Analysis and synthesis of modal and non-modal self-excited oscillations in a class of mechanical systems with nonlinear velocity feedback

Many devices and processes utilize self-excited oscillations either as the working principle or as the performance enhancer. The present paper investigates a nonlinear velocity feedback control method for generating artificial self-excited oscillations in a class of two degrees-of-freedom mechanical systems. The paper derives the conditions of existence and stability of the modal oscillations and numerically corroborates this. It also proposes a methodology to design the control system for inducing natural oscillations in one of the desired modes. Other than modal oscillations, the system can also be designed to oscillate in a non-modal state with the desired frequency and amplitude-ratio within a specific range (depending on the system). Numerical simulations confirm the analytical results. Further analysis shows that for each frequency of excitation, the control cost is minimum when the system operates at an optimal amplitude-ratio.