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

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，實驗頻寬為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 ElementMethod, 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，自然頻率最大誤差為第11 個模態，誤差為6.724%。

The Pseudo Mode Shape Method (PMSM) requires only themeasurements of the Frequency Response Functions (FRFs) at the jointsbetween the substructures and the mother structure. The modal parametersand a pseudo modal matrix of the substructure can then be derivedfrom the FRFs, and the equivalent mass, damping and stiffness matrices ofthe substructure may be subsequently obtained. The experimental proceduresare considerably simplified because only the FRFs at the joints arerequired, which solves the problems of incomplete modal shapes inmeasurement for large complicated structures. This paper extends theauthors’ previous work on the PMSM to include rigid body modes and tosubstructures involving multiple joints with the mother structure. Experi ments with a beam structure were conducted to evaluate the accuracy of theproposed method. The frequency range was set to 4000 Hz. A comparisonof the natural frequen- cies of the modeled substructure obtained by thePMSM versus experimental results shows good agreement. After joiningthe PMSM matrices of the substructure with the Finite Element Method(FEM) matrices of the mother structure, the FRFs of the integrated systemcompare well with experimental results. The largest error of naturalfrequency is 6.724% for the 11th mode.