Abstract
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.
Highlights
In the last few decades, considerable work has been invested in developing new methods for analytical and numerical solutions for several differential equations [1,2,3,4] such as strongly nonlinear oscillators, but it is still difficult to obtain convergent results in cases of strong nonlinearity. e Duffing oscillator model is one of the most important and most popular models in dynamic systems due to its importance in explaining many nonlinear phenomena in science and engineering
The nonlinear Duffing equation was devoted for studying the dynamical behavior of oscillations in plasma physics [5], plasma physics and rigid rotator [6], magneto-elastic mechanical systems [7], nonlinear vibration of beams and plates [8], fluid flow induced vibration [9], large amplitude oscillation of centrifugal governor systems [10], etc
The model becomes a nonconservative system and the oscillation amplitude reduces over time
Summary
An Exact Solution to the Quadratic Damping Strong Nonlinearity Duffing Oscillator. E 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. Us, 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. 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. The obtained solutions are camped to the Runge–Kutta fourth-order (RK4) numerical solution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
