A comparative study of the vibro-impact capsule systems with one-sided and two-sided constraints

This paper studies the dynamics of the vibro-impact capsule systems with one-sided and two-sided soft constraints under variations of various system and control parameters, including mass ratio, stiffness ratio, gap of contact, and amplitude and frequency of external excitation. The aim of this study is to optimise the progression speed and energy consumption of the capsule and minimise the required cabin length for prototype design used for engineering pipeline inspection. Our studies focus on three systems: the capsule with a right constraint, the capsule with a right and a weak left constraints, and the capsule with a right and a strong left constraints. Bifurcation analyses show that the behaviour of the capsule with one-sided constraint is mainly periodic, and the dynamic responses of the other two capsules with two-sided constraints become complex when the stiffness of the left constraint increases. Based on our extensive comparisons, the following optimisation strategies are recommended. When the capsule speed is paramount, one can employ the two-sided capsule with a weak left constraint under large amplitude of excitation. When energy consumption is taken into account, the one-sided capsule is preferable. When a miniaturized prototype is needed, the two-sided capsule with a strong left constraint is the best choice.