Path-following analysis of the dynamical response of a piecewise-linear capsule system

Acknowledgements The first author has been supported by a Georg Forster Research Fellowship granted by the Alexander von Humboldt Foundation, GermanyPeer reviewedPreprin

Marching bifurcations

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Optimization of the vibro-impact capsule system.

Optimization of the vibro-impact capsule system for the best progression is considered in this paper focusing on the choice of the excitation parameters and the shape of the capsule. Firstly, the fastest and the most efficient progressions are obtained through experimental investigations on a novel test bed. Control parameters, the amplitude and the frequency of harmonic excitation, and one of the system parameter, namely the stiffness ratio, are optimized. The experimental results confirm that the control parameters for the fastest progression are not the same as those for the most efficient progression from the energy consumption point of view. Therefore, the capsule system can be controlled either in a speedy mode or in an energy-saving mode depending on the operational requirements. In the second part of the paper, optimization of the capsule shape is studied using computational fluid dynamics (CFD) simulations. Here the aim of achieving the best progression is addressed through minimizing the drag and the lift forces acting on a stationary capsule positioned in the pipe within a fluid flow. The CFD results indicate that both drag and lift forces are dependent on capsule and arc lengths, and finally, an optimized shape of the capsule is obtained

Controlling multistability in a vibro-impact capsule system

This is the final version of the article. Available from Springer Verlag via the DOI in this record.This work concerns the control of multistability in a vibro-impact capsule system driven by a harmonic excitation. The capsule is able to move forward and backward in a rectilinear direction, and the main objective of this work is to control such motion in the presence of multiple coexisting periodic solutions. A position feedback controller is employed in this study, and our numerical investigation demonstrates that the proposed control method gives rise to a dynamical scenario with two coexisting solutions, corresponding to forward and backward progression. Therefore, the motion direction of the system can be controlled by suitably perturbing its initial conditions, without altering the system parameters. To study the robustness of this control method, we apply numerical continuation methods in order to identify a region in the parameter space in which the proposed controller can be applied. For this purpose, we employ the MATLAB-based numerical platform COCO, which supports the continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems.The second author has been supported by a Georg Forster Research Fellowship granted by the Alexander von Humboldt Foundation, Germany. The authors would like to thank Dr. Haibo Jiang for stimulating discussions and comments on this work

Calculating the Lyapunov exponents of a piecewise smooth soft impacting system with a time-delayed feedback controller

This is the final version. Available on open access from Elsevier via the DOI in this record.Lyapunov exponent is a widely used tool for studying dynamical systems. When calculating Lyapunov exponents for piecewise smooth systems with time delayed arguments one faces two difficulties: a high dimension of the discretized state space and a lack of continuity of the variational problem. This paper shows how to build a variational equation for the efficient construction of Jacobians along trajectories of the delayed nonsmooth system. Trajectories of a piecewise smooth system may encounter the so-called grazing events, where the trajectory approaches discontinuity surfaces in the state space in a non-transversal manner. For these events we develop a grazing point estimation algorithm to ensure the accuracy of trajectories for the nonlinear and the variational equations. We show that the eigenvalues of the Jacobian matrices computed by the algorithm converge with an order consistent with the order of the numerical integration method. Finally, we demonstrate the proposed method for a periodically forced impacting oscillator under a time-delayed feedback control, which exhibits grazing and crossing of the impact surface.EPSRCEuropean Union