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標題: | 兩平面挫屈彈性樑互相接觸的變形與穩定性分析 Contact between two planar buckled beams |
作者: | Lien-cheng Wang 王連成 |
指導教授: | 陳振山(Jen-San Chen) |
關鍵字: | 挫曲樑的點接觸,線接觸,振動法, Buckled beams point contact,line contact,vibration method, |
出版年 : | 2020 |
學位: | 碩士 |
摘要: | 本文中我們研究兩根挫曲樑互相擠壓時的行為,其中我們採用大變形樑的理論來推導運動方程式。一開始挫曲樑以點接觸的方式變形。點接觸有可能是對稱或是反對稱。當外力持續增加時,點接觸會變成線接觸,其中線接觸段可以是直線或是曲線。為了判斷靜態解的穩定性,我們採用振動法來分析。振動時樑與樑之間的接觸點有可能會改變,為了將這個物理現象更準確的描述,我們需要將運動方程式由傳統的Lagrangian形式改寫成Eulerian形式。將新的運動方程式及修改過的邊界條件線性化後,可由其中解出自然頻率。在方程式中自然頻率都是以平方的形式存在,假如解出來的自然頻率的平方有任何一個為負,則靜態變形為不穩定。只有穩定的靜態變形才可以被觀察到。接著我們利用實驗方法來量測外力與上樑基底之移動量的關係,且將每一變形的前幾個自然頻率紀錄下來並且與理論值做比較。挫曲彈性樑的穩定性會因不同的控制方式,而有不同的結果。其中包括位移控制與力量控制。當位移控制時,量測到的前兩個自然頻率與理論值相當的吻合;然而當採用力量控制時,量測得到的自然頻率比起位移控制較不理想。一般來說,在實驗中利用兩種控制方式所觀察到之挫曲樑變形的過程符合理論的預測。 In this paper we study the behavior of two buckled beams when they are crushed toward each other. Elastica model is adopted in the theoretical formulations. In the first stage, the buckled beams contact each other at one point, which may be symmetric or skew-symmetric. It then evolves to line contact when the external pushing force increases. The line-contact segment can be straight or curved. In order to determine the stability of the deformation, vibration method is adopted. To account for change of contact points during vibration, the equations of motion are reformulated into Eulerian forms and then linearized. The linearized equations and boundary conditions are solved for the square of the natural frequencies. If any of the square of the natural frequency is negative, the equilibrium is unstable. Experiments are conducted to measure the relation between the pushing force and the top clamp-line movement. For each stable deformation, several of the lowest natural frequencies are recorded and compared with the theoretical predictions. In displacement control the lowest two natural frequencies agree very well with the theoretical prediction. However, the measurement of natural frequencies for load control is less successful. Generally speaking, the deformation evolutions observed in experiments follow the load-deflection curves predicted theoretically for both control mechanisms. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/60750 |
DOI: | 10.6342/NTU202001278 |
全文授權: | 有償授權 |
顯示於系所單位: | 機械工程學系 |
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