Summary
This work aims to induce internal resonance through proportional feedback control. A two-Degrees-Of-Freedom (DOF) nonlinear oscillator consisting of two masses connected by cubic spring is considered. The first mass features a controlled force that feeds back this mass's position, equivalent to a grounded spring. The Frequency Energy Plot (FEP) of this class of systems can exhibit a 3:1 resonance tongue, but this phenomenon does not always appear. On this tongue, there is modal interaction between the nonlinear normal modes (NNMs). Its existence is of importance because it can influence the spatial energy distribution in the system, which is relevant to applications as vibration control and energy harvesting. The goal of this investigation is to find how one can guarantee the existence of internal resonance and what mechanisms are behind it. To achieve this, the equations of motion are inspected and the harmonic balancing method is applied to clarify the observed behaviour.
