MS13.2: Energy Transfer and Harvesting in Nonlinear Systems

A phenomenon called passive self-tuning resonance can be found during excitation of a system consisting of a beam and a moving mass. In this phenomenon, due to the nonlinear coupling between the vibration of the beam and the motion of the mass, the mass can move passively to one of the anti-nodes of some vibration mode along the beam under excitation, and as a result, the entire system can resonate. In this study, magnetic support utilizing the pinning effect of the superconductor is applied to this system with an eye to the application of this phenomenon to energy harvesting through vibrational power generation. The non-contact elastic support by nonlinear magnetic force is expected to increase the amplitude and the frequency bandwidth of the resonance, which may be advantageous for vibrational power generation. Through excitation experiments, it was observed that passive self-tuning resonance can occur even in magnetically supported systems. The amplitude of the resonance was larger than that of the fixed-supported system. Furthermore, resonance was observed over a wide frequency bandwidth under the excitation near the natural frequency of the second mode. According to the measurement results of the vibration mode shapes and frequencies, it was confirmed that the behavior of the system transitioned from the resonance of the second mode to the resonance of the first mode during the process of excitation. This may have been caused by nonlinear coupling of multiple modes.

In the present study, we analyze the transient response of locally excited chain of strongly anharmonic self-sustained oscillators. This discrete system under consideration models the dynamics of genuinely non-linear, aero-elastic metamaterial. We particularly focus on the transient evolution of the traveling dissipative breathers, forming in locally excited, homogeneous and inhomogeneous chains of self-sustained oscillators. The genuinely anharmonic nature of system under consideration, turns the asymptotic analysis of transient regimes arising in this type of models to a highly challenging task. In the present study, we formulate a special analytical approach which allows for a simple, explicit and fairly accurate analytical description of amplitude evolution of the breather core towards the steady-state as well as its instantaneous position.

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.