Periodic solutions of strongly non-linear oscillators by the multiple scales method

被引：30

作者：

Lakrad, F

Belhaq, M

机构：

[1] Free Univ Berlin, Inst Math 1, D-14195 Berlin, Germany

[2] Univ Hassan 2, Fac Sci Ain Chock, Lab Mech, Casablanca, Morocco

来源：

JOURNAL OF SOUND AND VIBRATION | 2002年 / 258卷 / 04期

关键词：

D O I：

10.1006/jsvi.2002.5145

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

The multiple scales method, developed for the systems with small non-linearities, is extended to the case of strongly non-linear self-excited systems. Two types of non-linearities are considered: quadratic and cubic. The solutions are expressed in terms of Jacobian elliptic functions. Higher order approximations, of solution as well as modulations of amplitude and phase, are derived. Comparisons to numerical simulations are provided and discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.

引用

页码：677 / 700

页数：24

共 50 条

[21] Strongly non-linear oscillators with slowly varying parameters
Cai, JP
Li, YP
JOURNAL OF SOUND AND VIBRATION, 2004, 275 (1-2) : 241 - 248
[22] The elliptic perturbation methods for strongly non-linear oscillators
Chen, SH
Cheung, YK
PROCEEDINGS OF THE 4TH INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS, 2002, : 1023 - 1027
[23] Quintication method to obtain approximate analytical solutions of non-linear oscillators
Escuela Nacional de Posgrado en Ciencias, Ingenieria y Tecnologias, Tecnologico de Monterrey, Campus Monterrey, E. Garza Sada 2501, Sur, C.P. 64849 Monterrey, N.L., Mexico
Appl. Math. Comput., (849-855):
[24] Melnikov's method for non-linear oscillators with non-linear excitations
Garcia-Margallo, J
Bejarano, JD
JOURNAL OF SOUND AND VIBRATION, 1998, 212 (02) : 311 - 319
[25] A modified elliptic Lindstedt-Poincare method for certain strongly non-linear oscillators
Yang, CH
Zhu, SM
Chen, SH
JOURNAL OF SOUND AND VIBRATION, 2004, 273 (4-5) : 921 - 932
[26] Non-linear dynamics of multiple friction oscillators
Galvanetto, U
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 178 (3-4) : 291 - 306
[27] An analytical approximate technique for a class of strongly non-linear oscillators
Wu, B. S.
Sun, W. P.
Lim, C. W.
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2006, 41 (6-7) : 766 - 774
[28] Invariants and approximate solutions for certain non-linear oscillators by means of the field method
Kovacic, Ivana
APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (09) : 3482 - 3487
[29] A PERTURBATION METHOD FOR CERTAIN NON-LINEAR OSCILLATORS
BURTON, TD
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1984, 19 (05) : 397 - 407
[30] APPROXIMATE ANALYTIC SOLUTIONS FOR SINGULAR NON-LINEAR OSCILLATORS
BOTA, KB
MICKENS, RE
JOURNAL OF SOUND AND VIBRATION, 1984, 96 (02) : 277 - 279

← 1 2 3 4 5 →