| 摘要: | 本文透過理論解析、有限元素模擬和實驗量測，探討單邊固定等向性矩形薄板施加點質量陣列的振動特性和與暫態波傳行為，並且藉由理論解反算問題並應用於平板上波源歷時求解。
振動分析使用疊加法(Superposition method)求解矩形薄板面外方向的自由振動特性，解析多質量點於平板任意位置對共振頻率與模態形狀等振動特性之影響；實驗量測使用聚偏二氟乙烯（Polyvinylidene fluoride, PVDF）壓電薄膜感測器，量測平板的暫態應變訊號，藉由實驗模態分析方法(Experimental Modal Analysis, EMA )，求得共振頻率與模態形狀。將理論解析、有限元素數值模擬及實驗量測的結果進行比較，確認理論計算之準確性，並以此探討平板因點質量負載所引起的共振頻率和模態形狀變化，分析點質量的施加位置、重量和數量對振動特徵之影響。
暫態波傳分析則結合以上振動分析結果為基礎，使用模態展開法，以模態形狀和時間函數建構平板的位移、應變或速度等暫態理論解。實驗量測使用敲擊槌及鋼珠落擊兩種方式引發薄板產生動態行為，並且同時量測其暫態位移、應變和波源歷時訊號。將實驗量測的波源歷時輸入至理論解計算和有限元素軟體模擬中進行比較。驗證暫態分析計算結果可吻合實驗量測結果。
最後，本文將暫態波傳理論解經由離散解耦，推導出波源歷時與暫態位移和應變之轉換關係矩陣，藉由逆矩陣運算，以暫態感測訊號反算平板上所施加的外力波源歷時內容。實驗設計多種物理量驗證反算效果，結果顯示應變訊號包含較多高頻資訊，因此相較於位移訊號具有較佳的反算效果，最後規劃多位置感測器之暫態訊號反算，確認可有效提升波源歷時反算的準確性。
;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. |
