Nonlinear shear wave interaction at a frictional interface: Energy dissipation and generation of harmonics

Abstract

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface.

Numerical and experimental study of the nonlinear interaction between a shear wave and a frictional interface

“…More recently, a similar analytical analysis and a numerical model were proposed in Ref. 17. The authors pointed out the relation between the energy dissipated by friction and the amplitude of higher harmonics.…”

“…This model is obviously simpler than the finite element (FE) model used in Ref. 17 but it captures what is believed to be the dominant physical processes. The results are in agreement with those of the FE model when investigating the effect of parameters such as the normal load or the input wave amplitude, confirming the model reasonably presents the physical reality.…”

Absolute measurement of ultrasonic non-linearity parameter at contact interface

“…FEM-based studies have been conducted to investigate CAN problems. [10,15,16] However, to the authors' knowledge, there has been no quantitative comparison between finite element simulations and the analytical results for the clapping mechanism. Therefore, it is desirable to build a numerical model and provide guidance for experimental measurement.…”

“…[14] Recently, both analytical and numerical analyses of the interaction of shear waves with frictional interfaces were implemented by Meziane et al, including the consideration of two different types of friction laws. [15] Although analytical models have been developed, [3,4,14] previous models have been limited to the analysis of idealised problems with simple boundary conditions. However, practical non-linear ultrasonic experiments involve complex boundary conditions and need to be set up carefully to avoid introducing other non-linearities from the experimental system.…”

Numerical simulation of Rayleigh wave interaction with surface closed cracks under external pressure

“…On the other hand, O'Neil et al extended Richardson's work to analyze the case of a shear wave crossing a friction-coupled interface, resulting from the "slipping" mechanism [17]. Recently, both analytical and numerical analyses of the interaction of shear waves with frictional interfaces have been implemented by Meziane, including the consideration of two different kinds of friction laws [18]. Based on this work, they also built FE model to study the nonlinear interaction between elastic waves and a crack of different orientations considering both clapping and slipping mechanisms [19].…”