Abstract
Discontinuous friction and impact exist in a variety of piecewise-smooth dynamical systems that exhibit rich and complex nonlinear phenomena. This paper aims to study the discontinuity-induced grazing and adding-sliding bifurcations in a piecewise-smooth capsule system subjected to bidirectional drifts. For this purpose, analytical and semi-analytical onset conditions of the impact-induced grazing and the friction-induced adding-sliding bifurcations are investigated by solving explicitly the underlying piecewise-linear model. In this way, parametric relations revealing the occurrence mechanisms of transitions of the system from stationary to forward progression are derived. This analytical approach is verified numerically using path-following techniques for piecewise-smooth dynamical systems. The numerical investigation includes a parametric study of the observed capsule's average velocity and power consumption suggesting optimum parameters for system operation.
Highlights
Vibro-impact systems appear naturally in a broad variety of engineering applications, such as drilling [1, 2], moling [3], nonlinear energy sink [4, 5], energy harvesting [6, 7] and medical diagnosis [8, 9]
A piecewise-smooth capsule system with bidirectional drifts was investigated in this paper via numerical and analytical approaches
The bifurcation analysis in this paper provides an in-depth understanding of the nonlinear behaviour of the piecewise-smooth capsule system when impact and friction are encountered
Summary
Vibro-impact systems appear naturally in a broad variety of engineering applications, such as drilling [1, 2], moling [3], nonlinear energy sink [4, 5], energy harvesting [6, 7] and medical diagnosis [8, 9]. The authors have studied this system in the past few years focusing on numerical modelling and analysis [12, 34, 36, 44, 45], control [10, 20, 38] and experimental verification [8, 9, 37, 39] Different from these works, the contribution of the present paper is on the development of numerical and analytical approaches for detecting the onset conditions of the impact-induced grazing bifurcation and the friction-induced adding-sliding bifurcation for the capsule system.
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