Response of Free Vibration of Dynamical Systems with Fractional Derivatives

• Main Authors: Chun-Chieh Yu, 游竣傑
• Other Authors: Ching-Tung Hung
• Format: Others
• Language: zh-TW
• Published: 2016
• Online Access: http://ndltd.ncl.edu.tw/handle/53443783416385973945

碩士 === 國立臺灣科技大學 === 營建工程系 === 104 === This study presents a fundamental solution based on the Laplace transform method for a dynamical system with fractional derivatives. The system being investigated is a typical spring-mass system with an additional fractional order damping. This study also observes the response variations by changing the coefficient and the order of fractional derivatives, and the damping ratio parameter. The Caputo fractional derivative is assumed with an order α satisfying 0＜α＜1. The results show that the displacement responses exhibit ossillatory behavier with amplitude decaying over time. The displacement ultimately reaches zero in a smooth form. Addition to the displacement response, the associated velocity response is also presented. Where a similarly decayed ossillatory response type is observed.