On the solutions and stability for an auto-parametric dynamical system

Abstract The main goal of this study is to look at the motion a damped two degrees-of-freedom (DOF) auto-parametric dynamical system. Lagrange’s equations are used derive governing (EOM). Up good desired order, approximate solutions achieved utilizing method multiple scales (MMS). Two cases resonance, namely; internal and primary external one examined simultaneously explore solvability conditions corresponding modulation (ME). These reduced algebraic equations, through elimination modified phases, in terms detuning parameters amplitudes. kind stable or unstable fixed point estimated. In certain plots, time histories graphs solutions, as well adjusted phases amplitudes depict system any instant. Routh–Hurwitz various stability zones their analysis. outcomes considered be novel original, which strategy applied on particular significance studied can observed its applications number disciplines, such swaying structures rotor dynamics.