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.

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.

Interaction of a shear wall with the soil for incident plane SH waves

1972 ◽  
Vol 62 (1) ◽  
pp. 63-83
Author(s):  
M. D. Trifunac
Keyword(s):  
Incidence Angle ◽  
Closed Form Solution ◽  
Shear Wall ◽  
Elastic Half Space ◽  
Form Solution ◽  
Angle Of Incidence ◽  
Sh Waves ◽  
Incident Plane ◽  
Interaction Equation ◽  
Plane Sh Waves

Abstract The closed-form solution of the dynamic interaction of a shear wall and the isotropic homogeneous and elastic half-space, previously studied only for vertically-incident SH waves, is generalized to any angle of incidence. It is shown that the interaction equation is independent of the incidence angle, while the surface-ground displacements heavily depend on it. For the two-dimensional model studied, it is demonstrated that disturbances generated by waves scattering and diffracting around the rigid foundation mass are not a local phenomenon but extend to large distances relative to the characteristic foundation length.

Torsional response of structures for SH waves: The case of hemispherical foundations

1976 ◽  
Vol 66 (1) ◽  
pp. 109-123
Author(s):  
J. E. Luco
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Basic Step ◽  
Sh Waves ◽  
Torsional Response ◽  
Obliquely Incident ◽  
Incident Plane ◽  
Interaction Problem ◽  
Plane Sh Wave ◽  
Plane Sh Waves

abstract A study is made of the harmonic torsional response of an elastic structure placed on a rigid hemispherical foundation which is supported on an elastic medium and is subjected to the action of obliquely incident plane SH waves. As a basic step in the solution of the torsion interaction problem, a closed-form solution is obtained for the torsional response of a rigid hemispherical foundation excited externally by a harmonic torque and through the soil by an obliquely incident plane SH wave. Comparisons between the results for a hemispherical foundation with those for a circular plate allow the estimation of the effects that the embedment of the foundation has on the torsional response of the superstructure.

Variational Formulation for Frictional Interface Dynamics

2012 ◽  
Author(s):  
Timothy Truster ◽  
Arif Masud ◽  
Lawrence A. Bergman
Keyword(s):  
Finite Element ◽  
Dynamic Response ◽  
Coulomb Friction ◽  
Bolted Joints ◽  
Lap Joint ◽  
Stick Slip ◽  
Element Simulation ◽  
Friction Models ◽  
Frictional Interface ◽  
Current Emphasis

The dynamic response of component bolted joints often plays a significant role in the overall behavior of a structural system. Accurate finite element simulation of these problems requires proper treatment of the interface conditions. We present a formulation carefully suited to these problems that incorporates discontinuous Galerkin (DG) treatment locally at the interface. The present work is an extension of our previous investigations of friction models within a finite element method for quasi-static problems. The current emphasis is on the treatment of the inertial term and ensuring that artificial resonance is not induced by the discrete interface. The weak imposition of continuity constraints allows the stick-slip behavior at the jointed surface to proceed smoothly, reducing the numerical instability compared to node-to-node contact techniques. As a model problem, we simulate the dynamic response of a lap joint subjected to an impulse axial force assuming Coulomb friction at the interface.

scholarly journals Stiffness of sphere–plate contacts at MHz frequencies: dependence on normal load, oscillation amplitude, and ambient medium

2015 ◽  
Vol 6 ◽  
pp. 845-856 ◽  
Author(s):  
Jana Vlachová ◽  
Rebekka König ◽  
Diethelm Johannsmann
Keyword(s):  
Imaginary Part ◽  
Coulomb Friction ◽  
Ambient Medium ◽  
Normal Load ◽  
Contact Stiffness ◽  
Oscillation Amplitude ◽  
Partial Slip ◽  
Squeeze Flow ◽  
Frictional Stress ◽  
The Real

The stiffness of micron-sized sphere–plate contacts was studied by employing high frequency, tangential excitation of variable amplitude (0–20 nm). The contacts were established between glass spheres and the surface of a quartz crystal microbalance (QCM), where the resonator surface had been coated with either sputtered SiO2 or a spin-cast layer of poly(methyl methacrylate) (PMMA). The results from experiments undertaken in the dry state and in water are compared. Building on the shifts in the resonance frequency and resonance bandwidth, the instrument determines the real and the imaginary part of the contact stiffness, where the imaginary part quantifies dissipative processes. The method is closely analogous to related procedures in AFM-based metrology. The real part of the contact stiffness as a function of normal load can be fitted with the Johnson–Kendall–Roberts (JKR) model. The contact stiffness was found to increase in the presence of liquid water. This finding is tentatively explained by the rocking motion of the spheres, which couples to a squeeze flow of the water close to the contact. The loss tangent of the contact stiffness is on the order of 0.1, where the energy losses are associated with interfacial processes. At high amplitudes partial slip was found to occur. The apparent contact stiffness at large amplitude depends linearly on the amplitude, as predicted by the Cattaneo–Mindlin model. This finding is remarkable insofar, as the Cattaneo–Mindlin model assumes Coulomb friction inside the sliding region. Coulomb friction is typically viewed as a macroscopic concept, related to surface roughness. An alternative model (formulated by Savkoor), which assumes a constant frictional stress in the sliding zone independent of the normal pressure, is inconsistent with the experimental data. The apparent friction coefficients slightly increase with normal force, which can be explained by nanoroughness. In other words, contact splitting (i.e., a transport of shear stress across many small contacts, rather than a few large ones) can be exploited to reduce partial slip.

Antiplane dynamic soil-bridge interaction for incident plane SH-waves

1977 ◽  
Vol 5 (2) ◽  
pp. 107-129 ◽  
Author(s):  
A. M. Abdel-Ghaffar ◽  
M. D. Trifunac
Keyword(s):  
Sh Waves ◽  
Incident Plane ◽  
Plane Sh Waves
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