虛擬模態振形法應用於多接點子結構之建模

Modeling of Substructures with Multiple Joints by Pseudo Mode Shape Method

楊大中(Ta-Chung Yang) ； 蔡盈安(Ying-An Tsai) ； 蒯光陸(Kwang-Lu Koai)

《技術學刊》 26卷3期 (2011/09) Pp. 179-186

https://doi.org/10.29507/JT.201109.0004

摘要

虛擬模態振形法(Pseudo Mode Shape Method, PMSM)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)。透過FRF可得到子結構的模態參數及接點處的虛擬模態矩陣，以此反推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。本文延伸作者過去發表的虛擬模態振形法，推導子結構之剛體模態和多接點子結構之應用。本文以一樑結構實驗驗證，實驗頻寬爲4000 Hz。PMSM對子結構建模，與實驗結果比較，自然頻率幾乎沒有誤差。將PMSM所建立子結構矩陣與有限元素法(Finite Element Method, FEM)所建立之母結構矩陣在接點處結合，與實驗FRF比較。比較結果良好，自然頻率最大誤差爲第11個模態，誤差爲6.724%。

關鍵字

子結構 ； 剛體模態 ； 多接點 ； 頻率響應函數

並列摘要

The Pseudo Mode Shape Method (PMSM) requires only the measurements of the Frequency Response Functions (FRFs) at the joints between the substructures and the mother structure. The modal parameters and a pseudo modal matrix of the substructure can then be derived from the FRFs, and the equivalent mass, damping and stiffness matrices of the substructure may be subsequently obtained. The experimental procedures are considerably simplified because only the FRFs at the joints are required, which solves the problems of incomplete modal shapes in measurement for large complicated structures. This paper extends the authors’ previous work on the PMSM to include rigid body modes and to substructures involving multiple joints with the mother structure. Experiments with a beam structure were conducted to evaluate the accuracy of the proposed method. The frequency range was set to 4000 Hz. A comparison of the natural frequencies of the modeled substructure obtained by the PMSM versus experimental results shows good agreement. After joining the PMSM matrices of the substructure with the Finite Element Method (FEM) matrices of the mother structure, the FRFs of the integrated system compare well with experimental results. The largest error of natural frequency is 6.724% for the 11th mode.

並列關鍵字

substructure ； rigid body mode ； multiple joint ； frequency response functions