چكيده به لاتين
In this thesis, simultaneous energy harvesting and vibration mitigation through a nonlinear multistable magnetopiezoelastic absorber is investigated. The main structure is a beam under a harmonic external excitation. Furthermore, the absorber is composed of a piezoelectric beam with a magnetic tip mass and two external magnets. The interaction of the magnets generates multistability in the absorber.
First, using the extended Hamilton’s principle, nonlinear equations governing the system were derived. Then, the response of the linear system, fixed-point solutions of the nonlinear system, and bifurcations of the absorber fixed-points were studied based on numerical methods. The results show that by varying the magnets gap, the nonlinear restoring force and potential energy of the absorber change. Moreover, the fixed-point solutions of the absorber undergo saddle-node and pitchfork bifurcations and cause the absorber to change from monstable to bistable and tristable types. Next, the dynamical response of the system was studied for investigating the response and performance of the absorber in the presence of the harmonic excitation. First, numerical solutions in time and frequency domains were obtained. The result showed that based on the frequency and amplitude of the external excitation, the absorber can exhibit small amplitude in-well periodic, high amplitude inter-well aperiodic, and high amplitude inter-well periodic oscillations. Furthermore, in case of the high amplitude inter-well aperiodic oscillations, the system experiences a strongly modulated response (SMR), and the absorber harvests a considerable level of electrical energy and suppresses vibrations over a broad frequency bandwidth. In this state, the absorber performance is better compared with the other regimes. Next, the response of the system was validated by harmonic balance method. Further, the performance of the absorber in bistable and tristable configurations was compared, and the results disclosed that compared to the system with a tristable absorber, the response of the system carrying a bistable absorber is less sensitive to initial conditions, owing to its potential function shape. Besides, the vibration mitigation and average harvested energy per average kinetic energy of the main system carrying a bistable absorber were found to be higher compared with the system with a tristable absorber.
Next, using the slow invariant manifold of the system, the minimum and maximum excitation amplitudes for the occurrence of the SMR in the vicinity of 1:1 resonance were obtained. Furthermore, the concept of potential well escape was utilized and the emergence and disappearance of SMR were studied in frequency-response and force-response bifurcation diagrams. Moreover, the performance of the bistable absorber was compared with its corresponding cubic nonlinear energy sink. The results show that the bistable absorber harvests energy over a broader frequency band and suppresses vibrations more compared with the nonlinear energy sink.
Finally, in order to validate the results experimentally, a prototype of the system carrying a linear absorber was constructed and comprehensive investigations were done. Besides, for considering the shaker force drop off phenomenon in a shaker frequency sweep test and keeping the excitation amplitude constant, the mathematical model of the shaker was derived and integrated into the structural model of the main beam and absorber. The experimental results show that the proposed model captures the system response as well as shaker force drop off phenomenon. Furthermore, the absorber concurrently harvests energy and mitigates vibrations. Therefore, the experimental results disclose that the findings of this research are valid. Finally, the maximum harvested power of the piezoelectric absorber and its corresponding load resistance were obtained experimentally.