Modeling of dissipation of vibration energy in problems of structural dynamics

Abstract

This paper has proposed a model that reflects a process of energy dissipation in dynamic oscillatory systems. According to the hereditary theory of viscoelasticity, a relationship between stress and strain is realized in an integral form. At the same time, the weakly singular kernel of heredity simultaneously describes both internal friction and deformation of aftereffects (creep and relaxation). Application of the developed model is shown through the description of free and forced vibrations of dissipative mechanical systems. A new opportunity can optimize the damping properties of materials of vibrating structures, which is important in solving the problem of introducing new materials. In mechanics, a new approach was proposed, which consists of the fact that by knowing the rheological parameters of material, one can find the damping coefficients directly without resorting to experiment.