Nonlinear Vibrations of Fractionally Damped Systems

Joe Padovan; Jerzy T. Sawicki

doi:10.1023/A:1008289024058

Nonlinear Vibrations of Fractionally Damped Systems

Joe Padovan
, Jerzy T. Sawicki

University of Akron

Research output: Contribution to journal › Article › peer-review

Abstract

This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincaré perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing's equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior.

Original language	American English
Journal	Nonlinear Dynamics
Volume	16
DOIs	https://doi.org/10.1023/A:1008289024058
State	Published - Aug 1 1998

Keywords

Fractionally damped; nonlinear systems; Duffing's equation; perturbation procedure

Disciplines

Mechanical Engineering

Access to Document

10.1023/A:1008289024058License: CC BY

Nonlinear Vibrations of Fractionally Damped SystemsFinal published version, 1.29 MBLicense: CC BY

http://journals.ohiolink.edu/ejc/article.cgi?issn=0924090x&issue=v16i0004&article=321_nvofds

Cite this

@article{34c8aab024a7423dbd5c9636b0a1e1e8,

title = "Nonlinear Vibrations of Fractionally Damped Systems",

abstract = " This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincar{\'e} perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing's equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior.",

keywords = "Fractionally damped; nonlinear systems; Duffing's equation; perturbation procedure",

author = "Joe Padovan and Sawicki, \{Jerzy T.\}",

note = "Padovan, J. and Sawicki, J.T., Non-Linear Vibrations of Fractionally Damped Systems, Nonlinear Dynamics, Kluwer Academic Publishers, 16, pp.321-336, 1998",

year = "1998",

month = aug,

day = "1",

doi = "10.1023/A:1008289024058",

language = "American English",

volume = "16",

journal = "Nonlinear Dynamics",

}

TY - JOUR

T1 - Nonlinear Vibrations of Fractionally Damped Systems

AU - Padovan, Joe

AU - Sawicki, Jerzy T.

N1 - Padovan, J. and Sawicki, J.T., Non-Linear Vibrations of Fractionally Damped Systems, Nonlinear Dynamics, Kluwer Academic Publishers, 16, pp.321-336, 1998

PY - 1998/8/1

Y1 - 1998/8/1

N2 - This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincaré perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing's equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior.

AB - This paper deals with the harmonic oscillations of periodically excited nonlinear systems where hysteresis is simulated via fractional operator representations. Employing a diophantine version of the fractional operational powers, the energy constrained Lindstedt–Poincaré perturbation procedure is utilized to establish the harmonic solution. The constrained perturbation procedure was employed since it allows for the handling of strong damping and exciting forces over the full span of the driving frequency range. Based on the approach taken, the long time behavior of the fractionally damped Duffing's equation is studied in detail. Of special interest is the determination of the influence of fractional order on the frequency amplitude response behavior.

KW - Fractionally damped; nonlinear systems; Duffing's equation; perturbation procedure

UR - https://engagedscholarship.csuohio.edu/enme_facpub/104

U2 - 10.1023/A:1008289024058

DO - 10.1023/A:1008289024058

M3 - Article

VL - 16

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

ER -

Nonlinear Vibrations of Fractionally Damped Systems

Abstract

Keywords

Disciplines

Access to Document

Other files and links

Cite this