虛擬模態振形法之理論與實驗驗證

On the Theory and Experimental Validation of Pseudo Mode Shape Method

蔡盈安(Ying-An Tsai)

指導教授 ： 楊大中

元智大學/工程學院/機械工程學系/碩士(2011年)

https://doi.org/10.6838/YZU.2011.00014

摘要

大型產業機械基座之結構相當複雜，導致模態實驗與有限元素法建模之困難及分析上之不便。現場進行模態測試時，不易取得完整的模態；有限元素法分析，常因結構大型且複雜，不易建模，並因元素過多造成計算費時。
虛擬模態振形法僅需在子結構與母結構接點處施力，量測其頻率響應函數(FRF)。以推導出子結構之等效質量、阻尼和勁度矩陣。由於僅需量測接點處的FRF，因此實驗過程可簡化許多。可有效解決大型複雜結構，無法進行完整模態測試的缺點，同時可以涵蓋頻寬內之所有模態。
本文首先探討虛擬模態振形法之理論，並證明本法之建模精準度與MRM相同。深入探討虛擬質量、阻尼和勁度矩陣之意義，所對應之模態向量之正確性，本方法之可行性及誤差來源。
接著本文以2D的樑結構為範例進行模擬，驗證本理論之建模精準度。並推導子結構之剛體模態和多接點子結構之應用。最後並以實驗驗證其可行性。
最後本文以轉子-軸承-基座系統實驗證虛擬模態振形法應用於基座結構建模上。本文第四章視基座為子結構，以虛擬模態振形法建模。視轉子部分為母結構，以3D Timoshenko beam元素建模。並討論虛擬模態振形法剛體模態之效應與其推導過程。

關鍵字

模型凝縮 ； 子結構 ； 頻率響應函數 ； 有限元素法 ； 剛體模態 ； 多接點 ； 基座

並列摘要

The foundations of most large industrial machines are complicated in configuration and shape that results in difficulty of modal testing and/or finite element modeling. Modal testing suffers from incomplete measurement of mode shapes, whereas, finite element method faces the problems of the complexity of structural configuration and computational time consuming due to huge amount of elements.
Pseudo Mode Shape Method (PMSM) needs only the measurement of frequency response functions at the joints of the substructure and the mother structure to derive the equivalent mass, damping, and stiffness matrices of the substructure, which greatly simplifies the modeling procedure of the complicated substructure. The established matrices can cover all the modes in the interested frequency range.
In this paper, theoretical aspects of the pseudo mode shape method were remarked. This method was validated to have the same modeling accuracy as Modal Reduction Method (MRM). The meanings of the resulted equivalent mass, damping, and stiffness matrices, as well as the corresponding modal vectors were clarified. Moreover, the feasibility and error sources of PMSM were discussed.
A 2-D beam is used to demonstrate the usage and modeling accuracy of this method. The substructures include rigid body modes and involve multiple joints with the mother structure. The effectiveness of these extensions was validated by experiment.
Experimental validation of PMSM was conducted by modeling the foundation of a rotor-bearing-foundation system. The foundation is treated as the substructure and modeled by PMSM. The rotor is treated as the mother structure and modeled by finite element method using 3D Timoshenko beam elements. The derivation and the effects of rigid body modes of PMSM in this experiment are also investigated.

並列關鍵字

Frequency response function ； Finite element method ； Rigid body mode ； Multiple joint ； Foundation ； Model reduction ； Substructure

參考文獻

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