ABSTRACT
Duffing oscillators play a crucial role in applied mathematics, physics, and engineering problems. Thus, various numerical techniques and perturbation methods have been used to handle Duffing oscillator equations. Nourazar and Mirzabeigy employed the modified differential transformation method to solve Duffing oscillator with damping effect. An approximate solution of force-free Duffing–van der Pol oscillator equations using the homotopy perturbation method has been developed by Khan et al. This chapter discusses the solution of unforced and forced Duffing oscillator equations using the single-layer functional link artificial neural network method. It considers single-layer simple orthogonal polynomial–based neural network (SOPNN) and Hermite neural network models to handle these equations. The chapter includes unforced damped Duffing oscillator equations to show the powerfulness of the SOPNN method. It discusses a Duffing oscillator equation used for extracting the features of early mechanical failure signal and detect early fault.
