**4. Conclusions**

Mechanical vibrations are currently undesirable in many cases. Therefore, this vibration must be eliminated in appropriate ways. One of the possible elimination methods is the application of suitable vibro-insulating materials. This paper was focused on the study of the mechanical and vibro-isolation properties of rubber compounds containing different carbon black particle sizes. Nevertheless, their volume concentration was the same. On the basis of the evaluated measurements, it can be stated that the particle size of the carbon black in the rubber composites had a significant effect on the stiffness of the rubber, and thus on its mechanical and vibro-isolation properties.

The mechanical properties of the tested rubber mixtures were investigated for reflective elasticity, tensile, viscoelastic, and vibro-insulating properties. It was found in this work that the stiffness of the rubber samples generally decreased with an increase in the particle size, resulting in higher reflective elasticity and lower mechanical properties, including lower hardness (decrease from 69 to 55 Sh A), breaking stress, and real components of the complex modulus of elasticity (tensile and shear). On the other hand, the higher particle size in the rubber mixtures led to a greater loss factor and deformations in terms of sample breakage.

The above facts were in good agreemen<sup>t</sup> with the vibro-isolation tests for the observed rubber materials, which were examined using the forced oscillation method based on the transfer damping function. At the same time, a material´s ability to dampen mechanical vibrations under dynamic stress is associated with the first resonance frequency, which is generally lower for materials that better dampen mechanical oscillation (or for materials with lower stiffness). Based on this method, it was verified that the first resonant frequency generally decreased with an increase in the carbon black particle size. Therefore, larger carbon black particles of the same volume concentration in rubber patterns contributed to better damping of mechanical vibrations, resulting in a higher transformation of input mechanical energy into heat under dynamic loading of these rubber composite samples. Vibration damping properties were also evaluated for the investigated rubber samples, which were harmonically loaded by a compression force. It can be concluded that a higher number of loading cycles led to a stiffness reduction in the investigated rubber composites, which was accompanied by a shift of the first resonance frequency peak position to lower excitation frequencies. Depending on the rubber type and the inertial mass, the decrease of the first resonance frequency after 750,000 loading cycles was between 37% and 65%. Furthermore, it has been found in this work that the material´s ability to damp mechanical vibrations generally increased with an increase in the excitation frequency of mechanical vibration, inertial mass, and thickness of the investigated rubber samples.

**Author Contributions:** Conceptualization, M.P. and M.V.; methodology, M.P., M.V., and P.Z.; preparation of rubber composites, P.Z. and M.P.; experimentation, P.Z., M.P., M.V., and M.Ž.; data analysis, P.Z., M.P., and M.V.; resources, M.V. and M.P.; writing—original draft preparation, M.V., M.P., and D.M.; writing—review and editing, M.V., M.P., D.M., and P.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Research Center of Advanced Mechatronic Systems project, number CZ.02.1.01/0.0/0.0/16\_019/0000867, within the Operational Program of Research, Development, and Education; and by gran<sup>t</sup> IGA/FT/2018/008 and gran<sup>t</sup> NPU I LO1504.

**Conflicts of Interest:** The authors declare that they have no conflicts of interest.
