虛擬模態振形法應用於懸臂結構之建模研究

Dynamic Modeling of Cantilever-typed Structures Using Pseudo Mode Shape Method

楊大中(Ta-Chung Yang) ； 鄭文源(Wen-Yuan Cheng) ； 蒯光陸(Kwang-Lu Koai)

《先進工程學刊》 3卷1期 (2008/01) Pp. 9-16

https://doi.org/10.29948/JAE.200801.0002

摘要

轉子高速旋轉時，葉片輪與轉軸有振動耦合。轉軸上若有多級的葉片輪，有限元素建模時若採用三維元素來建模，因元素數量太龐大，模擬分析實際上並不易進行，故在進行力學分析時必須予以適當地凝縮簡化。虛擬模態振形法利用接點處少數的頻率響應函數，取共振頻率附近的振幅與相位資訊，反推出複雜形狀之子結構凝縮模型的質量、勁度、阻尼矩陣，解決子結構有限元素模型元素過多所造成模擬分析之困擾。本文延伸Yang等人之虛擬模態振形法理論，同時涵蓋剛體模態與變形模態情況，可應用於懸臂形態之子結構。在汽輪發電機組轉子振動之應用上，高速轉軸之振動行為是關心之重點，葉片輪模型須予以凝縮簡化，所以轉軸為母結構，葉片輪即為子結構。本文以二維懸臂樑為例，驗證此方法的可行性。

關鍵字

虛擬模態振形法 ； 模型凝縮 ； 子結構 ； 頻率響應函數

並列摘要

Vibration coupling occurs between bladed disks and shafts in high-speed rotors. If solid elements are used in the finite element modeling of multiple-bladed-disk rotors, problems of huge amount of elements and time consuming in computation often make simulation and analysis impractical. Therefore, techniques of model condensation are highly demanded. Pseudo mode shape method tackles the element quantity problems by using the frequency response functions of substructures obtained at the joints with mother structure. The data of frequency response functions near resonance are used to derive the condensed mass, damping, and stiffness matrices for the substructures. This paper extends the theory of pseudo mode shape method developed previously to cover rigid body modes and deformation modes of the substructures. The extended theory can be applied to the analysis of cantilever-typed structures, such as the bladed disks of steam turbine generators. In rotordynamic analyses, the major concern is on the vibration of rotating shafts and the models of the bladed disks need to be condensed. Consequently, the shaft is the mother structure and the bladed disks are the substructures. A 2-D cantilevered beam is used to demonstrate and validate this method.

並列關鍵字

pseudo mode shape ； model condensation ； substructure ； frequency response function