具局部黏滯阻尼樑之振動分析

Vibration analysis of a beam with locally distributed viscous damping

曹家豪(Jia-Hau Tsau)

指導教授 ： 蔡定江

國立臺北科技大學/機電學院/製造科技研究所/碩士(2006年)

摘要

本文主要探討具局部黏滯阻尼之Timoshenko樑的自由與強迫振動特性。沿用Clough及Penzien對黏滯阻尼的定義，利用能量法推導出具內部黏滯阻尼之Timoshenko樑的運動方程式，再利用傳遞矩陣法（Transfer Matrix Method）求得系統具有局部均勻分佈阻尼時之自由及強迫振動的各種特性。由數值計算的結果可以得知，當黏滯阻尼均勻分佈於整個樑內部時，在自由振動的方面，其阻尼頻率會隨著阻尼值的上升而下降，並有一個臨界阻尼的出現；而在強迫振動的方面，其外力響應會隨阻尼值的上升而下降，相位亦隨之而改變。而當內部黏滯阻尼為局部分佈時，系統的頻率、振型、及外力響應會因為阻尼分佈的位置及長度，而有明顯的改變。由本文方法作以上各種實例之分析可以很方便的歸納出最佳的阻尼分佈位置，來達到抑制振動的效果。

關鍵字

Timoshenko樑 ； 內部黏滯阻尼 ； 傳遞矩陣法

並列摘要

In this study, based on conceive of Clough, the equation of motion of the Timoshenko beam with the internal viscous damping is derived by using energy principle. Using the Transfer Matrix Method, the characteristic of the system are determined. The cases of the beam with local internal viscous damping are also studied. From the numerical calculation, when the internal viscous damping distributed in the whole beam, the free vibration natural frequency decrease with the damp increase and a critical damping is accordingly appeared. The force vibration response also decreases with the damp. If the damp distributed locally, the characteristic of the system vary with the length and position of the damped section. The optimal location of the damped section, for minimizing the vibration response, is also estimated in present study for a beam.

並列關鍵字

Timoshenko beam ； internal viscous damping ； Transfer matrix method

參考文獻

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