8th. World Congress on Computational Mechanics (WCCM8) 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) June 30 –July 5, 2008 Venice, Italy Influence of Contact Force Models on the Global and Local Dynamics of Drifting Impact Oscillator Olusegun Ajibose 1 , * Marian Wiercigroch 2 , Ekaterina Pavlovskaia 3 and Alfred Akisanya 4 Centre for Applied Dynamic Research, School of Engineering, Kings College, University of Aberdeen, Aberdeen AB24 3UE, UK 1 o.k.ajibose@abdn.ac.uk, 2 m.wiercigroch@abdn.ac.uk, 3 e.pavlovskaia@abdn.ac.uk, 4 a.r.akisanya@abdn.ac.uk Key Words: Nonlinear dynamics, Impact Oscillator, Contact Mechanics. ABSTRACT The effect of the contact forces on the global and local dynamics of the drifting impact oscillators introduced in [1] is examined in this paper. The oscillator has been extensively studied in our earlier investigations. In particular, the drift was seperated from the bounded dynamics [2] and the five dimen- sional flow was reduced to one dimensional iterative map [3]. The current work builds upon previous studies by P˙ ust and Peterka [4] and Muthukumar et al [5]. In [4] the nonlinearity of restoring forces between solid bodies is modelled as function of the defor- mation and velocity for non-drifting impact oscillators where the free and forced vibration of systems with Hertz contact were considered, while [5] uses a Hertz contact force model, which incorporates non-linear hysteresis damping, to simulate pounding, a phenomenon which occurs during the collision of building structures in earthquakes. Three models are considered in the current study, namely the Kelvin-Voigt (KV), the Hertz stiff- ness (HS) and nonlinear contact stiffness and damping (NSD) models. The Kelvin-Voigt model was studied extensively in our previous work (e.g. [1–3]) and is a reference for the current two models. In the HS model, the contact force is a sum of spring force obeying the Hertz’s law and a linear damping force. The NSD model presents the contact forces as a combined effect of Hertz’s spring and a nonlinear hysteresis damping element. The equations of motion of the different models are written concisely in terms of dimensionless displacements and time: x ′ = y, (1) y ′ = a cos(ωτ + ϕ)+ b - P 1 P 2 (1 - P 3 )L 1 (z,v,z ′ ) - P 1 P 3 , (2) z ′ = P 1 y - (1 - P 1 )L 2 (z,v)/2ξ, (3) v ′ = P 1 P 3 P 4 (L 3 (z,v)/2ξ + y). (4) where x, z and v are the displacement of the mass, slider top and bottom respectively. y is the mass velocity, g the initial gap between the mass and top slider, a is the amplitude of the dynamic force, b is the static force and P 1 ,P 2 ,P 3 and P 4 are Heaviside functions defined as: P 1 = H (x - z - g), P 2 = H (L 2 (z,v)), P 3 = H (L 2 (z,v) - 1), P 4 = H (v ′ ).