On the motion of a harmonically excited damped spring pendulum in an elliptic path. (January 2019) - Amer, T.S.; Bek, M.A.; Abohamer, M.K.
Highlights: This work touches an important problem which is the motion of a nonlinear damped spring pendulum carrying a rigid body. The supported point moves in an elliptic path. The method of multiple scales is used to obtain the analytical solutions of the governing equations of motion. All resonance cases are analyzed and discussed. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures. Abstract: In this work the problem of a nonlinear damped spring pendulum in which the motion of its pivot point in an elliptical path is investigated. The second end of the spring is connected with the body. A linear force acting along the pendulum arm besides two anticlockwise moments; one at the suspension point of the body with the damped spring and the other at the pivot point. One of the important perturbation techniques called the multiple scales (MS) technique is utilized to obtain the approximate solutions of the governing equations of motion till the third approximation. The modulation equations and the solvability conditions are obtained in view of the emerging resonance cases. The time history and the resonances curves are performed in some plots to show the good effect of the physical parameters on the behavior of the considered dynamical model.