0
Research Papers

Surface Instabilities in Linear Orthotropic Half-Spaces With a Frictional Interface

[+] Author and Article Information
M. A. Agwa1

Departamento de Engenharia Civil e Arquitectura and ICIST, Instituto Superior Técnico, Universidade Técnica de Lisboa, Avenida Rovisco Pais, Lisboa 1049-001, Portugalagwa@civil.ist.utl.pt

A. Pinto da Costa2

Departamento de Engenharia Civil e Arquitectura and ICIST, Instituto Superior Técnico, Universidade Técnica de Lisboa, Avenida Rovisco Pais, Lisboa 1049-001, Portugalapcosta@civil.ist.utl.pt

1

Present address: Department of Mechanical Engineering, Zagazig University, Egypt.

2

Corresponding author.

J. Appl. Mech 78(4), 041002 (Apr 12, 2011) (9 pages) doi:10.1115/1.4003744 History: Received June 15, 2010; Revised January 17, 2011; Posted March 03, 2011; Published April 12, 2011; Online April 12, 2011

This paper studies the friction induced vibrations that may develop in the neighborhood of steady sliding states of elastic orthotropic half-spaces compressed against a rigid plane moving tangentially with a prescribed speed. These vibrations may lead to flutter instability associated to a surfacelike oscillation. The system of dynamic differential equations and boundary conditions that governs the small plane oscillations of the half-space about the steady sliding state is established. The general form of the surface solutions to the plane strain case is given. The way how the coefficient of friction varies with changes in some of the system’s parameters is investigated. It is shown that for certain combinations of material data, low coefficients of friction are found for surface flutter instability (lower than in the isotropic case).

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 8

Momentary deformation stage at nondimensional time T=0.1 of the square (X,Y)∊[0,2]×[0,2] near the frictional contact surface Y=0. Left (right): displacement parallel (perpendicular) to the frictional interface. The nondimensional velocity c/cT=3.28387+0.037947i, corresponding to E1/E2=2, ν12=0.1, ν=0.4, G12/E2=0.1, θ=90 deg, and μ=1. The undetermined wave number k was set to 2π.

Grahic Jump Location
Figure 9

Momentary deformation stage at nondimensional time T=0.1 of the square (X,Y)∊[0,2]×[0,2] near the frictional contact surface Y=0. Left (right): displacement parallel (perpendicular) to the frictional interface. The nondimensional velocity c/cT=3.24766+1.02474i, corresponding to E1/E2=4, ν12=0.1, ν=0.4, G12/E2=0.1, θ=120 deg, and μ=1.5. The undetermined wave number k was set to 2π.

Grahic Jump Location
Figure 11

Time evolution of the nondimensional displacement components (U,V)=(Re(u/A′),Re(v/A′)) of particles located at X=0.5 and several depths Y. Nondimensional velocity c/cT=3.24766+1.02474i. Data: E1/E2=4, ν12=0.1, ν=0.4, G12/E2=0.1, θ=120 deg, and μ=1.5.

Grahic Jump Location
Figure 7

Coefficient of friction at the onset of flutter instability for an orthotropic half-space for several orientations of the principal directions of orthotropy and E1/E2=2 (●) or 4 (▲). Data: ν=0.4, ν12=0.1, and G12/E2=0.1.

Grahic Jump Location
Figure 6

Real and imaginary parts of c/cT versus the coefficient of friction μ for some orientations θ of the principal directions of orthotropy. Between the parentheses are the values of the coefficients of friction μcr at the onset of flutter instability. Data: E1/E2=4, ν=0.4, ν12=0.1, and G12/E2=0.1. (a) θ(μcr)=0 deg (1.76), 15 deg (0.961), 30 deg (2.98), 90 deg (0.6). (b) θ(μcr)=105 deg (0.484), 120 deg (1.06), 135 deg (2.127).

Grahic Jump Location
Figure 5

Real and imaginary parts of c/cT versus the coefficient of friction μ for some orientations θ of the principal directions of orthotropy. Between the parentheses are the values of the coefficients of friction μcr at the onset of flutter instability. Data: E1/E2=2, ν=0.4, ν12=0.1, and G12/E2=0.1. (a) θ(μcr)=0 deg (1.3), 15 deg (0.572), 30 deg (1.52), 45 deg (5.0), 90 deg (1.0). (b) θ(μcr)=105 deg (0.47), 120 deg (1.1), 135 deg (2.424).

Grahic Jump Location
Figure 2

Real and imaginary parts of c/cT versus the coefficient of friction μ for some values of Poisson’s ratio ν12=ν and with G12/E2=G/E2=1/2(1+ν). Data: θ=0 deg, E1/E2=0.5 (red), 1 (black), E1/E2=2 (blue), and 4 (green).

Grahic Jump Location
Figure 1

Relative sliding between a rigid surface and an orthotropic elastic half-space

Grahic Jump Location
Figure 10

Time evolution of the nondimensional displacement components (U,V)=(Re(u/A′),Re(v/A′)) of a particle located at X=0.5 and several depths Y. Nondimensional velocity c/cT=3.28387+0.037947i. Data: E1/E2=2, ν12=0.1, ν=0.4, G12/E2=0.1, θ=90 deg, and μ=1.

Grahic Jump Location
Figure 4

Real and imaginary parts of c/cT versus the coefficient of friction μ for several values of G12/E2 indicated near the curves. Other data: θ=90 deg, E1/E2=8, ν12=0.3, and ν=0.2.

Grahic Jump Location
Figure 3

Real and imaginary parts of c/cT versus the coefficient of friction μ for several values of Poisson’s ratio ν12 indicated near the curves. Other data: θ=90 deg, E1/E2=8, G12/E2=0.1, and ν=0.3.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In