An inerter-enhanced piezoelectric tuned mass damper for integrated structural vibration mitigation and energy harvesting

This study proposes an inerter-enhanced piezoelectric tuned mass damper (IEP-TMD) for integrated structural vibration mitigation and vibration energy harvesting under lightweight installation conditions. The proposed device combines a tuned oscillator, an inerter, and a piezoelectric transduction path. The inerter amplifies the apparent inertia of the auxiliary branch and enhances vibration-energy transfer from the primary structure, while the piezoelectric element converts part of the transferred mechanical energy into electrical power. An electromechanically coupled model of the controlled structure equipped with the IEP-TMD is established under base excitation, and the frequency response functions, stationary random responses, and power balance relationships are analytically derived. Based on these formulations, a dual-objective optimization framework is developed to minimize the structural kinetic energy and maximize the harvested electrical power. The results show that the inerter modifies the input-energy mechanism through apparent inertia amplification, whereas the piezoelectric transduction path redistributes the transferred vibration energy and introduces frequency-dependent equivalent stiffness and damping. Comparative analyses demonstrate that the proposed IEP-TMD achieves better vibration mitigation and energy harvesting performance than conventional TMD, TMDI, and PE-TMD systems under the same physical mass condition. Across eight selected earthquake records, the IEP-TMD reduces the average RMS displacement response of the primary structure by approximately 44% compared with the uncontrolled structure. Compared with the PE-TMD, the average RMS relative displacement of the absorber is reduced by approximately 84%, while the average harvested power is increased by approximately 79%. These results indicate that the proposed IEP-TMD provides an effective and compact solution for lightweight structural vibration mitigation and structural monitoring powered by harvested vibration energy.