Mechanical systems oscillations with hysteresis energy dissipation

In the work, when considering problems of mechanical systems oscillations, taking into account the dissipation of energy in the material, it is assumed that there are hysteresis losses in the mechanical oscillating system, which is caused by elastic imperfections of the material. In the relationship between stress and strain, which actually exists in all materials, there is some deviation from the linear law. In this case, the elastic imperfection manifests itself in the form of a hysteresis loop, the area of which characterises the ability of the material to absorb energy during mechanical vibrations. The article analyses the influence of hysteresis friction of mechanical systems close to resonance. Of particular importance is the generalisation of this approach to real structures with a larger degree of freedom. The work obtains analytical relationships linking stresses and strains taking into account hysteresis energy dissipation. To determine the dynamic properties of mechanical systems, a variational grid approach has been used to construct Rayleigh-type functionals and then minimize them using non-linear programming methods.