輸送流體之提摩憲柯樑的非線性振動分析

Nonlinear Vibration Analysis of Timoshenko Beams Conveying Fluid

林益煌(Yih-Hwang Lin) ； 蔡耀坤(Yau-Kun Tsai)

《中華民國振動與噪音工程學會論文集》 1996 (1996/04) Pp. 93-104

https://doi.org/10.30028/CSSVANNUAL.199604.0093

摘要

本研究之目的係在於探討有限元素法應用於輸送流體之提摩憲科樑的非線性結構振動分析，早期之研究大多分析線性之模型而求其臨界流速與其他系統參數之相關性，而此線性分析結果在臨界流速以上及結構產生大變位時即產生相當大的誤差，甚至錯誤的結果。因此，臨界流速以上及大變位之非線性行爲分析顯得格外重要，本研究之有限元素模型係採虛擬力(Fictitious Forces)之分析方式建立系統模型，其優點在於具有較佳之收斂性及無需逐次加載(Load Steps)而使問題解析更爲簡易，本研究將探討懸臂樑因流體引致振動所造成之複變模態(Complex mode)的顫振(Flutter)行爲，線性理論所無法預估之極限循環(Limit Cycle)及其振幅大小亦予慮及，由分析結果與文獻資料之比較，顯示了本研究之正確性，最後，本分析顯示極限循環振幅隨流速及流體／樑之質量比的增加而增加的情形，細長比的效應亦在文中有進一步的討論。

關鍵字

非線性振動 ； 顫振 ； 極限循環 ； 虛擬力

並列摘要

This paper presents a finite element approach for nonlinear vibration analysis of Timoshenko beams conveying fluid. Linear models are usually used in the past to evaluate the relationship between the critical flow speed and system parameters. The analysis results from the linear models are in serious error when the flow speed is above the critical one and the structure undergoes large deformations. Therefore, nonlinear analysis of structures with large deformations when the flow speed is above the critical one becomes a very important issue to be addressed. An approach using the concept of fictitious forces is applied to establish the finite element model, which exhibits good convergence characteristics and does not require separate load steps for analysis. This study first investigates the flow induced vibration characteristics of a cantilever beam, in which a complex mode flutters. Limit cycle and its associated vibration amplitude are examined subsequently, which is unobtainable from the linear analysis. The analysis results from this work are found to be in good agreement with those available in the literature. Finally, the increase of limit cycle amplitude with the increase of the flow speed and the fluid/beam mass ratio is illustrated. The influence of slenderness ratio on the limit cycle amplitude is also reported.

並列關鍵字

Nonlinear vibration ； Flutter ； Limit cycle ； Fictitious Forces