New approximate solutions for the strongly nonlinear cubic-quintic duffing oscillators

Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analyti...

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Bibliographic Details
Main Authors: Karahan, M. M. Fatih, Pakdemirli, Mehmet
Format: Conference Proceeding
Language:English
Subjects:
Computer simulation
Duffing oscillators
Frequency response
Oscillators
Online Access:Get full text
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Summary:Strongly nonlinear cubic-quintic Duffing oscillator is considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.4952117