| 摘要: | 板、殼問題在工業領域中是非常重要的研究項目，有相當多的文獻探討平板與各式連續體介質耦合的動態行為。但平板耦合離散體的行為機制至今尚未深入研究與釐清。本文透過實驗量測、有限元素法與離散元素法雙向耦合技術(Two-Way Coupled FEM-DEM Method) 探討等向性矩形平板部分埋沒於顆粒體中的振動特性，以及顆粒對於平板動態行為的振動抑制效果，分析顆粒體的堆積高度、粒徑、楊氏係數及質量密度對於顆粒體-平板耦合系統振動特性的影響。
本文使用有限元素與離散元素雙向耦合之模擬技術，計算平板受動態外力激振之後的時域位移和應變，搭配快速傅立葉轉換(Fast Fourier transform, FFT)至頻譜觀察頻率域之反應，並使用實驗模態分析法(Experimental modal analysis, EMA)獲得平板耦合顆粒體的模態形狀。在實驗量測上，分別使用鋼珠撞擊和激振器推動兩種方法激發平板動態行為，使用貼附於平板上的聚偏二氟乙烯(Polyvinylidene fluoride, PVDF)壓電薄膜感測器量測平板受外力作用後的暫態應變訊號，藉由 FFT轉換至頻域獲得共振頻率和頻率響應。將實驗量測結果與有限元素法模擬之結果比較，驗證有限元法與離散元素法耦合模擬技術之準確性與可行性，並探討顆粒體對於平板動態行為之影響。
本文的研究結果顯示：(1)隨著顆粒堆積高度增加，平板的共振頻率和模態形狀都會出現變化，共振頻率隨堆疊高度增加而上升，模態形狀的腹點區域也向上偏移。(2)與平板耦合的顆粒粒徑越大，離散程度越高，實驗量測結果之訊雜比越差。(3)顆粒的幾何與材料性質中，以顆粒的質量密度對平板動態行為的影響最為顯著。顆粒密度越高，顆粒-板耦合系統將有較高的剛性，因此具有較高的共振頻率。(4)以阻尼因子判斷系統之減振效果得知，粒徑小、楊氏係數小與質量密度小的顆粒體能產生較多的碰撞、摩擦行為，因此將具有較高的系統耗能效果。
總結而言，本研究運用實驗量測、耦合有限元素與離散元素模擬，提供顆粒 板的耦合系統之動態行為的深入研究及探討，將提供工業領域設計及檢測相關的運用價值。;Plate and shell are very important research problems in the industrial field, and there are quite a lot of literatures discussing the dynamic problem of plates coupled with various continuum media. However, the dynamic behavior of plates coupled with discrete bodies has not yet been studied and clarified in detail. In this study, the vibration characteristics of an isotropic rectangular plate partially buried in particles and the vibration suppression effects of particles on the plate are investigated by the experimental measurement, and the Two-Way Coupled FEM-DEM Method. Additionally, the influences of particle size, Young′s modulus, and mass density on the vibration characteristics of the particle-plate coupled system were also investigated.
We employed the Two-Way Coupled FEM-DEM Method to calculate the time depend transverse displacement and in-plane strain of the plate excited by a dynamic external force and utilized the Fast Fourier transform (FFT) to observe the response in the frequency spectrum. In addition, the experimental modal analysis (EMA) was applied to obtain the mode shapes of the particle-plate system. In the experimental measurements, we employed two methods to generate the dynamic behavior of the particle-plate coupled system, a steel ball impact, and a shaker, respectively. The PVDF film sensors attached to the plate are utilized to measure the transient strain so that can be converted by FFT to obtain resonant frequencies and frequency responses. To verify the accuracy and achievability of the Coupled FEM-DEM simulation approach and study the influence of the granular nature on the dynamic behavior of the plate, the results of the experiment and numerical calculation were compared.
The results illustrate that: (1) The mode shapes of the particle-plate coupled system are different from the pure plate. The resonant frequencies increase with the packed height increasing. (2) The signal-to-noise ratio (SNR) becomes worse due to the larger particles resulting in higher discretization. (3) The results show that the particle density has the most significant influence on the dynamic behavior of the plate. The higher density of particles results in higher stiffness so that the resonant frequency of the particle-plate coupled system increases as well. (4) The damping factor is applied to study the vibration suppression of the system. The results show that particles with smaller size, Young’s modulus, and mass density cause more energy consumption. |
