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。 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.
