Study the Stability and the Control of Non-Linear Dynamical Systems : Study the stability and the control of spring pendulum system represented by non-linear differential equations

The use of passive control strategy is a common way to stabilize and control dangerous vibrations in a nonlinear spring pendulum which is describing the ship's roll motion. The main task of this work is to show the effect of the control device on the nonlinear spring pendulum by connecting to the transverse or longitudinal absorber. Multiple scale perturbation method (MSPT) is applied to obtain the approximate solutions for the differential equations describing the system. The stability of the steady-state solution near the resonance case is investigated and studied using frequency response equations. The effects of the absorber and some system parameters on the vibrating system are studied numerically.