scholarly journals Friction-induced vibration and stick-slip waves

2011 ◽  
pp. 167-188
Author(s):  
Abdelbacet Oueslati
Keyword(s):  
Half Space ◽  
Short Review ◽  
Solution Procedure ◽  
Elastic Half Space ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Stick Slip ◽  
Method Of Solution ◽  
Transition Points ◽  
Friction Induced Vibration

This paper presents a short review and new results about the self-excited responses under the form of stick-slip regimes. First, the Van-der Pol oscillator with one degree of freedom is considered. Then it is shown that it is possible to build semi-analytical and numerical (by the FEM.) solutions of stick-slip-separation waves for a brake-like system. Then, we present new results concerning the mechanical model composed of a rigid half space in frictional sliding with an elastic half-space. The method of solution, based on periodic complex Radoks potentials, is novel and differs from those in literature. Besides, in contrast with many works, we shall consider the longitudinal elongation which plays a crucial rule in the solution procedure. A unique and weakly singular solution is found and satisfies all stick-slip conditions except over a narrow zone at transition points which implies a cracklike behaviour at the stick-slip borders.

The Residue Harmonic Balance Method for Duffing-Van Der Pol Oscillator with Fractional Derivative

2013 ◽  
Vol 774-776 ◽  
pp. 103-106
Author(s):  
Xin Xue ◽  
Lian Zhong Li ◽  
Dan Sun
Keyword(s):  
Fractional Derivative ◽  
Harmonic Balance ◽  
Numerical Solutions ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Solution Procedure ◽  
Balance Method ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Fractional Orders

Duffing-van der Pol oscillator with fractional derivative was constructed in this paper. The solution procedure was proposed with the residue harmonic balance method. The effect of different fractional orders on resonance responses of the system in steady state were analyzed for an example without parameters. The approximate solutions were contrasted with numerical solutions. The results show that the residue harmonic balance method to Duffing-van der Pol differential equation with fractional derivative is very valid.

The Dynamic Response of an Elastic Half Space With an Overlying Acoustic Fluid

1976 ◽  
Vol 43 (1) ◽  
pp. 39-42 ◽  
Author(s):  
B. E. Bennett ◽  
G. Herrmann
Keyword(s):  
Dynamic Response ◽  
Half Space ◽  
Elastic Solid ◽  
Elastic Half Space ◽  
Plane Interface ◽  
Dynamic Problems ◽  
Normal Loading ◽  
The Past ◽  
Method Of Solution ◽  
Acoustic Fluid

A class of dynamic problems involving a semi-infinite elastic solid with an overlying semi-infinite acoustic fluid, subjected at the plane interface to arbitrary normal loading is investigated. A method of solution is proposed which reduces the class of problems under study to that in which the fluid is absent. This latter class has received considerable consideration in the past. A specific example is presented for an expanding disk-shaped load including numerical results for the subseismic range.

Two-Dimensional Contact on an Anisotropic Elastic Half-Space

1994 ◽  
Vol 61 (2) ◽  
pp. 250-255 ◽  
Author(s):  
Hui Fan ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Contact Problem ◽  
Half Space ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Solution Procedure ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Anisotropic Elastic ◽  
The One

The two-dimensional contact problem for a semi-infinite anisotropic elastic media is reconsidered here by using the formalism of Es he I by et al. (1953) and Stroh (1958). The approach of analytic function continuation is employed to investigate the half-space contact problem with various mixed boundary conditions applied to the half-space. A key point of the solution procedure suggested in the present paper is its dependence on a general eigenvalue problem involving a Hermitian matrix. This eigenvalue problem is analogous to the one encountered when investigating the behavior of an interface crack (Ting, 1986). As an application, the interaction between a dislocation and a contact strip is solved. The compactness of the results shows their potential for utilization to solve the problem of contact of a damaged anisotropic half-space.

Disturbance produced in an elastic half-space by impulsive normal pressure

1964 ◽  
Vol 60 (3) ◽  
pp. 683-696 ◽  
Author(s):  
M. Mitra
Keyword(s):  
Half Space ◽  
Surface Displacement ◽  
Normal Pressure ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Point Load ◽  
Definite Integrals ◽  
Operational Solution ◽  
Method Of Solution ◽  
Pressure Area

1. Introduction. The disturbance produced in an elastic half-space by different types of buried sources have been studied by various authors. However, the only exact solutions of problems for the half-space in which the disturbance is produced by impulsive surface tractions are due to Pekeris (9) and Chao (4), though for the half-plane such problems have been studied by de Hoop (5), Ang (1) and Mitra (8). Pekeris (9) evaluated the surface displacement produced by a normal point load on the surface using a method of inversion of the operational solution developed earlier (Bateman & Pekeris (2)). A finite pressure-area, however, represents physical situations better than a point load. In this paper, the displacement produced in the half-space by uniform impulsive pressure acting over a circular portion of the surface has been obtained in terms of definite integrals. On the surface, the displacement has been split up into a number of terms some of which represent the P-wave contribution, while others give the Rayleigh-wave contribution to the displacement. The method of solution involves the use of integral transforms and Cagniard's (3) method; Pekeris's method is not applicable in this case since the appropriate transformation of an integral along the real axis to one along the imaginary axis cannot be carried out.

The efficiency of application of virtual cross-sections method and hypotheses MELS in problems of wave signal propagation in elastic waveguides with rough surfaces

2016 ◽  
pp. 3564-3575 ◽  
Author(s):  
Ara Sergey Avetisyan
Keyword(s):  
Half Space ◽  
Cross Sections ◽  
Classical Method ◽  
Signal Propagation ◽  
Elastic Half Space ◽  
Layered Systems ◽  
Surface Layers ◽  
Inhomogeneous Surface ◽  
Wave Signal ◽  
The Impact

The efficiency of virtual cross sections method and MELS (Magneto Elastic Layered Systems) hypotheses application is shown on model problem about distribution of wave field in thin surface layers of waveguide when plane wave signal is propagating in it. The impact of surface non-smoothness on characteristics of propagation of high-frequency horizontally polarized wave signal in isotropic elastic half-space is studied. It is shown that the non-smoothness leads to strong distortion of the wave signal over the waveguide thickness and along wave signal propagation direction as well.  Numerical comparative analysis of change in amplitude and phase characteristics of obtained wave fields against roughness of weakly inhomogeneous surface of homogeneous elastic half-space surface is done by classical method and by proposed approach for different kind of non-smoothness.

NUMERICAL SOLUTION FOR DUFFING-VAN DER POL OSCILLATOR VIA BLOCK METHOD

2020 ◽  
Vol 10 (1) ◽  
pp. 1857-8365
Author(s):  
A. F. Nurullah ◽  
M. Hassan ◽  
T. J. Wong ◽  
L. F. Koo
Keyword(s):  
Numerical Solution ◽  
Van Der Pol Oscillator ◽  
Block Method ◽  
Van Der Pol
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