Oscillators with a fractional-order restoring force: High-order approximations for motion via a modified Ritz method
Oscillators with a fractional-order restoring force: High-order approximations for motion via a modified Ritz method
In this paper conservative single-degree-of-freedom oscillators with a fractional-order restoring force are considered. In order to obtain the solution for motion in higher approximations, the Ritz method is adjusted by introducing an approximate Lagrangian and by using the exact value of the frequency of vibrations.
Explicit expressions for the amplitudes of the second and third approximations are derived. The results obtained are compared with numerical results and with the existing approximate result for the first approximation.
conservative oscillator, fractional-order restoring force, lagrangian, Ritz method
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Rakaric, Zvonko
f7d5f2bb-5ad9-4918-942b-e68d321c2c2a
2009
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Rakaric, Zvonko
f7d5f2bb-5ad9-4918-942b-e68d321c2c2a
Kovacic, Ivana and Rakaric, Zvonko
(2009)
Oscillators with a fractional-order restoring force: High-order approximations for motion via a modified Ritz method.
Communication in Nonlinear Science and Numerical Simulations, In Press.
(doi:10.1016/j.cnsns.2009.09.030).
Abstract
In this paper conservative single-degree-of-freedom oscillators with a fractional-order restoring force are considered. In order to obtain the solution for motion in higher approximations, the Ritz method is adjusted by introducing an approximate Lagrangian and by using the exact value of the frequency of vibrations.
Explicit expressions for the amplitudes of the second and third approximations are derived. The results obtained are compared with numerical results and with the existing approximate result for the first approximation.
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Published date: 2009
Keywords:
conservative oscillator, fractional-order restoring force, lagrangian, Ritz method
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Local EPrints ID: 79135
URI: http://eprints.soton.ac.uk/id/eprint/79135
ISSN: 1007-5704
PURE UUID: 5fa408fc-0bbb-409e-a5b4-5324323c59b2
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Date deposited: 12 Mar 2010
Last modified: 14 Mar 2024 00:28
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Author:
Ivana Kovacic
Author:
Zvonko Rakaric
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