| dc.description.abstract | In this study, the equation of motion and system analysis of a Piezoelectric-Tuned Mass Damper (Piezo-TMD) in the form of a piezoelectric cantilever beam are derived. The piezoelectric TMD is firstly derived from the piezoelectric constitutive equation combined with the cantilever beam according to the Euler–Bernoulli beam theory. Then, the piezoelectric cantilever beam is divided into element blocks with the finite element concept to superimpose in the form of a matrix equations. Afterward, the resistance and inductance are connected in series within the circuit to form a complete circuit loop. To verify the correctness of the derived matrix equations, the frequency response function is plotted to confirm the consistency with reference which is derived according to distributed parameters. The Piezo-TMD is not only designed to reduce the vibration of the structure, but also to harvest the vibration energy of the main structure. Therefore, the power generation efficiency is also considered as a second priority in design process. The piezoelectric damping ratio defined in this paper can be used as an indicator to represent the power generation efficiency. In order to understand which parameters will affect the maximum piezoelectric damping ratio, the sensitivity analysis of parameters of the Piezo-TMD is conducted. Accordioning to the sensitivity analysis, only the thickness ratio of the piezoelectric layer to the base layer will affect the maximum piezoelectric damping ratio. The best thickness layer ratio can be found to achieve the maximum piezoelectric damping ratio. The analysis results also shown that simply increasing the amount of piezoelectric materials cannot increase the piezoelectric damping ratio so that the piezoelectric damping ratio has its upper limit, that is, the power generation efficiency has its upper bound. Because of the limitation of the maximum piezoelectric damping ratio, the proposed design method of the Piezo-TMD is different from the traditional TMD, the damping ratio is determined before the mass ratio. In the design, each dimension of the piezoelectric cantilever beam can be preset as a preliminary value, and the maximum piezoelectric damping ratio can be calculated accordingly. The mass ratio is therefore calculated by the optimum damping ratio design formula of the traditional tuned mass damper. To optimize the other parameters of the Piezo-TMD, the Direct Search method is used to find the optimum beam length, resistance, and inductance when the structural velocity H2-norm is minimum. The designed Piezo-TMD is analyzed numerically, the frequency response function and time history analysis of subjected to wind force shows that the Piezo-TMD performs well in both structural vibration reduction and power generation. Finally, according to the analysis of polarized range of the piezoelectric material on the cantilever beam, the best polarized length ratio can be found to achieve maximum power generation efficiency in the first mode. However, the power generation efficiency will be reduced in high modes due to the different bending directions.
Keywords: piezoelectric cantilever beam, tuned mass dampers, finite element model, piezoelectric materials, energy harvesting, RLC circuit, optimal design, H2-norm optimization | en_US |