Exploiting knowledge of jump-up and jump-down frequencies to determine the parameters of a Duffing oscillator

This work concerns the application of certain non-linear phenomena - jump frequencies in a base-excited Duffing oscillator - to the estimation of the parameters of the system. First, approximate analytical expressions are derived for the relationships between the jump-up and jump-down frequencies, the damping ratio and the cubic stiffness coefficient. Then, experimental results, together with the results of numerical simulations, are presented to show how knowledge of these frequencies can be exploited.