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

E. Bologna, Luca 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
PublisherCentro Servizi d'Ateneo S.r.l.
Pages969-976
Number of pages8
Volume5
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

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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