A STATE-SPACE APPROACH TO DYNAMIC STABILITY OF FRACTIONAL-ORDER SYSTEMS: THE EXTENDED ROUTH-HURWITZ THEOREM

Emanuela, B.; Luca, D.; Massimiliano, Z.

Risultato della ricerca: Paper

1 Citazione (Scopus)

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 (C; ) 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.
Lingua originaleEnglish
Stato di pubblicazionePublished - 2017

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A STATE-SPACE APPROACH TO DYNAMIC STABILITY OF FRACTIONAL-ORDER SYSTEMS: THE EXTENDED ROUTH-HURWITZ THEOREM. / Emanuela, B.; Luca, D.; Massimiliano, Z.

2017.

Risultato della ricerca: Paper

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title = "A STATE-SPACE APPROACH TO DYNAMIC STABILITY OF FRACTIONAL-ORDER SYSTEMS: THE EXTENDED ROUTH-HURWITZ THEOREM",
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 (C; ) 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.",
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T1 - A STATE-SPACE APPROACH TO DYNAMIC STABILITY OF FRACTIONAL-ORDER SYSTEMS: THE EXTENDED ROUTH-HURWITZ THEOREM

AU - Emanuela, B.; Luca, D.; Massimiliano, Z.

AU - Zingales, Massimiliano

AU - Bologna, Emanuela

PY - 2017

Y1 - 2017

N2 - 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 (C; ) 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.

AB - 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 (C; ) 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.

UR - http://hdl.handle.net/10447/262983

M3 - Paper

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