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

• Main Authors: Te-Wei Liu, 劉得偉
• Other Authors: Wu-Yao Chiou
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/13939892173889638651

碩士 === 國立高雄應用科技大學 === 模具工程系 === 99 === 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 problems. The sensitivity coefficients of Beck’s nonlinear estimation procedure are modified by the fourth-order Runge-Kutta numerical method, improves the accuracy of the program to accelerate the iteration convergence rate, and so reverse forecast multiple unknown stiffness and damping coefficients. Baker's estimate of the original program is a non-linear first-order Taylor series of precision, and this research is an amendment to Baker's non-linear estimation procedures to enhance the accuracy of four-order Taylor series. Beck's nonlinear estimation procedure is applied with Runge-Kutta numerical method, reverse to solve sets of unknown spring and damping factor, is a major innovative features of this study. The convergence rate is better than the original Baker's non-linear estimation procedures, is a major focus of development in this study. The results showed that the inverse algorithm for solving the cases of three non-linear force able to effectively improve the original Beck's nonlinear estimation procedure, the best convergence rate can be increased to 33.3%. From the numerical computation of the elasticity and damping, compare with the exact solutions under the measurement errors on the assumption that 1%, 5% and 10% of the conditions, the real percentage of error are less than 0.9%, 4.5% and 9.2%, and the measurement error is proportional to the percentage of the real error.