應用時頻域分析法萃取結構桿件之模態反應

Application of Time-Frequency Analysis to Extract Modal Responses of Structural Elements

楊青景(Ching-Ching Young)

指導教授 ： 張家銘

國立臺灣大學/工學院/土木工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201801732

摘要

結構在地震發生時，其反應主要是多個模態的效應所組成，對於不同的振動頻率，結構可以有多個模態的振動方式，欲觀察其個別模態反應，傳統方法是利用傳感器進行資料前處理，再經由系統識別方法繪製出結構之模態形狀，然而點式檢測所繪出之模態形狀為不連續的，近年來，影像量測日漸普及，而影像量測相較於傳感器之最大的優點在於，可以同時針對大量的檢測點進行高度自動化之量測，因此可繪出幾乎連續的結構模態形狀。在此，本文將介紹一種以時頻域分析配合影像量測獲得模態反應的方法，其主要透過對時頻域中的相位運動因子進行濾波，相位運動因子包含了影像間之位移資訊，透過帶通濾波可進一步分離出模態反應，本文藉由影像處理技術追蹤模態反應之邊緣位置，最終能獲得分離模態之位移反應與模態形狀。
為驗證此方法之準確性，本研究以包含三個振動模態之懸臂梁，建構模擬影片作為實驗對象，嘗試將三個振動模態的位移反應分離出來。模擬結果顯示，此方法成功地濾出三個模態反應，且在位移結果比較中有良好的準確度。最後，藉由混凝土柱在地震力下之振動影片，以及鋼片振動台影片，進行模態分離，實驗結果顯示兩者皆未觀察到高頻率模態反應，因此僅濾出低頻模態，實驗比較結果顯示，模態分離的位移反應接近真實，證明本方法於實驗應用之可行性且透過影像量測能比以往加速度計或應變計獲得更完整的模態形狀。

關鍵字

影像量測 ； 模態分離 ； 時頻域分析 ； 非接觸式 ； 模態形狀

並列摘要

Seismic responses of structures are comprised from several vibrational modes. Conventional approaches employ signal pre-processing from measurements, apply system identification to extract individual modes, and consequently derive modal responses through discrete measurement points (e.g., sensor locations). In recent years, optical measurement technology significantly improves the capability of acquiring structural displacements/deformations. The same technology can also provide almost continuous displacements/deformations of a structure or structural member. In this research, an innovative method, which can derive modal responses of structural members through optical measurement technology, is developed. This method integrates time-frequency analysis of signals into image processing to a video. Thus, the motion information of structural members are extracted and presented as differential phases. By processing these phases, modal responses over a structural member can be extracted.
To verify the effectiveness and correctness of the proposed method, an animation of a vibrating cantilever beam is utilized. Responses of this beam contain the combinations of three distinct modes. The verification is completed by applying the proposed method to extracting three modes. As shown in the simulation results, the proposed method successfully extracted three distinct modal responses. By comparing displacements, this method can have a good agreement. Moreover, this method is also employed in the experimental results of a concrete column of a building under seismic excitation and of a steel plate in shaking table testing. As seen in results, the proposed method can accurately and correctly extract modal responses in both experimental tests. Therefore, this research verifies the feasibility of modal response extraction from recorded videos of vibrational structural members.

並列關鍵字

Image processing ； Modal responses ； Time-frequency analysis ； Non-contact measurements ； Modal extraction

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