Analysis of vibration of three-degree-of-freedom dynamical system with double pendulum

The nonlinear response of a three-degree-of-freedom vibratory system with a double pendulum in the neighborhood of internal and external resonances has been examined. Numerical and analytical methods have been applied for these investigations. Analytical solutions have been obtained by using the multiple scales method. This method is used to construct first-order non-linear ordinary differential equations governing the modulation of amplitudes and phases. Steady state solutions and their stability are computed for selected values of the system parameters.