Identification of Parameters of Mechanical Vibrating Systems Using the Amplitude-Frequency Relationship in Analytical Form

The subject of the paper is the concept of a method serving to the determination of the parameters that describe the damping and nonlinear elastic properties of mechanical vibrating systems. The possibility of the identification is provided by the analytical form of the relationship between the amplitude and frequency of periodic steady oscillations in the main resonance. The dependence is obtained using the multiple scale method (MSM) in the domain of time. The proposed method applies only when this dependency reduces to an algebraic equation of the third degree. The considerations for a single degree of freedom system described by the Duffing equation explain the main idea of the identification. However, under certain assumptions, the method can also be employed for systems with several degrees of freedom. The numerical simulations of the real experiment were carried out and discussed. The results confirm the usefulness and accuracy of the method and lead to practical conclusions determining the conditions for performing measurements.