Investigation of a Tuned Mass Damper with Piezoelectric Stack Energy Harvester Attached to an Undamped Primary Structure Under Harmonic Base Excitation

This paper develops the fixed-point theory for the optimal design of tuned mass dampers with piezoelectric stack energy harvesters under harmonic base excitation. The existence of two fixed points of the amplitude-frequency curve of the primary structure is proved. Based on the requirements for suppressing the vibration of the primary structure and enlarging the harvested power, the optimal tuning, damping, and resistance ratios are determined. Numerical examinations of the system with the obtained optimal parameters are performed, demonstrating a very good compatibility between theory and computation. More specially, it is shown that not only the vibration of the primary structure is effectively reduced but also a large amount of the harvested energy can be captured in the main resonance domain.