附加動態減振器之於三維非線性弦線振動的研究

本文研究一兩端固定的三維非線性弦線之振動情況，其下方及側面以非線性彈性基底支撐之，以模擬埋置於土壤或海床的情況。此弦線系統可用來模擬一般精密量測儀器內之線材的振動；亦可模擬海底纜線受海流之影響等各項工程分析，應用極為廣泛。首先，吾人以牛頓第二運動定律為基礎，推導出埋置於彈性基座內之弦線系統運動方程，再以多尺度法解析此非線性系統。吾人發現此弦線在某彈性介質情況，存在第一模態及第四模態之一對三內共振的可能性；而後利用Fixed Points plots 得到各模態之頻率響應圖(Frequency Response)，藉此觀察其振幅及振動模態以判斷系統之內共振現象(Internal Resonance)。此外，為達避開I.R.及減振的效益，吾人將此弦線加載一Tuned Mass Damper(TMD)，分析此弦線系統，在不同的TMD質量、彈簧係數、阻尼係數以及擺放位置對於整體振動之影響，利用各模態(Mode)之系統最大振幅的3D振幅及投影之3D Maximum Amplitude Contour Plot(3D MACP)表示之，以觀察TMD的最佳組合，達到本系統之最佳減振目的。

關鍵字

三維非線性弦線之振動；調質量減振器；內共振；減振

並列摘要

This study examined the vibrations of a fixed-fixed nonlinear 3D string placed on a nonlinear elastic foundation. We found that specific combinations of elastic modulus in the elastic foundation resulted in 1:3 internal resonances in the 1st and 4nd modes of the string. This prompted us to add a tuned mass damper (TMD) on the string in order to prevent internal resonance and suppress vibrations. In general, the idea of TMD can be applied on the vibration reduction of any string-like structures resting on elastic foundations, for example, the device of TMD can be installed between anchor points of the submarine cables or offshore pipelines placed on seabed to avoid internal resonance or other vibrations due to external loads. We analyzed this nonlinear system using the method of multiple scales (MOMS). Fixed points plots were also used to facilitate the observation of internal resonance. We also examined the combination of optimal mass ratio and elastic modulus for the TMD in order to prevent internal resonance and achieve optimal damping effects. In the nonlinear string investigated in this study, the placement of a TMD of 0.5l from the fixed end of the string proved the most effective for damping. Finally, numerical methods were studied to compare the results from MOMS and demonstrate the effects of the TMD of this model.

並列關鍵字

3D Nonlinear string vibration ； Tuned Mass Damper(TMD) ； Internal response ； Vibration reduction

參考文獻

[2] J. W. Miles, “Resonant, nonplanar motion of a stretched string,” Journal of the Acoustical Society of America, Vol. 75, 1984, pp. 1505-1510.

[3] K. Yasuda, and T. Torii, “Nonlinear forced oscillations of a string, 2nd report: Various types of responses near resonance points,” Bulletin of the JSME, Vol. 29, 1986, pp. 1253-1260.

[4] J. M. Johnson, and A. K. Bajaj, “Amplitude modulated and chaotic dynamics in resonant motion of strings,” Journal of Sound and Vibration, Vol. 128, 1989, pp. 87-107.

[5] S. A. Nayfeh, A. H. Nayfeh, and D. T. Mook, “Nonlinear response of a taut string to longitudinal and transverse and excitation,” Journal of Vibration and Control, 1995, pp. 307-334.

[6] M. Pakdemirli, A. G. Ulsoy, and A. Ceranoglu, “Transverse vibration of an axially accelerating string,” Journal of Sound and Vibration, Vol. 169, 1994, pp. 179–196.

國際替代計量

附加動態減振器之於三維非線性弦線振動的研究

全文下載

主題瀏覽