Chaotic vibration affected by initial conditions in a parametrically and externally excited system with backlash

In the present paper, the influence of initial conditions on the occurrence of regular and chaotic vibrations of the system with backlash, described by a non-linear differential equation with a periodic coefficient, was investigated. For specified parameters, using the Lyapunov exponent, intervals of the initial conditions leading to chaotic motion were determined. The effect of external excitation amplitude on the character of motion was analysed. For the initial conditions determining regular and chaotic motion, Poincare maps, bifurcation diagrams, phase trajectories and time histories were compared, respectively.