A sharp stability criterion for single well Duffing and Duffing-like equations

Power Series -Aftertreatment Technique for Nonlinear Cubic Duffing and Double-Well Duffing Oscillators

Modeling of large amplitude of structures such as slender, flexible cantilever beam and fluid-structure resting on nonlinear elastic foundations or subjected to stretching effects often lead to strongly nonlinear models of Duffing equations which are not amendable to exact analytical methods. In this work, explicit analytical solutions to the large amplitude nonlinear oscillation systems of cub...

Boundedness for Semilinear Duffing Equations at Resonance

In this paper, we prove the boundedness of all solutions for the equation x + n 2 x + φ(x) + g (x)q(t) = 0, where n ∈ N, q(t) = q(t + 2π), φ(x) and g(x) are bounded.

Boundedness of solutions for semilinear duffing equations

Duffing equations with cubic and quintic nonlinearities

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

Robust Control for a Class of Modified Duffing Equations

In this paper, a new class of modified Duffing equations with coupled periodic forcing and damping terms is developed, and the robust control problem for the system with structural uncertainty is studied systematically. This type of modified Duffing equations originates from swimming dynamics of a shape-changing underwater vehicle. The set-point control problem is studied for the system with co...