Dynamic response of multi-degree-of-freedom systems with a Coulomb friction contact under harmonic excitation

Abstract This paper investigates the steady-state response of a harmonically excited multi-degree-of-freedom (MDOF) system with Coulomb contact between: (1) mass and fixed wall; (2) two different masses; (3) an oscillating base. Although discrete MDOF models are commonly used at early design stages to analyse dynamic performances engineering structures, current understanding friction damping effects on behaviour is still limited due absence analytical solutions. In this contribution, closed-form expressions continuous time response, displacement transmissibility phase angle each derived validated numerically for 2DOF 5DOF systems. Moreover, features investigated, obtaining following results: (i) determination minimum amounts which resonant peaks become finite (ii) stick-slip motion can be observed high frequencies; (iii) equation evaluation invariant points transmissibilities; (iv) better phenomena such as inversions curves onset additional permanent sticking in contact. All these results show that systems exhibit significantly behaviours depending whether harmonic excitation applied same or masses.