A state-space approach to dynamic stability of fractional-order systems: The extended Routh-Hurwitz theorem

E. Bologna, L. Deseri, M. Zingales

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

This paper considers the case of Beck's column, a linear elastic cantilever column subjected to a constant follower load at its free end. The column foundation is modeled as bed of hereditary elements that react with a vertical force distributed along the beam axis. The reacting supports are modeled with spring-pot element that is a two parameters mechanical elements (Cβ β) with an intermediate behavior between spring and dashpot. The constitutive equation of the spring-pot involves the so called fractional order derivatives and dynamic stability problem in presence of fractional-order operator must be faced for the Beck's column. In this study, the authors generalize Routh-Hurwitz theorem of stability on the fractional order differential equation (FODE), system that governs the dynamic stability. Some numerical examples has been reported in the paper for two-degree of freedom system.

Original languageEnglish (US)
Title of host publicationAIMETA 2017 - Proceedings of the 23rd Conference of the Italian Association of Theoretical and Applied Mechanics
EditorsLuciano Feo, Fernando Fraternali, Luigi Ascione, Valentino Paolo Berardi, Antonio Michele Tralli
PublisherCentro Servizi d'Ateneo S.r.l.
Pages969-976
Number of pages8
ISBN (Electronic)9788894248470
StatePublished - 2017
Event23rd Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2017 - Salerno, Italy
Duration: Sep 4 2017Sep 7 2017

Publication series

NameAIMETA 2017 - Proceedings of the 23rd Conference of the Italian Association of Theoretical and Applied Mechanics
Volume5

Other

Other23rd Conference of the Italian Association of Theoretical and Applied Mechanics, AIMETA 2017
CountryItaly
CitySalerno
Period9/4/179/7/17

Keywords

  • Dynamic stability
  • Fractional order differential equation
  • Routh-hurwitz theorem

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials

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