The article aims to study the spectral properties of oscillating mechanical systems that comprise hysteretic components. The authors modeled the treated hysteretic systems as systems of nonlinear differential equations and used the MATLAB environment to obtain the respective numerical solutions. The results were then transformed into the frequency domains using the Fourier transform. The corresponding linear system used as a reference was processed in the same manner. The frequency domains were then analyzed and compared in order to investigate the influence of hysteresis on the treated systems. The obtained results show that the hysteretic components have a considerable impact on the natural frequencies of the studied systems. These varied according to the changes in stiffness that are a natural result of the hysteresis. Moreover, the hysteretic components introduced an additional energy dissipation to these systems. This resulted in increased damping, consequently leading to more stable behavior, compared to the reference linear system.

Acknowledgement: This work was supported by the projects VEGA, No. 1/0423/23 and KEGA, No. 005ŽU-4/2024.