the steady-state frictional sliding of a finite-thickness elastic layer pressed against a moving rigid and flat surface of infinite extent. The elastic layer is fixed on its bottom surface; on its entire top surface, the rigid surface slides with constant speed and with a constant friction coefficient. The plane-strain equations of motion for a linear isotropic elastic solid are solved analytically for small dynamic disturbances. The analysis shows that even with a constant (speed-independent) friction coefficient, the steady solution is dynamically unstable for any finite friction coefficient. Eigenvalues with positive real parts lead to self-excited vibrations which occur for any sliding speed and which increase with increasing coefficient of friction. This is in contrast to the behavior of an elastic half-space sliding against a rigid surface in which the instability only occurs if the coefficient of friction is greater than unity. This work and its extensions are expected to be relevant in the theoretical aspects of sliding friction as well as in a variety of areas such as earthquake motion and brake dynamics.

scholarly journals Rotation and Magnetic Field Effect on Surface Waves Propagation in an Elastic Layer Lying over a Generalized Thermoelastic Diffusive Half-Space with Imperfect Boundary

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
S. M. Abo-Dahab ◽  
Kh. Lotfy ◽  
A. Gohaly
Keyword(s):  
Magnetic Field ◽  
Surface Waves ◽  
Half Space ◽  
Attenuation Coefficient ◽  
Elastic Layer ◽  
Finite Thickness ◽  
Relaxation Times ◽  
Magnetic Field Effect ◽  
Plane Boundary ◽  
Special Cases

The aim of the present investigation is to study the effects of magnetic field, relaxation times, and rotation on the propagation of surface waves with imperfect boundary. The propagation between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half-space with rotation in the context of Green-Lindsay (GL) model is studied. The secular equation for surface waves in compact form is derived after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness, and then deduced for normal stiffness, tangential stiffness and welded contact. The amplitudes of displacements, temperature, and concentration are computed analytically at the free plane boundary. Some special cases are illustrated and compared with previous results obtained by other authors. The effects of rotation, magnetic field, and relaxation times on the speed, attenuation coefficient, and the amplitudes of displacements, temperature, and concentration are displayed graphically.

scholarly journals Limiting shape of profile due to dual-mode fretting wear in contact with an elastomer

2015 ◽  
Vol 230 (9) ◽  
pp. 1417-1423 ◽  
Author(s):  
Xinyu Mao ◽  
Wei Liu ◽  
Yuanzhi Ni ◽  
Valentin L Popov
Keyword(s):  
Coefficient Of Friction ◽  
Contact Area ◽  
Constant Coefficient ◽  
Analytic Solutions ◽  
Slip Zone ◽  
Fretting Wear ◽  
Contact Interface ◽  
Dual Mode ◽  
Elastic Bodies ◽  
Initial Forms

We consider fretting wear due to superimposed normal and tangential oscillations of two contacting bodies, one of which is an elastomer with a linear rheology. Similarly to the contact of elastic bodies, at small oscillation amplitudes, the wear occurs only in a circular slip zone at the border of the contact area and the wear profile tends to a limiting form, in which no further wear occurs. It is shown that under assumption of a constant coefficient of friction at the contact interface, the limiting form of the wear profile does depend neither on the particular wear criterion nor on the rheology of the elastomer and can be calculated analytically in a general form. The general calculation procedure and explicit analytic solutions for two initial forms, parabolic and conical, are presented for various combinations of frequencies and phases of normal and tangential oscillations as well as for various linear rheologies of the elastomer.

Friction Reduction in the Sliding of an Elastic Half-Space Against a Rigid Surface Due to Incident Rectangular Dilatational Waves

1999 ◽  
Vol 122 (1) ◽  
pp. 10-15 ◽  
Author(s):  
George G. Adams
Keyword(s):  
Normal Stress ◽  
Half Space ◽  
Coefficient Of Friction ◽  
Tangential Velocity ◽  
Elastic Half Space ◽  
Body Waves ◽  
Friction Reduction ◽  
Rigid Surface ◽  
Rectangular Wave ◽  
The Coefficient Of Friction

The steady sliding of a flat homogeneous and isotropic elastic half-space against a flat rigid surface, under the influence of incident plane dilatational waves, is investigated. The interfacial coefficient of friction is constant with no distinction between static and kinetic friction. It is shown here that the reflection of a harmonic wave under steady sliding consists of a pair of body waves (a plane dilatational wave and a plane shear wave) radiated from the sliding interface. Each wave propagates at a different angle such that the trace velocities along the interface are equal and supersonic. The angles of wave propagation are determined by the angle of the incident wave, by the Poisson’s ratio, and by the coefficient of friction. The amplitude of the incident waves is subject only to the restriction that the perturbations in interface contact pressure and tangential velocity satisfy the inequality constraints for unilateral sliding contact. It is also found that an incident rectangular wave can allow for relative sliding motion of the two bodies with a ratio of remote shear to normal stress which is less than the coefficient of friction. Thus the apparent coefficient of friction is less than the interface coefficient of friction. This reduction in friction is due to periodic stick zones which propagate supersonically along the interface. The influences of the angle, amplitude, and shape of the incident rectangular wave, the interfacial friction coefficient, the sliding speed, and of the remotely applied normal stress, on friction reduction are determined. Under appropriate conditions, the bodies can move tangentially with respect to each other in the absence of an applied shear stress. [S0742-4787(00)00201-0]

Thermal and Mechanical Model for Rigid Cylinder Indenting an Elastic Layer Resting on Rigid Base: Application to Turned Surfaces

2003 ◽  
Vol 125 (2) ◽  
pp. 186-191
Author(s):  
Zhe Zhang ◽  
E. E. Marotta ◽  
J. M. Ochterbeck
Keyword(s):  
Mechanical Properties ◽  
Mechanical Model ◽  
Elastic Layer ◽  
Mixed Boundary ◽  
Linear Equations ◽  
Finite Thickness ◽  
Half Width ◽  
Rigid Base ◽  
Wide Range ◽  
Analytical Thermal Model

Models are presented for the solution of the thermal and mechanical problem of a rigid metallic cylinder indenting an elastic layer with finite thickness which rests on a rigid substrate without friction. The models were extended to turned surfaces applications. With introduction of an equivalent isothermal flux distribution for the mixed boundary problem—constant temperature over the contact area while adiabatic elsewhere along the top surface—an approximate analytical thermal model was developed. The solution was compared to a numerical solution under certain cases. Both solutions in turn compare very well with the generalized three-dimensional expression proposed by prior investigators. The mechanical model predicts the contact half-width under varying mechanical properties, layer dimensions, and applied load. The mechanical contact problem was solved numerically by substituting the displacement variable with a truncated polynomial to get a system of linear equations from which the dimensionless contact half-width was derived. The model is valid throughout a wide range of parameters, including mechanical properties and geometric dimensions. To explicitly predict the dimensionless contact half-width as a function of dimensionless load, a curve was fitted to the numerically obtained solution.

The impact of a rigid sphere with an elastic layer of finite thickness

1995 ◽  
Vol 112 (1-4) ◽  
pp. 83-93 ◽  
Author(s):  
Yu. A. Rossikhin ◽  
M. V. Shitikova
Keyword(s):  
Elastic Layer ◽  
Finite Thickness ◽  
Rigid Sphere ◽  
The Impact
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