An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator

被引：28
|
作者：
Salas, Alvaro H. [1 ,2 ]
El-Tantawy, S. A. [3 ,4 ]
Aljahdaly, Noufe H. [5 ]
机构：
[1] Univ Nacl Colombia, Dept Math, Nubia Campus, Manizales, Colombia
[2] Stat FIZMAKO Res Grp, Nubia Campus, Manizales, Colombia
[3] Port Said Univ, Dept Phys, Fac Sci, Port Said 42521, Egypt
[4] Al Baha Univ, Fac Sci & Arts, Dept Phys, Res Ctr Phys RCP, Al Baha, Saudi Arabia
[5] King Abdulaziz Univ, Fac Sci & Arts, Dept Math, Rabigh Campus, Jeddah 21911, Saudi Arabia
来源：
MATHEMATICAL PROBLEMS IN ENGINEERING | 2021年 / 2021卷
关键词：
HOMOTOPY; BALANCE; VAN;
D O I：
10.1155/2021/8875589
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The nonlinear equations of motion such as the Duffing oscillator equation and its family are seldom addressed in intermediate instruction in classical dynamics; this one is problematic because it cannot be solved in terms of elementary functions before. Thus, in this work, the stability analysis of quadratic damping higher-order nonlinearity Duffing oscillator is investigated. Hereinafter, some new analytical solutions to the undamped higher-order nonlinearity Duffing oscillator in the form of Weierstrass elliptic function are obtained. Posteriorly, a novel exact analytical solution to the quadratic damping higher-order nonlinearity Duffing equation under a certain condition (not arbitrary initial conditions) and in the form of Weierstrass elliptic function is derived in detail for the first time. Furthermore, the obtained solutions are camped to the Runge-Kutta fourth-order (RK4) numerical solution.
引用
收藏
页数：8
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