Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach

详细信息    查看全文

• 作者：Giulio Cottone ; Mario Di Paola ; Salvatore Butera
• 关键词：Stochastic differential equations ; Power-law drift ; Fractional calculus ; Fractional differential equations ; Characteristic function ; Nonlinear viscous– ; elastic damper
• 刊名：Probabilistic Engineering Mechanics
• 出版年：2011
• 出版时间：January 2011
• 年：2011
• 卷：26
• 期：1
• 页码：101-108
• 全文大小：1145 K

文摘

Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous–elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem.

This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.