Harmonics Suppression in a Class of Switched Mechanical System: A Contraction Theory Approach

This article studies the behaviour of switched mechanical systems with respect to periodic perturbations. The switching considered is due to the one-sided stiffness present in many practical engineering systems. Due to one-sided stiffness, the overall system behaves like nonlinear dynamics. One peculiar phenomenon of nonlinear dynamics is the presence of harmonics in the response along with fundamental components when excited with periodic input. Hence, the response of these types of mechanical systems contains k-periodic solutions
$(\mathrm{k}=2,3,4)$
. Existence of these leads to the cause of unintended vibrations, which is adversarial for the system. In this paper, Contraction theory has been explored to suppress the components of k-periodic solutions in the output. The contractivity of the overall system ensures entrainment property which makes the output frequency the same as that of the input perturbation. A matrix measure is used to verify the Contraction of the overall switched system, which suggests the parameter regime for entrainment. Simulation results are attached to validate the proposition.