On fractional forced oscillator

Fractional calculus is widely used in formulation of constitutive relations for viscoelastic materials. Problems of vibration of continuous structures, when such constitutive relations are used, leads to fractional differential equations similar to the equation of forced, damped, harmonic oscillator...

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Bibliographic Details
Main Authors: Łabędzki, Paweł, Pawlikowski, Rafał, Radowicz, Andrzej
Format: Conference Proceeding
Language:English
Subjects:
Constitutive relationships
Differential equations
Fractional calculus
Harmonic oscillators
Mathematical models
Vibration control
Viscoelastic materials
Viscoelasticity
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Summary:Fractional calculus is widely used in formulation of constitutive relations for viscoelastic materials. Problems of vibration of continuous structures, when such constitutive relations are used, leads to fractional differential equations similar to the equation of forced, damped, harmonic oscillator. In this paper two fractional oscillators are investigated (corresponding to two constitutive relations of viscoelastic materials). Closed-form solutions are obtained using Laplace Transform method, resonance curves for these oscillators are calculated numerically, and influence on its shape of the model parameters are analyzed.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5091897