Mathematical Modelling and Experimental Validation of Bifurcation Dynamics of One-Degree-of-Freedom Oscillator with Duffing-Type Stiffness and Rigid Obstacle.

Purpose: In the work there are presented results of the synthesis and additional validation of previously developed mathematical models of two different mechanical oscillators with 1 degree of freedom and harmonic excitation: (i) with magnetically modified elasticity generating a double symmetrical minimum of potential; (ii) with linear mechanical springs and with a one-sided limiter of motion. Methods: In the first case, original mathematical models of non-linear magnetic springs were developed, allowing for effective and fast numerical simulations of the bifurcation dynamics of a real mechanical oscillator with Duffing type stiffness. In the second system, various models of impact were proposed and tested: continuous models based on the generalized Hunt–Crossley model and original discontinuous versions of this model based on the restitution coefficient and with a finite duration of the collision. In the frame of the present work, a system consisting of magnetic springs used in the first system and obstacles from the second oscillator was built and investigated. The system was built as a new configuration of a special universal stand used in the earlier studies mentioned here. Results and Conclusion: In the current study, the parameters of the models identified in previous studies on two different systems were used, the synthesis of which is the current work. A very good agreement was obtained between numerical simulations and experimental data, thus demonstrating the correctness and effectiveness of the adopted mathematical models. [ABSTRACT FROM AUTHOR]