An approximation technique for solving nonlinear oscillators

被引：1

作者：

Huq, Md Ashraful ^{[1
]}

Hasan, M. Kamrul ^{[1
,2
]}

Alam, M. S. ^{[1
]}

机构：

[1] Rajshahi Univ Engn & Technol RUET, Dept Math, Kazla, Bangladesh

[2] Rajshahi Univ Engn & Technol RUET, Dept Math, Rajshahi 6204, Bangladesh

来源：

JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL | 2024年 / 43卷 / 01期

关键词：

Differential transform method; Duffing oscillator; quadratic oscillator; pendulum equation; DIFFERENTIAL TRANSFORM METHOD; HOMOTOPY PERTURBATION METHOD;

D O I：

10.1177/14613484231195267

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

Recently, an approximation technique was presented for solving strong nonlinear oscillators modeled by second-order differential equations. Due to the arising of an algebraic complicity, the method fails to determine suitable solution of some important nonlinear problems such as quadratic oscillator, cubical Duffing oscillator of softening springs, and pendulum equation. However, suitable solutions of these oscillators are found by rearranging only an algebraic equation related to amplitude and frequency. The determination of solutions is simpler than the original version.

引用

页码：239 / 249

页数：11

共 50 条

[1] An approximation technique for solving anti-symmetric constant force and anti-symmetric quadratic nonlinear oscillators
Huq, Md Ashraful
Hasan, M. Kamrul
Alam, M. S.
JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2024, : 1498 - 1508
[2] Application of the consine generalized Padé approximation method in solving periodic solutions of strongly nonlinear oscillators
Li Z.
Tang J.
Zhendong yu Chongji/Journal of Vibration and Shock, 2019, 38 (22): : 162 - 170
[3] A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators
李震波
唐驾时
蔡萍
Chinese Physics B, 2014, (12) : 82 - 88
[4] A generalized Pade approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators
Li Zhen-Bo
Tang Jia-Shi
Cai Ping
CHINESE PHYSICS B, 2014, 23 (12)
[5] A novel analytical approximation technique for highly nonlinear oscillators based on the energy balance method
Hosen, Md. Alal
Chowdhury, M. S. H.
Ali, Mohammad Yeakub
Ismail, Ahmad Faris
RESULTS IN PHYSICS, 2016, 6 : 496 - 504
[6] An Analytical Approximation Method for Strongly Nonlinear Oscillators
Wang Shimin
Yang Lechang
JOURNAL OF APPLIED MATHEMATICS, 2012,
[7] An Analytical Technique for Solving Nonlinear Oscillators of the Motion of a Rigid Rod Rocking Bock and Tapered Beams
Ismail, G. M.
JOURNAL OF APPLIED AND COMPUTATIONAL MECHANICS, 2016, 2 (01): : 29 - 34
[8] A technique for solving nonlinear problems
Dubey, RN
Jahed, H
Kumar, A
TRENDS IN STRUCTURAL MECHANICS: THEORY, PRACTICE, EDUCATION, 1997, 54 : 15 - 20
[9] A new analytical approach for solving quadratic nonlinear oscillators
Mondal, Md. Mahtab Hossain
Molla, Md. Helal Uddin
Razzak, Md. Abdur
Alam, M. S.
ALEXANDRIA ENGINEERING JOURNAL, 2017, 56 (04) : 629 - 634
[10] Generic numerical and analytical methods for solving nonlinear oscillators
Kontomaris, Stylianos Vasileios
Mazi, Ioanna
Chliveros, Georgios
Malamou, Anna
PHYSICA SCRIPTA, 2024, 99 (02)

← 1 2 3 4 5 →