Nonlinear Dynamics for Engineering Design: Good Vibrations

In this lecture I will paint a broad picture of the nonlinear world and examine implications of this view on science and engineering. Through carefully chosen examples from everyday life, science and engineering I will show just how nonlinear and dynamic our world really is.

In the first part, I will define nonlinearity and nonlinear dynamics. Specifically I will focus on a class called non-smooth dynamical systems. Then I will show how such problems can be effectively modelled and analysed by low dimensional dynamical systems [1,2]. The generic complexity of non-smooth dynamics will be demonstrated by a soft impact oscillator – an archetypal model for the high frequency vibro-impact drilling [3,5].

The second part will be devoted to what we might call Nonlinear Dynamics for Engineering Design where I will present results from my recent projects, where nonlinear dynamic interactions have been used to enhance the performance of real systems and structures. I will put a special emphasis on one large project from oil and gas industry, where we have developed a revolutionary downhole drilling technology [5]. I will argue that this would not be possible in a linear and static world!

1. Ing, J., Pavlovskaia, E., Wiercigroch, M. and Banerjee, S. 2010 Physica D 239, 312-321. Bifurcation analysis of an impact oscillator with one sided elastic constraint near grazing.
2. Cao, Q. Wiercigroch, M., Pavlovskaia, E.E., Thompson, J.M.T. and Grebogi, C. 2008 Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics. Philosophical Transactions of the Royal Society – Part A 366, 635-652.
3. Pavlovskaia, E., Hendry, D.C. and Wiercigroch, M. 2015 International Journal of Mechanical Sciences 91, 110-119. Modelling of high frequency vibro-impact drilling.
4. Wiercigroch, M., Wojewoda, J. and Krivtsov, A.M. 2005 Dynamics of ultrasonic percussive drilling of hard rocks. Journal of Sound and Vibration 280(3-5), 739-757.
5. Wiercigroch, M. 2007 Resonance Enhanced Drilling: Method and Apparatus. Patent No WO2007141550.