An application of chaos for vibration control

Chaos anti-control is considered for mechanical vibration control. The linear system under period excitation is guided to a chaotic system by a traditional control method. After the dynamic equation of the system is transferred to a dimensionless one, it was made to track Duffing system by adding a controller. The control parameters were selected according to Mélnikov criterion instead of calculation of Lyapunov exponents. So the process of parameters selecting become simple. According to the different relative damping coefficient of the system, the number that for transforming the dynamic equation to dimensionless form could be regulated. It shows that for the system we study this method is effective only if the dimensionless angular frequency is not large, chaos could appear within the range. A numerical example was given, its time histories and phase portrait and the power spectral density diagram show the effectiveness of this method.