The application of momentum equilibrium to solve nonlinear dynamic equations by time integration method

• Main Authors: Chia-En Lin, 林嘉恩
• Other Authors: Shyh-Rong Kuo
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/93069459609823934127

碩士 === 國立臺灣海洋大學 === 河海工程學系 === 99 === This paper is to propose a new method of analyzing time history response of dynamics, in order to improve the traditional method of direct integration of dynamic, and to better the problem of less accuracy while analyzing discontinuous or rapid changing loading and acceleration. In this paper, the model of equivalent momentum equilibrium, which is based on state variable related by displacement and velocity, was established by combining the physical concepts of energy conservative and momentum equilibrium, and adopting the integral techniques of weight function. Differed from the traditional model of time integration which approximates displacement, velocity, and acceleration by differential equation, this model can avoid response distortion from discontinuous acceleration, but still has characters of time integration, such as high accuracy and wide margin of gait time. Whereas the analysis of problems in non-linear dynamics must go through the iterative process, this paper proposes a method to solve system response by establishing the incremental pattern of momentum equilibrium, which identify convergence and frequency of iterations by unbalanced momentum. The model of equation in this paper presents a method which possesses advantages of high efficiency and fourth-order accuracy while been applied to wild margin gait time operation, and also besteads the study of non-linear system study of impact loading.