This paper proposes a low-cost and efficient piezoelectric tuned mass damper (Piezo-TMD) for structural vibration reduction and energy harvesting. The Piezo-TMD consists of not only a proof mass, piezoelectric materials deforming in the d33 mode, and an electrical resistance, but also a spring and an inductor which enable the mechanical frequency and electrical frequency of the Piezo-TMD to be tuned to the structural resonance frequency. The equations of motion of a structure with the Piezo-TMD are derived, and an optimal design procedure for the Piezo-TMD is proposed to achieve a simultaneous maximum vibration reduction and energy harvesting. The performance of the Piezo-TMD is compared with that of a conventional optimal TMD installed in a footbridge under a pedestrian loading. The simulation results show that the Piezo-TMD performs better than the optimal conventional TMD in terms of vibration reduction while efficiently converting the absorbed mechanical energy to electricity with a high energy harvesting ratio. The innovative development of simultaneously tuning the mechanical and electrical systems leads to a much lower number of PZT stacks (saving 88% of piezoelectric materials in an illustrated case). The parametric study shows that the Piezo-TMD achieves the best performance when the optimal values for the spring stiffness, resistance, inductance, and the number of piezoelectric stacks are adopted from the proposed optimal design. If the selected spring stiffness and inductance are uncertain in a range between 0.94-1.07 times the optimal values, the vibration reduction performance of the Piezo-TMD remains similar, and the energy harvesting performance reduces less than 5%, as compared to the optimal performance. The effect of the number of piezoelectric stacks was also investigated. An insufficient number of piezoelectric stacks reduces the Piezo-TMD performance, and an excessive stack number does not improve the Piezo-TMD performance but increases the Piezo-TMD cost. Finally, the proposed Piezo-TMD employs inductance to significantly reduce the PZT stack number, thereby significantly reducing the cost of Piezo-TMDs.
SUMMARYIn this paper, an optimal energy dissipation control algorithm is applied into a semi-active suspension-type tuned mass damper (SA-STMD) to suppress excessive vibration by means of variable pendulum length. The SA-STMD mechanism consists of a mass block, a suspension rope, and a movable fulcrum that can be a short tube driven by a linear motor to vertically move along the suspension rope. As the fulcrum goes up, the pendulum length is extended, resulting in a smaller stiffness of the SA-STMD, and vice versa. Accordingly, the restoring force in the SA-STMD can be adjusted by varying the fulcrum positions. In the case where the energy dissipation ability by the original STMDs is insufficient, the movable fulcrum in the SA-STMD system can compensate the STMDs for stiffness according to the proposed optimal energy dissipation control algorithm to provide controllable restoring forces. The controllable restoring forces are designed to act as viscous dampers that can make up for the lack of energy dissipation capacity. The numerical results from the time domain and frequency domain analyses show that the proposed approach utilizing the optimal energy dissipation control algorithm to adjust the pendulum length can induce controllable restoring forces with a butterfly-shaped hysteresis loop, supplying a sufficient energy dissipation capacity to reduce responses to the unexpectedly large external vibration. Another potential benefit is cost reduction because of use of a less number of conventional viscous dampers in the STMD system.
Summary
The present study aims at demonstrating the feasibility of semi‐active phase control of tuned mass dampers (TMDs) implemented in structures for simultaneous reduction in translational and torsional vibration. The semi‐active phase control, which employs a semi‐active friction device, applies the friction force at certain situations to adjust the TMD phase back to the 90° phase lag. Thus, the phase control tuned mass dampers (PC‐TMDs) can develop the best power flow to reduce the structural vibration. In this paper, a complete phase control algorithm is proposed by considering a full range of phase differences. The proposed PC‐TMDs not only improve the control performance but also prevent the TMD power from flowing back to the main structure. Furthermore, conventional suspension‐type TMDs have only one tuning frequency and exhibit a potential off‐tuning issue, lacking an ability to simultaneously suppress the structural translational and torsional vibration. The feasibility of application of the PC‐TMDs is verified through various numerical simulations, and a practical mechanism for the PC‐TMDs is introduced. The simulation results reveal the robustness of the PC‐TMDs, particularly when the PC‐TMDs are de‐tuned to the structure. Therefore, the PC‐TMDs outperform the conventional TMDs in terms of suppressing the structural responses in all the translational and torsional directions.
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