Journal of Sound and < ibration (2000) 229(5), 1171 } 1192 doi:10.1006/jsvi.1999.2594, available online at http://www.idealibrary.com on COULOMB FRICTION OSCILLATOR: MODELLING AND RESPONSES TO HARMONIC LOADS AND BASE EXCITATIONS H.-K. HONG AND C.-S. LIU Department of Civil Engineering, ¹ aiwan ;niversity, ¹ aipei, ¹ aiwan (Received 1 June 1999, and in ,nal form 6 August 1999) In this paper we revisit a mass}spring}friction oscillator, where the friction refers to Coulomb's perfect dry contact friction. We re"ne the model formulation of the friction force and "nd that the equation of motion of the oscillator is a two-phase linear system with a slide-stick switch, rather than the usual three-phases equations. Also we obtain a simple slide}slide condition. Then the exact solution of the response to simple harmonic loading is obtained. With the aid of the long-term behavior of the exact solution, the steady motions of the oscillator with 0, 1, 2, 4, 6, 8, 10, 12, 14 stops per cycle are categorized in the parametric space of the ratios of forces and frequencies. Stops of zero duration are further classi"ed into two types: normal stops and abnormal stops, the criteria of which are also given.  2000 Academic Press 1. INTRODUCTION The study of non-linear, hysteretic behavior of mechanical systems has been of great interest to engineers and researchers in a variety of engineering "elds, since many engineering systems exhibit hysteretic behavior under cyclic loading. A survey of various non-linear oscillators was given in, for example, Nayfeh and Mook [1]. In this paper, we study a single-degree-of-freedom oscillator with the parallel presence of a linear spring and a Coulomb friction device, which is subjected to external loading or base excitation. A schematic drawing is given in Figure 1 displaying a mass}spring system with the mass possibly sliding against a dry surface when subjected to an external load p (t). The equation of motion of the oscillator is mx K (t)#k [x (t)!x  ]#r  (t)"p (t), (1) where a superposed dot represents time di!erentiation: x, x R , x K and m are the position co-ordinate, velocity, acceleration and mass, respectively, of the body of the oscillator; k is the sti!ness of the spring; x  is the (static equilibrium) position of the body of the oscillator at which the spring is not stretched so that the spring force is zero; r  is the friction force acting in a direction opposite to the direction of the 0022-460X/00/051171#22 $35.00/0  2000 Academic Press