Dynamical Stability of a 3-DOF Auto-Parametric Vibrating System

Abstract Purpose This article concentrates on the oscillating movement of an auto-parametric dynamical system comprising a damped Duffing oscillator and associated simple pendulum in addition to rigid body as main secondary systems, respectively. Methods According generalized coordinates, controlling equations motion are derived utilizing Lagrange's approach. These solved applying perturbation methodology multiple scales up higher orders approximation achieve further precise unique outcomes. The fourth-order Runge–Kutta algorithm is employed obtain numerical outcomes governing system. Results comparison between both solutions demonstrates their high level consistency highlights great accuracy adopted analytical strategy. Despite conventional nature applied methodology, obtained results for studied considered new. Conclusions In light solvability criteria, all resonance scenarios classified, which two fundamental exterior resonances examined simultaneously with one interior resonances. Therefore, modulation achieved. conditions Routh–Hurwitz inspect stability/instability regions analyze them accordance steady-state case. For various factors structure, temporary history solutions, curves terms adjusted amplitudes phases, stability zones graphically presented discussed. Applications current study will be interest wide range experts fields mechanical aerospace technology, well those working reduce rotors vibrations attenuate vibration caused by swinging structures.