Usage of Coulomb friction acting on a wedge to attenuate vibration

Considered herein is a small wedge-shaped block that contacts a rough surface on its angled face, with contact maintained by precompressed springs. The wedge is connected to a large mass that is subjected to a harmonic excitation. The development begins with a derivation of equations for the normal and friction forces, which are shown to depend on the displacement and acceleration of the wedge as well as the external force. Enforcing Coulomb's law for sliding leads to a differential equation of motion in which the effective inertia and stiffness coefficients switch values according to whether the wedge advances or retreats. Algebraic expressions for the displacement in either state are supplemented by an assessment of sticking based on Coulomb's static friction rule. The solutions for motion and the assessment of sticking are assembled in a simple, yet general, algorithm that only requires calculation of algebraic formulas. Transient waveforms of displacement, acceleration, and transmitted force are calculated for a harmonic excitation at the natural frequency of the frictionless system. It is found that very large viscous damping ratios would be required to obtain the same steady-state amplitude.