Influence Of Micro Gap On Wave Transmission With Consideration Of Frictional Contact

The study of wave transmission through a micro gap with consideration of contact is of important significance on seismic engineering and non-destructive evaluation. In the bridge structure, the interface between the ground and foundation is a contact interface, where micro gaps may exist. When struck by strong stress waves, sliding and separating may happen between the ground and foundation. In addition, the initial crack (taken as a micro gap in a component) has great effects on the remaining fatigue life of critical details on steel bridge in the non-destructive testing. Therefore, the research on wave transmission through a micro gap is meaningful both in theory and practice.The present paper studied the influence of a micro gap on wave transmission with consideration of frictional contact theoretically. Since the contact and non-contact zones are unknown as a part of the solution and the boundary conditions involve inequalities, the problem is indeed a nonlinear one. The analytical solutions exhibit their advantages in the qualitative analysis in a physical sense, thus we aim to study the problem theoretically. Based on the Fourier analysis technique and the analytical method for unilateral interface developed by Comninou and Dundurs, we solved the problem by adding a corrective solution to the common solution of a half-space. The locations and extents of the separation, slip and stick zones, the interface tractions and slip velocities, the reflection and refraction coefficients and energy partition were displayed. Moreover, the effects of initial gap width, coefficients of friction, incident angles and transmitter parameters were discussed. The conclusions are listed as follows.(1) The results depend on the gap width, incident amplitude, frictional coefficient, incident angle and transmitter parameters. The separation zones are determined only by the normalized initial gap d/A0 and increase with d/A0 increasing.(2) There exists a slip zone in the leading edge of the separation zone in all cases, which increases with f decreasing. As incident angle increases, the extents of the slip zones at both edges of the separation zones increase while the stick zones decrease. The interface tractions and slip velocities act discontinuously at the leading edge of the contact zone due to the fact that the solids come to contact with different velocities.(3) Due to initial gap, reflected and refracted waves contain all higher frequencies. For higher harmonics of m=2, the reflected and refracted waves increase as d/A0 increases until a critical value is reached and then decrease. These relations are quite effective on non-destructive testing of a pre-existing gap.(4) The initial gap width has significant effects on the energy partition. With the initial gap width increasing, the energy carried by the reflected waves increases while that by the refracted waves decreases, but the energy dissipated by friction has no significant changes. The energy extracted by the refracted waves increases with the ratio of wave impedance increasing. These provide a theoretical foundation for bridge engineering when considering the energy transmission between the ground and foundation.