文章基本信息

标题：Formulation and solutions of fractional continuously variable order mass–spring–damper systems controlled by viscoelastic and viscous–viscoelastic dampers
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作者：S Saha Ray ; S Sahoo ; S Das 等
期刊名称：Advances in Mechanical Engineering
印刷版ISSN：1687-8140
电子版ISSN：1687-8140
出版年度：2016
卷号：8
期号：5
DOI：10.1177/1687814016646505
语种：English
出版社：Sage Publications Ltd.
摘要：This article presents the formulation and a new approach to find analytic solutions for fractional continuously variable order dynamic models, namely, fractional continuously variable order mass–spring–damper systems. Here, we use the viscoelastic and viscous–viscoelastic dampers for describing the damping nature of the oscillating systems, where the order of fractional derivative varies continuously. Here, we handle the continuous changing nature of fractional order derivative for dynamic systems, which has not been studied yet. By successive recursive method, here we find the solution of fractional continuously variable order mass–spring–damper systems and then obtain closed-form solutions. We then present and discuss the solutions obtained in the cases with continuously variable order of damping for oscillator through graphical plots.
关键词：Fractional continuously variable order; viscoelastic oscillator; viscous–viscoelastic oscillator; Riemann–Liouville fractional integral; Riemann–Liouville fractional derivative; Mittag-Leffler function; successive recursive method