Approximating amplitude of a nonlinear oscillator at resonance. (June 2022) - Verenkar, Saeesh; Naik, Raghavendra Datta
In this study, we propose a methodology to obtain the approximate amplitude of a nonlinear forced system at resonance that satisfies Lyapunov's global stability criterion. This analytical method is formulated using the Lyapunov stability criterion and nonlinear approximations. The results obtained were compared with those obtained from the fourth-order Runge–Kutta method. The proposed methodology can approximate the amplitude of a nonlinear non-autonomous system to reasonably good accuracy. This theory will be useful in experimental vibration analysis to approximate the damping in a system. The proposed methodology can also be extended to other nonlinear forced systems. The results also showed that the vibration attenuation or stability of the system depends mainly on the linear coefficients and is least dependent on the cubic stiffness.