振動平板之邊界條件參數鑑別

On the Parameter Identification of Boundary Condition for Constrained Plates under Vibration

顏啟峻(Chi-Chuan Yen)

指導教授 ： 楊大中

元智大學/工程學院/機械工程學系/碩士(2002年)

摘要

近年來因電子產業的蓬勃發展，高科技產品不斷開發，各式印刷電路板的使用越來越廣泛。依據統計，電子設備因振動引發之故障原因僅次於因溫度所引發之故障。因此，了解印刷電路板的動態特性成為一個重要的課題。
本文利用次結構合成法，配合有限元素模型，發展平板之邊界條件參數鑑別的新方法，並應用次結構合成法鑑別接點旋轉自由度之勁度值。
文中首先針對次結構合成法加以討論，並說明利用頻率響應函數鑑別接點勁度之原理。之後將結構旋轉自由度效應納入考慮，推導出可鑑別接點旋轉自由度的理論。文中提出不同的接點假設，且討論各種接點假設的鑑別法。
近來部份接點鑑別相關的研究，皆假設接點處為平移彈簧及旋轉彈簧組合，本研究提出接點處為矩陣形式的觀點，且分析及實驗的方式驗證此接點假設的可行性。
受限不易量測旋轉自由度於實際結構，且欲鑑別旋轉方向自由度之勁度必須使用結構中部份旋轉自由度之資料，故本文應用有限元素軟體ANSYS，配合以最佳化方式鑑別，逼近真實材料參數，做為分析工具，有效的模擬實驗結構於無拘束狀態下之動態特性，以做為取得旋轉自由度之頻率響應函數的來源。如此結合實驗資料與分析資料的鑑別結果，代入含有平移和旋轉彈簧的有限元素模型中，可得到與實驗吻合之頻率響應函數。
最後利用受楔型夾持器拘束的平板結構做為例子，驗証本文所提邊界參數鑑別法確實可應用於實際案例上；並對實驗與模擬分析時，楔型夾持器所施扭力、衝擊鎚、材料參數、接點元素、鑑別模型等因素對鑑別結果之影響加以探討。

關鍵字

有限元素法 ； 次結構合成法 ； 邊界條件 ； 接點鑑別 ； 頻率響應函數

並列摘要

Failure of the electronic devices due to vibration has become frequent, only less than those caused by temperature in some statistics data. Hence, it is important to study the vibration characteristics of printed circuit boards.
In this thesis, a new identification method for joint stiffness has been developed by using the substructure synthesis method and finite element modeling. Stiffness of the rotational degree of freedom for the joint identified by this method can be considered as a special point of this work. The idea of how to identify the boundary condition with frequency response function is discussed, including the effects of rotational degree of freedoms.
Assembly of transverse and rotational stiffness is assumed for the joint models in the recently related research works on joint identification. However, the coupling effects of the transverse and rotational stiffness of joins has not been investigated to the best knowledge of the author. A matrix form for the joint model was proposed in this thesis.
The data related to the rotational degree of freedom of the structure is essential in identifying the joint parameters of rotational degree of freedoms. But due to the difficulty of measurement on the rotational degree of freedom, this part of data is obtained form the free-free finite element models. The material properties of the finite element models used are calibrated with the least square method from experimental data. With the new joint model, the joint parameters are identified from the dynamic response of the free-free finite element model and the experimental results of the constrained structure.
Identifying the boundary conditions of plates constrained with wedge locks at one or two of their edges was conducted. The calculated results of the frequency response functions of the constrained plates with the properly identified boundary conditions agree with the experimental results satisfactorily. The comparison results of analysis and experiment justify the validity of the approach of this research.
The effects of the torque in the wedge lock, impact hammer, material properties, joint element, on the identified resulted were presented.

並列關鍵字

Finite element method ； Substructure synthesis method ； Boundary condition ； Joint identification ； Frequency response function

參考文獻

Barker, D. B. and Chen, Y. S. 1993, “Modeling the vibration restraints of wedge lock card guides,” ASME Transaction Journal of Electronic Packaging, Vol. 115, pp. 189-194.

Beards, C. F., 1986, “The damping of structural vibration by controlled interfacial slip in joints,” ASME Publication, 81-DET-86.

Chou, Y. F. and Tsai, J. S., 1988, “The identification of dynamics characteristics of a single bolt joint,” Journal of Sound and Vibration, Vol. 125, No. 3, pp. 487-502.

Ewins, D. J., 1986, ”Modal testing: theory and practice,” Research studies Press Ltd., England.

Hong, S. W. and Lee, C. W., 1991, “Identification of linearised joint structural parameter by combined use of measured and computed frequency responses,” Mechanical System and Signal Processing, Vol.5, pp.267-277.