Generalized synchronization by coupling of restoring force and determination of parameters in vibration systems

For a class of vibration systems excited by external harmonic force, generally the restoring force cannot be given an accurate analytical expression. For such system, a derived system of generalized synchronization (GS) is set up. The GS between the two systems is proved. Since there is no time element in the equations of the derived system, the derived system can reach GS with the original system automatically, even if the frequency and amplitude of external force are varied. By using GS, a novel method to determine parameters in a vibration system, e.g., the damping coefficient and the amplitude and frequency of external exciting force, is presented and proved. From the simulation of Duffing system, it can be seen that the presented method is effective and can give a result of high accuracy.