逆向求解彈簧係數與阻尼係數之多自由度非線性外力系統振動問題

An Inverse Vibration Problem of Estimating Coefficients of Stiffness and Damping for the Multiple Degrees of Freedom System with Non-linear External Forces

邱武耀(Wu-Yao Chiou) ； 劉得偉(Te-Wei Liu) ； 陳彥伊 ； 林慶豪 ； 柯佳宏

《中華民國振動與噪音工程學會論文集》 2011 (2011/06) Pp. 144-153

https://doi.org/10.30028/CSSVANNUAL.201106.0144

摘要

本研究應用貝克之非線性估算程序結合倫基－庫達法，逆向求解多自由度非線性外力振動問題。以四階倫基－庫達數值方法改善，將原貝克之非線性估算程序之敏感度係數做修正，並提昇精度使程式疊代收斂速度加快，逆向預測多組未知的彈簧與阻尼係數。研究結果顯示，本逆算法在求解三個非線性外力案例中，在假設模擬量測誤差小於10%之條件下，皆能有效改善原貝克之非線性估算程序收斂速度。從數值運算出的彈性與阻尼係數和正解相比較，在假設模擬量測誤差小於5%之條件下，其真實誤差百分比皆小於4.5%。

關鍵字

貝克之非線性估算程序 ； 倫基－庫達法 ； 彈簧係數 ； 阻尼係數

並列摘要

In this study the Beck's nonlinear estimation procedure coupled with Runge-Kutta method is applied to solve the reverse of multiple degrees of freedom with nonlinear external force vibration problem. The sensitivity coefficient of Beck's nonlinear estimation procedure is modified by the fourth-order Runge-Kutta numerical method, and improves the accuracy of the program to accelerate the iteration convergence rate; reverse forecast multiple unknown stiffness and damping coefficients.The results show that the inverse algorithm in solving nonlinear external force three cases, the simulated measurement error of less than 10% of cases, this algorithm able to effectively improve the Beck's nonlinear estimation procedure. The simulated measurement error of less than 5% of cases, coefficients of stiffness and damping compared with exact solutions for the percentage of the program computation real errors are less than 4.5%.

並列關鍵字

Beck's nonlinear estimation procedure ； Runge-Kutta method ； stiffness coefficient ； damping coefficient