NONLOCAL IN TIME DYNAMIC DEFORMATION MODEL AND ITS CALIBRATION BASED ON THE BEAM VIBRATION EXPERIMENT RESULTS

The article is devoted to the development of a nonlocal in time model of a material dynamic deformation and its calibration on the basis of the beam vibration experiment results. The model is based on the defining relations of nonlocal mechanics. Elastic forces in a system are considered dependent on the entire history of its deformation, and not only on the instantaneous deformed state under consideration. The nonlocal in time model of a dynamic deformation is proposed as an alternative to detailed three-dimensional models when modeling the dynamic behavior of elements and systems made of materials characterized by an inhomogeneous structure or anisotropic properties. The model is incorporated into the FEA algorithm to make it usable for applied engineering problems. As a numerical example, the oscillation of a bending beam is considered. A method for the identification of the governing parameter of a nonlocal in time model based on the least squares method is being implemented based on the results of laboratory tests of bent beams for free vibrations.