MS12.2: Nonlinear Dynamics for Engineering Design

A simplified mechanical model of shimmying towed wheel subjected to stochastic excitation has been investigated by using the method of bifurcation theory and numerical simulation. A Gaussian white noise is used to model the stochastic disturbance originated in side wind effects. Unstable periodic motions of the wheel are identified with Hopf bifurcation calculations. The stochastic jump phenomenon is observed through the probability density figures.

The vibro-impact capsule robot, which experiences vibrations, frictions, and impacts, is known as a non-smooth dynamical system. It exhibits a rich variety of different long-term behaviours that coexist for a given set of parameters, referred to as multistability or coexisting attractors. When the capsule moves in the gut, a particular attractor may dominate its dynamics, while other coexisting attractors could fade away. This significant change in dynamics poses challenges in locommotion control. In this study, I will introduce how we addressed these challenges through a ‘fantastic voyage’, encompassing mathematical modelling, numerical analysis, control and optimisation, experimental investigation, proof-of-concept validation, and ex vivo testing. Specifically, my study will focus on the non-smooth dynamics of the robot and how to fine-tune its system and control parameters for optimal performance in terms of progression rate and force generation. Numerical and experimental results from our recent studies will be presented to demonstrate its feasibility for lower gastrointestinal examinations. Finally, key challenging issues of the capsule robot are summarised, and new directions for future development are suggested.

To calculate the exact basin of attraction of a solution is a challenging task. For this very reason, various estimates are defined in the literature to gain an understanding on the dynamical robustness of a solution of a nonlinear system. Computing dynamical integrity measures efficiently is non-trivial. The MATLAB based DynIn Toolbox can estimate the local integrity measure of an equilibrium point effectively. In this study we extended the algorithm to compute the local integrity measure values for limit cycles. Therefore the local integrity measure had to be redefined for autonomous periodic orbits. The algorithm is capable of identifying periodic solutions while varying system parameters. Moreover, it can handle nonsmooth systems as well.