Paper Info
Title
Oscillator with a Sum of Noninteger-Order Nonlinearities.
Abstract
Free and self-excited vibrations of conservative oscillators with polynomial nonlinearity are considered. Mathematical model of the system is a second-order differential equation with a nonlinearity of polynomial type, whose terms are of integer and/or noninteger order. For the case when only one nonlinear term exists, the exact analytical solution of the differential equation is determined as a cosine-Ateb function. Based on this solution, the asymptotic averaging procedure for solving the perturbed strong non-linear differential equation is developed. The method does not require the existence of the small parameter in the system. Special attention is given to the case when the dominant term is a linear one and to the case when it is of any non-linear order. Exact solutions of the averaged differential equations of motion are obtained. The obtained results are compared with "exact" numerical solutions and previously obtained analytical approximate ones. Advantages and disadvantages of the suggested procedure are discussed.
Year
DOI
Venue
2012
10.1155/2012/649050
JOURNAL OF APPLIED MATHEMATICS
Field
DocType
Volume
Order of accuracy,Differential equation,Mathematical optimization,Nonlinear system,Mathematical analysis,Linear differential equation,Exact differential equation,Integrating factor,Homogeneous differential equation,Mathematics,Universal differential equation
Journal
2012
ISSN
Citations 
PageRank 
1110-757X
6
1.29
References 
Authors
2
2
Name
Order
Citations
PageRank
Livija Cveticanin1178.17
Tibor Pogány23213.73