Reflection, Refraction, and Absorption of Elastic Waves at a Frictional Interface: P and SV Motion

1981 ◽  
Vol 48 (1) ◽  
pp. 155-160 ◽  
Author(s):  
R. K. Miller ◽  
H. T. Tran
Keyword(s):  
Closed Form ◽  
Approximate Method ◽  
Elastic Waves ◽  
Coulomb Friction ◽  
Broad Class ◽  
Angle Of Incidence ◽  
Elastic Solids ◽  
Time Harmonic ◽  
Frictional Interface ◽  
Refracted Waves

An approximate method of analysis is presented for determining the reflection, refraction, and absorption of obliquely incident planar time-harmonic P or SV waves at a frictional interface between dissimilar elastic solids. The solids are pressed together with sufficient pressure to prevent separation, and the angle of incidence is subcritical. General expressions for the amplitudes and phases of all reflected and refracted waves are developed in closed form for a broad class of models for bonding friction. Specific results are presented for the case of identical elastic solids bonded by Coulomb friction, as an example of application of the general approach.

Reflection, Refraction, and Absorption of Elastic Waves at a Frictional Interface: SH Motion

1979 ◽  
Vol 46 (3) ◽  
pp. 625-630 ◽  
Author(s):  
R. K. Miller ◽  
H. T. Tran
Keyword(s):  
Coulomb Friction ◽  
General Procedure ◽  
Frictional Stress ◽  
Elastic Solids ◽  
Sh Waves ◽  
Relative Slip ◽  
Transmission And Reflection Coefficients ◽  
Incident Plane ◽  
Frictional Interface ◽  
Transmission And Absorption

The reflection, refraction, and absorption of obliquely incident plane harmonic antiplane strain (SH) waves at a frictional interface between dissimilar semi-infinite elastic solids is investigated by an approximate analytical approach. The frictional stress at the interface is assumed to depend on the normal stress and the relative slip across the interface, but remains otherwise arbitrary throughout the analysis. General expressions are developed for the transmission and reflection coefficients, and the partitition of incident wave energy into reflection, transmission, and absorption. The special case of bonding by Coulomb friction is examined in detail as an example of application of the general procedure. An exact solution is also presented for the case of bonding by Coulomb friction, and a comparison between approximate and exact solutions provides an indication of the accuracy of the approximate method of analysis.

A computer program for the application of Zoeppritz's amplitude equations and Knott's energy equations

1976 ◽  
Vol 66 (6) ◽  
pp. 1881-1885 ◽  
Author(s):  
G. B. Young ◽  
L. W. Braile
Keyword(s):  
Computer Program ◽  
Elastic Waves ◽  
Displacement Amplitude ◽  
Plane Interface ◽  
Angle Of Incidence ◽  
Amplitude Equations ◽  
Elastic Solids ◽  
Displacement Potential ◽  
Energy Equations ◽  
Sample Case

abstract A computer program is presented which calculates Zoeppritz's displacement amplitude coefficients, displacement potential coefficients, and Knott's energy coefficients for plane harmonic elastic waves of P or SV type incident on a plane interface between two isotropic, homogeneous elastic solids. A discussion of these three basic types of coefficients is included. Results of applying the program to a sample case are presented in the form of a graph of the energy coefficients computed for all possible wave types and over a range of angle of incidence of 0° to 90°.

Disturbance at a Frictional Interface Caused by a Plane Elastic Pulse

1982 ◽  
Vol 49 (2) ◽  
pp. 361-365 ◽  
Author(s):  
Maria Comninou ◽  
J. R. Barber ◽  
John Dundurs
Keyword(s):  
Closed Form ◽  
Coefficient Of Friction ◽  
Graphical Representation ◽  
Critical Value ◽  
Elastic Solids ◽  
Supersonic Speed ◽  
The Coefficient Of Friction ◽  
Frictional Interface

We consider a plane pulse striking the frictional interface between two elastic solids which are held together by compressive applied tractions and sheared. The pulse causes a disturbance involving separation or slip between the bodies, which propagates along the interface at supersonic speed. The extent of these zones is determined using a convenient graphical representation and the interface tractions are given in closed form. It is found that the results change qualitatively when the coefficient of friction exceeds a critical value.

An Approximate Method of Analysis of the Transmission of Elastic Waves Through a Frictional Boundary

1977 ◽  
Vol 44 (4) ◽  
pp. 652-656 ◽  
Author(s):  
R. K. Miller
Keyword(s):  
Exact Solutions ◽  
Approximate Method ◽  
Analytical Method ◽  
Elastic Waves ◽  
Coulomb Friction ◽  
Shear Waves ◽  
Elastic Media ◽  
Approximate Analytical Method ◽  
Harmonic Shear ◽  
Transmission And Reflection

An approximate analytical method is presented for determining the transmission and reflection of elastic waves at a frictional boundary. The method is applied to the case of plane harmonic shear waves normally incident on a Coulomb friction boundary between semi-infinite elastic media. The accuracy of the method is determined by comparison of approximate and exact solutions in a numerical example.

Similarity problems of the theory of unsteady concentration boundary layer

1983 ◽  
Vol 48 (10) ◽  
pp. 2751-2766
Author(s):  
Ondřej Wein ◽  
N. D. Kovalevskaya
Keyword(s):  
Boundary Layer ◽  
Approximate Method ◽  
Steady Flow ◽  
Broad Class ◽  
Concentration Boundary Layer ◽  
Concentration Change ◽  
Concentration Boundary ◽  
Flow Problems

Using a new approximate method, transient course of the local and mean diffusion fluxes following a step concentration change on the wall has been obtained for a broad class of steady flow problems.

scholarly journals Simple and Exact Closed-Form Expression for Determination of a Penetrated Ray Path in a Ray Tracing

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hyun Wook Moon ◽  
Woojoong Kim ◽  
Sewoong Kwon ◽  
Jaeheung Kim ◽  
Young Joong Yoon
Keyword(s):  
Closed Form ◽  
Approximate Method ◽  
Ray Tracing ◽  
Conventional Method ◽  
Closed Form Expression ◽  
Indoor Environments ◽  
Straight Line ◽  
Ray Path ◽  
Ray Tracing Simulation

A simple and exact closed-form equation to determine a penetrated ray path in a ray tracing is proposed for an accurate channel prediction in indoor environments. Whereas the penetrated ray path in a conventional ray tracing is treated as a straight line without refraction, the proposed method is able to consider refraction through the wall in the penetrated ray path. Hence, it improves the accuracy in ray tracing simulation. To verify the validation of the proposed method, the simulated results of conventional method, approximate method, and proposed method are compared with the measured results. The comparison shows that the proposed method is in better agreement with the measured results than the conventional method and approximate method, especially in high frequency bands.

scholarly journals On some nonlinear inverse problems in elasticity

2011 ◽  
Vol 38 (2) ◽  
pp. 125-154 ◽  
Author(s):  
S. Andrieux ◽  
H.D. Bui
Keyword(s):  
Inverse Problems ◽  
Closed Form ◽  
Variational Equation ◽  
Material Constant ◽  
Displacement Discontinuity ◽  
Crack Plane ◽  
Nonlinear Case ◽  
Elastic Solids ◽  
Linear Inverse Problems ◽  
Statics And Dynamics

In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack plane, then the crack plane and finally the geometry of the crack, defined by the support of the crack displacement discontinuity, are determined explicitly. We also consider the problem of a volumetric defect viewed as the perturbation of a material constant in elastic solids which satisfies the nonlinear Calderon?s equation. The nonlinear problem reduces to two successive ones: a source inverse problem and a Volterra integral equation of the first kind. The first problem provides information on the inclusion geometry. The second one provides the magnitude of the perturbation. The geometry of the defect in the nonlinear case is obtained in closed form and compared to the linearized Calderon?s solution. Both geometries, in linearized and nonlinear cases, are found to be the same.

New Insights Into Slip-Stick Vibrations From Compact, Closed-Form Analysis

2017 ◽  
Author(s):  
Deborah Fowler ◽  
David Peters
Keyword(s):  
Closed Form ◽  
Coulomb Friction ◽  
Sliding Friction ◽  
Piecewise Linear ◽  
Limited Range ◽  
System Behavior ◽  
Form Analysis ◽  
Mass Damper ◽  
The Times ◽  
Sticking Point

A mechanical system sliding on a moving surface with Coulomb friction is a rich area for study. Despite much past work, there is still something to be gleaned by closed-form expressions for the system behavior. Consider a spring-mass-damper system (K, M, C) with deflection x, base moving in the +x direction at velocity V, sliding friction F, and sticking friction Fs. An initial condition of x0 at rest can be considered general because all possible motions will follow. Two dimensionless schemes are used. For the abstract, we focus on the scheme normalized by x0 with variable z = x/x0, τ = (ωnt, ωn = [K/M]1/2, ζ = c/[2(KM)1/2], ν̄ = V / (ωnx0), f = F/(Kx0), and fs = Fs/(Kx0). Since the solution is piecewise linear, this allows closed-form results. For this abstract, we consider C = 0, Fs = F. (Other cases are in the paper.) There are three critical ground speeds. The first, ν̄d, is when sticking first occurs (at z = f). At the second speed, ν̄c, sticking has moved to z = −f. Thereafter, the sticking point again increases, reaching z = f at the third speed, ν̄b. For higher ν̄, there is no sticking. In this paper, closed form expressions are presented for the three critical speeds:(1)ν¯d=[(1+3f)(1−5f)]12,ν¯c=[(1+f)(1−3f)]12,ν¯b=1−f These formulas are verified by numerical simulation. The insight is that there is a limited range of f for which certain critical points can be reached. Thus, 0 < f < 1/5 has different dynamics than 1/5 < f < 1/3. Formulas are also derived for the second maximum of z, which gives an indication of decay or growth of the system. For example, with f = fs and C = 0, the second maximum z with f < 1/5 is:(2)zmax=f+((1−f)2−ν¯2−4f)2+ν¯2ν¯d<ν¯<ν¯czmax=ν¯+fν¯c<ν¯<ν¯bzmax=1ν¯>ν¯c Formulas will also be given for the times at which the maximum occurs and the times at which a transition occurs from static to sliding for all cases.

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