A comprehensive study on the behavior of a rigid block on an oscillating ground with friction, elastic and viscous forces. (July 2017) - Nicolas, M.
Abstract: This paper investigates the behavior of a non-linear mechanical model where a block is driven by an oscillating ground through Coulomb friction, a linear viscous damper and a linear spring. The governing equation is solved analytically for different partial configurations: friction only, friction with viscous damping, friction with a linear restoring force, and for the complete model. Using dimensionless groups, the analysis of the block motion provides a comprehensive set of information on the motion regime (stick, stick-slip or permanent sliding), on the dominant energies or forces, on the resonance and on the amplification of the ground oscillation by the system. The limit between the stick-slip regime and the permanent slipping regime is found either analytically or numerically. It is also shown that there exists a set of parameters for which the friction force, the viscous dissipative force and the elastic restoring force are equal. Abstract : Highlights: A comprehensive method of solving friction/viscous/elastic ground-driven oscillator. The limit between the stick-slip and the permanent slipping regimes is proposed. Sub-harmonic and super-harmonic resonances are observed. Existence of a triple point for which the three friction/viscous/elastic forces are equal.