Periodic Motion in an Excited and Damped Cubic Nonlinear Oscillator

L. Cveticanin, U. Kozmidis Luburic and Gy. Mester

Mathematical Problems in Engineering, 2018, vol. 2018, 1-6

Abstract:

This paper investigates the steady-state periodic motion in the excited and damped one-degree-of-freedom Duffing oscillator. The oscillator is of the pure cubic type. The excitation is periodical and described by the product of two Jacobi elliptic functions. The mathematical model of the oscillator is a nonhomogeneous second-order strong nonlinear differential equation. The paper develops a procedure for obtaining the steady-state solution of the equation. Conditions for the existence of the steady-state motion of the oscillator are obtained. The influence of the excitation and of the damping on the steady-state motion is analyzed. The paper also investigates the transient to the steady-state motion in the parameter perturbed systems. An analytical method based on the time variable amplitude and the time variable phase is developed. The analysis of the obtained results shows that the damping parameter is an adequate control parameter for the steady-state motion of the oscillator. Analytically obtained results are compared with numerically obtained ones. The difference between solutions is negligible.

Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2018/3841926.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2018/3841926.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:3841926

DOI: 10.1155/2018/3841926

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().