On the use of two classical series expansion methods to determine the vibration of harmonically excited pure cubic oscillators
On the use of two classical series expansion methods to determine the vibration of harmonically excited pure cubic oscillators
An analytical approach to determine the steady-state response of a damped and undamped harmonically excited oscillator with no linear term and with cubic non-linearity is presented. The governing equation is transformed into a form suitable for the application of a classical series expansion technique. The Linstedt–Poincaré method and the method of multiple scales are then used to determine the amplitude-frequency response and approximate solution for the response at the excitation frequency. The results obtained are compared with numerical solutions and analytical solutions found in the literature for the case when there is strong non-linearity.
expansion, amplitude-frequency response, strong non-linearity
4028-4032
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Brennan, Michael J.
87c7bca3-a9e5-46aa-9153-34c712355a13
26 May 2008
Kovacic, Ivana
a84bc948-5aa9-444f-8a58-12a731808a20
Brennan, Michael J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Kovacic, Ivana and Brennan, Michael J.
(2008)
On the use of two classical series expansion methods to determine the vibration of harmonically excited pure cubic oscillators.
Physics Letters A, 372 (22), .
(doi:10.1016/j.physleta.2008.03.019).
Abstract
An analytical approach to determine the steady-state response of a damped and undamped harmonically excited oscillator with no linear term and with cubic non-linearity is presented. The governing equation is transformed into a form suitable for the application of a classical series expansion technique. The Linstedt–Poincaré method and the method of multiple scales are then used to determine the amplitude-frequency response and approximate solution for the response at the excitation frequency. The results obtained are compared with numerical solutions and analytical solutions found in the literature for the case when there is strong non-linearity.
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Published date: 26 May 2008
Keywords:
expansion, amplitude-frequency response, strong non-linearity
Identifiers
Local EPrints ID: 65248
URI: http://eprints.soton.ac.uk/id/eprint/65248
ISSN: 0375-9601
PURE UUID: 4c2b3ace-30b9-46f7-940c-94b1845ccd4f
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Date deposited: 13 Feb 2009
Last modified: 15 Mar 2024 12:07
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Author:
Ivana Kovacic
Author:
Michael J. Brennan
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