【作者】 廖少锴； 张卫；

【Author】 LIAO Shao-kai~1 ZHANG Wei~2 (1.Department of Mechanics & Civil Engineering,Jinan University,Guangzhou 510632,China;2.Research Institutes of Applied Mechanics,Jinan University,Guangzhou 510632,China)

【机构】 暨南大学力学与土木工程系； 暨南大学应用力学研究所；

【摘要】 本文结合Zhang-Shimizu法与Newmark法,解决了二次非线性的Riemann-Liouville分数导数中奇异性问题,从而得到了非线性分数微积分求解的单步数值积分算法。在此基础上对非线性分数阶微分振子的动力学行为进行数值探讨,分别讨论了振子自由振动及强迫振动下参数变化对振子非线性特性的影响。数值计算结果表明,该数值方法具有较好的稳定好,收敛速度快,精度较高,编程简单容易等优点。更多还原

【Abstract】 An algorithm,considering Zhang-Shimizu method and Newmark method together,by which the singularity of the Riemann-Liouville fractional derivative with quadratic nonlinearity functional can be solved,was deduced.Nonlinear fractional oscillator’s dynamics properties can be studied based on the algorithm that we have. Free vibration and forced vibration of the nonlinear fractional oscillator were discussed. Numerical computational result indicated that:the algorithm for nonlinear fractional differential is of better convergence,preferable stability and higher computation precision.更多还原