Applying an oscillatory load is one of the most efficient ways to alter friction forces. Several theoretical and experimental studies on the influence of oscillatory loads on friction have been conducted, investigating the effect of both in-plane and out-of-plane oscillations for different tribological pairings. However, in the literature, the effect of an oscillatory load on the friction force has been studied with an emphasis on dynamic loads characterized by a high-frequency content, while a clear statement as to what is considered “high-frequency” is missing. Moreover, the effect of a combination of load directions on the friction reduction is not accounted for. Therefore, this study aims to determine the vibration-induced effect on friction regardless of the frequency range and direction of harmonic force for a single and multi-degree-of-freedom system. Analytical methods are used to obtain the friction modulation due to harmonic loads, considering a classical mass–spring–dashpot system on a moving belt and the Amontons–Coulomb law. It is found that, in the case of continuous slip, a general relation for the vibration-induced friction modulation is obtained utilizing the velocity response function of the investigated system. The latter is used to highlight a threshold from which the high-frequency regime starts and to determine the stick–slip boundaries. Moreover, through the velocity response function, the influence of different external harmonic forces is investigated and discussed. This includes considerations of phase, excitation frequency, system characteristics, and the choice of the normal contact force expression.@en

The Harmonic Balance Method (HBM) is often used to determine the stationary response of nonlinear discrete systems to harmonic loading. The HBM has also been applied to nonlinear continuous systems, but in many cases the nonlinearity consists of discrete nonlinear elements. This chapter demonstrates the application of the HBM to dissipative continua with distributed nonlinearity by analysing three canonical problems: (a) 1-D layer with a free surface and rigid base (interfering upward and downward propagating shear waves), (b) 1-D half-space with a rigid base (vertically propagating shear waves), and (c) 2-D axially symmetric semiinfinite medium with a circular cavity (radially propagating compressional waves), all of them subject to harmonic excitation at a boundary. Results show that systems (a) and (c) exhibit softening behaviour and super-harmonic resonances, while only the former displays multiple response amplitudes for certain excitation frequencies; the unique frequency-amplitude relationship of system (c) is due to the strong damping (i.e., radiation damping and internal dissipation). Furthermore, although system (b) essentially does not resonate, the third-harmonic component exhibits a maximum caused by the interplay between the dissipative and nonlinear effects, a phenomenon that also occurs in system (c). Finally, the considered systems have applications in earthquake and geotechnical engineering, among others, but the presented methodology is generic.@en