Analytical Approximate Solutions for the Cubic-Quintic Duffing Oscillator in Terms of Elementary Functions

被引：13

作者：

Belendez, A. ^{[1
,2
]}

Alvarez, M. L. ^{[1
,2
]}

Frances, J. ^{[1
,2
]}

Bleda, S. ^{[1
,2
]}

Belendez, T. ^{[1
,2
]}

Najera, A. ^{[3
]}

Arribas, E. ^{[4
]}

机构：

[1] Univ Alicante, Dept Fis Ingn Sistemas & Teoria Senal, E-03080 Alicante, Spain

[2] Univ Alicante, Inst Univ Fis Aplicada Ciencias & Tecnol, E-03080 Alicante, Spain

[3] Univ Castilla La Mancha, Fac Med, Dept Ciencias Med, Albacete 02006, Spain

[4] Univ Castilla La Mancha, Escuela Super Ingn Informat, Dept Fis Aplicada, Albacete 02071, Spain

来源：

JOURNAL OF APPLIED MATHEMATICS | 2012年

关键词：

HARMONIC BALANCING APPROACH; SIMPLE PENDULUM; NONLINEAR OSCILLATIONS; PERIOD;

D O I：

10.1155/2012/286290

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Accurate approximate closed-form solutions for the cubic-quintic Duffing oscillator are obtained in terms of elementary functions. To do this, we use the previous results obtained using a cubication method in which the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a cubic Duffing equation. Explicit approximate solutions are then expressed as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function cn. Then we obtain other approximate expressions for these solutions, which are expressed in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean is used and the rational harmonic balance method is applied to obtain the periodic solution of the original nonlinear oscillator.

引用

页数：16

共 18 条

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