Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

- A new method of identification of time-varying parameters of damped oscillators is elaborated.
- Coupled oscillators approach is applied.
- A discrete fractional derivative of measurement series is used.
- Synchronization of two dynamical systems indicates correctness of the performed identification.
- Numerical simulations of two mathematical models of an asymmetric pendulum are performed.

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.