Available online at www.sciencedirect.com International Journal of Mechanical Sciences 45 (2003) 623–641 Modelling of vibro-impact system driven by beat frequency Ekaterina Pavlovskaia, Marian Wiercigroch ∗ Centre for Applied Dynamics Research, Department of Engineering, Fraser Noble Building, King’s College, University of Aberdeen, Aberdeen AB24 3UE, Scotland, UK Received 24 May 2002; received in revised form 28 April 2003; accepted 9 May 2003 Abstract A mathematical model of vibro-impact system accounting for oscillatory and progressive motion, and ca- pable of transferring a high-frequency low-amplitude excitation into low-frequency high-amplitude response is developed. A special beat frequency kinematic excitation was used, which has two distinctive features: (i) the low-frequency modulated excitation is tuned to the natural frequency of the oscillating system, and (ii) the excitation is asymmetric. The model considers also visco-elastic properties of the media. It is demonstrated that this mechanism allows to overcome the resistance force of the media and to move forward. Several dierent ways to achieve a steady progression without supplying additional energy are ex- plored, however, in all these cases progression rates are relatively low. A signicant increase of progression rates is only possible by controlling the motion of the system. A simple control strategy enhancing progression rates substantially is proposed and implemented. ? 2003 Elsevier Ltd. All rights reserved. Keywords: Vibro-impact system; Beat frequency excitation; Drift; Dry friction; Control; Nonlinear oscillator 1. Introduction Impacting oscillators or vibro-impact systems have numerous engineering applications, for exam- ple, pile driving [1], percussive drilling [2,3] and ground moling [4]. For a better illustration of the problem, let us consider a particular engineering application such as a vibro-impact ground moling. During operation the generated impact forces are used to drive a penetrating head into the ground. This can result in complex dynamic responses, as the system not only oscillates but also moves for- ward. Studies conducted by Woo et al. [4] and Lok et al. [5] have indicated that eective operation of ground moling machine is dependent upon the generation of an optimal combination of stable ∗ Corresponding author. Tel.: +44-1224-272509; fax: +44-1224-272497. E-mail address: m.wiercigroch@eng.abdn.ac.uk (M. Wiercigroch). URL: http://wwwcad.eng.abdn.ac.uk/∼eng373/ 0020-7403/03/$ - see front matter ? 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0020-7403(03)00113-9