The vibrational motion of a spring pendulum in a fluid flow

In this work, the response of two degrees of freedom for a nonlinear dynamical model represented by the motion of a damped spring pendulum in an inviscid fluid flow is investigated. The governing system of motion is obtained using Lagrange's equations. The equations of this system are solved utilizing the multiple scales method to obtain the asymptotic solutions up to the second approximation. Resonance cases of the system are classified and the modulation equations are achieved. The steady state solutions are examined in view of the solvability conditions. The dynamical behavior regarding the time history of the considered motion, the resonance curves and the steady state solutions are performed graphically. The effect of different parameters on the motion is analyzed using non-linear stability analysis. The importance of this model is due to its various applications which centric on engineering vibrating systems.