Stability analysis of beck’s column over a fractional-order hereditary foundation

Massimiliano Zingales, Emanuela Bologna, Emanuela Bologna, Massimiliano Zingales

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Abstract

This paper considers the case of Beck’s column resting on a hereditary bed of independent springpots. The springpot possesses an intermediate rheological behaviour among linear spring and linear dashpot. It is defined by means of couple (Cß, ß) that characterize the material of the element and is ruled by a Caputo’s fractional derivative. In this paper, we investigate the critical load of the column under the action of a follower load by means of a novel complex transform that allows to use the Routh–Hurwitz theorem in the complex half-plane for the stability analysis.
Lingua originaleEnglish
pagine (da-a)20180315-
Numero di pagine8
RivistaPROCEEDINGS OF THE ROYAL SOCIETY OF LONDON. SERIES A
Volume474
Stato di pubblicazionePublished - 2018

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Fractional Order
Stability Analysis
Derivatives
Critical Load
half planes
Fractional Derivative
Half-plane
beds
theorems
Transform
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

Cita questo

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abstract = "This paper considers the case of Beck’s column resting on a hereditary bed of independent springpots. The springpot possesses an intermediate rheological behaviour among linear spring and linear dashpot. It is defined by means of couple (C{\ss}, {\ss}) that characterize the material of the element and is ruled by a Caputo’s fractional derivative. In this paper, we investigate the critical load of the column under the action of a follower load by means of a novel complex transform that allows to use the Routh–Hurwitz theorem in the complex half-plane for the stability analysis.",
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AU - Zingales, Massimiliano

PY - 2018

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N2 - This paper considers the case of Beck’s column resting on a hereditary bed of independent springpots. The springpot possesses an intermediate rheological behaviour among linear spring and linear dashpot. It is defined by means of couple (Cß, ß) that characterize the material of the element and is ruled by a Caputo’s fractional derivative. In this paper, we investigate the critical load of the column under the action of a follower load by means of a novel complex transform that allows to use the Routh–Hurwitz theorem in the complex half-plane for the stability analysis.

AB - This paper considers the case of Beck’s column resting on a hereditary bed of independent springpots. The springpot possesses an intermediate rheological behaviour among linear spring and linear dashpot. It is defined by means of couple (Cß, ß) that characterize the material of the element and is ruled by a Caputo’s fractional derivative. In this paper, we investigate the critical load of the column under the action of a follower load by means of a novel complex transform that allows to use the Routh–Hurwitz theorem in the complex half-plane for the stability analysis.

UR - http://hdl.handle.net/10447/338357

M3 - Article

VL - 474

SP - 20180315-

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

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