| 摘要(英) |
This thesis investigates the vibration characteristics and transient wave propagation behaviors of a mass array applied to a rectangular cantilever plate, through theoretical analysis, finite element method, and experimental measurement. The transient wave solution is also used to solve the inverse problem, which, through inputs of transient signals, calculates the impact history on the plate.
In this study, the vibration characteristics of the rectangular plate is calculated by the superposition method so as to analyze the influence of the resonance frequency and mode shape of the multi-mass point at any position on the plate. Polyvinylidene fluoride (PVDF) piezoelectric thin-film sensor is used to measure the transient strain signal of the thin plate, and obtain the resonance frequency and modal shape through experimental modal analysis (EMA). Comparing the results of theoretical analysis, finite element numerical simulation and experimental measurement to confirm the accuracy of the theoretical calculation, the research, thus, aims to discuss the resonant frequency and mode shape of the plate changes caused by mass effect, and analyzes the influence of position and weight of the additional mass.
Transient wave propagation analysis is based on the vibration analysis results, and uses the normal mode method to construct transient solutions such as displacement, strain and velocity of the plate. In this study, transient behaviors of the rectangular cantilever plate, caused by impact hammer or steel ball dropping, are measured with PVDF and FS. The impact history was input into transient solution and finite element software for comparison. It is verified that the calculation results of transient theory analysis and finite element method are consistent with the experimental measurement results.
Finally, to get the transformation matrix of the impact history and transient signal by discretizing the force via the theoretical solution of transient wave propagation. Through the inverse matrix calculation, the impact history applied on the plate could be calculated by the transient sensing signal. Experiments were designed to compare the impact history calculation effects of various physical quantities. According to comparison, using more transient signal to do the inverse calculation, the result will be more accuracy and noise will be reduced. Compared with displacement, strain is the better physical quality for inverse calculation since strain signal contains more high-frequency information. It is observed that to calculate with various transient signals can improve effectively the accuracy of the impact history. |
| 參考文獻 |
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[14] De Simone, Mario Emanuele, Francesco Ciampa, and Michele Meo, “A Hierarchical Method for the Impact Force Reconstruction in Composite Structures”, Smart Materials and Structures, Vol 28.8, 2019.
[15] Liu, Junjiang, et al., “Impact Force Reconstruction and Localization Using Nonconvex Overlapping Group Sparsity”, Mechanical Systems and Signal Processing, Vol 162, 2022.
[16] 吳亦莊、馬劍清：〈理論解析與實驗量測壓電平板的面外振動及特性探討〉。 碩士論文，國立台灣大學機械工程研究所，2009年。
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[18] 廖展誼、馬劍清：〈矩形平板於流固耦合問題的振動特性與暫態波傳之理論分析、數值計算與實驗量測〉。博士論文，國立台灣大學機械工程研究所，2018年。 |
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