Evaluation of the stability of a two degrees-of-freedom dynamical system

This work studies a two degrees-of-freedom (DOF) dynamical system whose governing is solved analytically using the multiple scales approach (MSA). The solvability requirements are obtained in light of elimination secular terms. All resonance states classified to understand equilibrium system. Two them examined parallel get associated equations for system’s modulation. probable fixed points identified at stability and instability criteria Routh-Hurwitz (RH). curves behavior during motion plotted analyzed. numerical solutions (NS) method Runge-Kutta fourth-order, they compared with analytical (AS). comparison reveals high consistency between proves accuracy MSA. To determine positive effects different parameters on motion, zones studied from perspective their graphs. applications such works very important our daily lives were reason development several things, including protection earthquakes, car shock absorbers, structure vibration, human walking, television towers, buildings, antennas.