二維非線性振動系統減振分析

A Study of The Two-Dimensional Three-Degree-of-Freedom Nonlinear Vibration System

陳柏翰(Po-Han Chen)

指導教授 ： 王怡仁

淡江大學/工學院/航空太空工程學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00010

摘要

本研究係採取非線性的物理模式來模擬整個振動體之運動，非線性的物理模式係將彈簧模擬成三次方的變化量 (cubic spring) ，以使振動變成非線性的模式。非線性的問題雖然已被研究多年，但非線性的模式再輔之以非線性或非穩態空氣動力，同時再加入減振裝置，並探討各參數之影響，則尚待分析。本論文第一部分為利用牛頓法推導加入減振器之二維三自由度非線性振動系統的運動方程式。本研究減振器係採用一個質量、彈簧及阻尼裝置作為減振裝置，其安裝的位置及材料特性將視系統之彈性軸、質心、風速及外力頻率而定。

第二部份簡化吾人之運動系統與前人之研究結果比對之後，第三部份則利用“古典振顫分析法” (Classic Flutter Analysis) 求出系統各自由度振幅在頻率域的運動方程式；並使用 Multiple Scales Analysis 求得時間域動態解析解。上述非線性系統之解析解，將與頻率域的數值解作比對，以驗證本論文之結果。

本研究中之二維振動系統可視為翼剖面 (airfoil)，亦可視為吊橋；而減振器可視為一般之派龍架，亦可視為吊橋下之減振裝置。吾人在考慮不變動大部分的設計之下，改變減振器位置以及材料特性，達到最經濟的減振效果。

關鍵字

非穩態空氣動力學 ； 減振裝置 ； 三次方非線性彈簧

並列摘要

There has been a long history in research and development of structural vibration worldwide. In early stage, scholars only emphasized on the design of the structure. With the improvement of technologies, bridges and buildings are more complex today. Aerodynamics and fluid mechanics are also incorporated into the design for further studies.

The Newton’s second law is used to analyze a system of nonlinearly vibrational rigid body, doing pitching and plunging in conjunction with an unsteady nonlinear aerodynamic force and an absorber. The cubic spring is employed to simulate a nonlinear vibration system. Several analytic methods are employed to get the solutions of this nonlinear aeroelastic system. The“Classic Flutter Analysis”is utilized to get the amplitude-frequency function of this system. The“Multiple Scales Analysis”is used to get the analytic solution in time domain. The analytic solutions will be correlated with the numerical results to ensure the nonlinear model and the effects of the absorber.

By using the mathematical model presented in this study, one can adjust the position or design of the absorber to reduce vibration, without changing the main configuration or original design. In conclusion, this model has an enormous applicable value towards applied engineering and related fields.

並列關鍵字

Unsteady Aerodynamic ； Absorber ； Cubic Spring

參考文獻

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