Slip-stick steady-state solution for simple coulomb-damped mass

A new, passive, dissipation element that utilizes Coulomb friction between slipping elements to brake horizontal building motions has been recently introduced. In concept, the device is composed of a large number of staggered braking rods that approximate a continuous pattern. Its behavior is highly nonlinear, and the numerical integration method must be used to study the dynamic response of structures damped with this device. An oscillator damped by a simple Coulomb-damped mass consisting of a single massless rod, however, will yield closed-form solutions. This paper presents a closed-form solution for the slip-stick behavior of the proposed system. Conditions for the three steady-state motions, as well as analytical and numerical results, are also presented.