dc.description.abstract | This study focuses on the Piezoelectric-Tuned Mass Damper (Piezo-TMD) with variable cross-section cantilever beams. The complete electromechanical coupled equations are derived and transformed into state-space representation for system analysis. Firstly, the mechanical and electrical motion equations of the piezoelectric cantilever beam are derived by the piezoelectric constitutive equation with the Euler-Bernoulli beam structure. Then, the finite element concept is used to divide the piezoelectric cantilever beam with different cross-sections into multiple element blocks. The polynomial shape functions and superimposed element blocks are introduced to derive the matrix form of the motion equations for the variable cross-section piezoelectric cantilever beam, so that the problem of the size different between piezoelectric layer and the basic layer can be analysized easily. Finally, an external mass is attached to the end of the cantilever beam to form the complete mechanical equation, and an external resistance is added to the circuit loop to form the complete electrical circuit equation. The design purpose of the Piezo-TMD is to absorb structural vibration energy into the Piezo-TMD and convert its vibration energy into electrical energy for harvesting. Thus, the power generation efficiency of the Piezo-TMD is a key concern, and this study uses the piezoelectric damping ratio as an efficiency indicator. After establishing the numerical model, the Piezo-TMD can be analyzed. By drawing the frequency response function diagram, the number of the observable modes and the accuracy of the modal frequency affected by the number of elements can be understood. It is also possible to understand that the response of the Piezo-TMD is controlled by the first mode after adding an external mass block. In order to understand the influence of various piezoelectric material parameters on the piezoelectric damping ratio, sensitivity analysis of piezoelectric material parameters is conducted. The analysis shows that the softness and hardness of the piezoelectric material, the electromechanical coupled coefficient, and the size of the parasitic capacitance all have different effects on the maximum piezoelectric damping ratio, which provides a basis for selecting piezoelectric materials.
Based on the previous research by our team, it is known that simply increasing the amount of piezoelectric material cannot improve the maximum piezoelectric damping ratio. It was also found that when the Piezo-TMD exist the maximum piezoelectric damping ratio, the mass ratio between the Piezo-TMD and the structure cannot be further improved to achieve better results. Therefore, this study further aims to combine multiple Piezo-TMDs into Piezoelectric-Multiple Tuned Mass Dampers (Piezo-MTMDs) to break through the limitation of the mass ratio. The motion equations for the aeroelastic model structure with Piezo-MTMDs are derived, and the optimization design method is used to find the unknown parameters of the external mass and external resistance to design the Piezo-MTMDs. During the design process, priority is given to design the fundamental piezoelectric cantilever beam that the dimensions and the parameters are applied to each set of Piezo-TMDs before installed on the aeroelastic model structure. The study uses the Pattern-Search method for optimization design to find the combination of the external mass and external resistance of each individual Piezo-TMD; the structure velocity H2-norm value is the smallest, thus completing the design of the Piezo-MTMDs. The designed Piezo-MTMDs are used for numerical analysis, drawing frequency response function diagrams, and conducting dynamic analysis with design wind force, which show that the Piezo-MTMDs can achieve excellent power generation efficiency while effectively reducing vibrations. Finally, a designed Piezo-TMD which is manufactured is applied to system identification and model fitting analysis. During the system identification, the static identification method is proposed firstly: the actual parameters of the Piezo-TMD are identified through static loading tests with static force and DC voltage. Next, the dynamic model fitting results are analyzed: the displacement history and voltage history of the Piezo-TMD are measured through free vibration tests. By comparing the experimental results with the numerical analysis results, it is found that the analysis results can successfully match the dynamic experimental data of the Piezo-TMD by adding geometric stiffness matrices and rotational inertias into the numerical analysis model. The matched results can confirm the correctness of the material parameters, and complete the numerical analysis simulation method. | en_US |