Nonlocal in Time Model of Material Damping in Composite Structural Elements Dynamic Analysis

In this paper the problem of numerical simulation of composite bending elements dynamic considering internal (material) damping. For this purpose the nonlocal in time damping model, called damping with memory, is proposed as an alternative to the classic local Kelvin-Voigt model. Damping with memory makes damping forces not only dependent on the instant value of the strain rate, but also on the previous history of the vibration process. Since finite element analysis is the most common method of structural analysis, the nonlocal damping model is integrated into FEA algorithm. The FEA dynamic equilibrium equation is solved using the explicit scheme. The damping matrix was developed using the stationary full energy requirement. One-dimensional nonlocal in time model was implemented in MATLAB software package. The results of three-dimensional numerical simulation of the composite beam vibration obtained in SIMULIA Abaqus were used for model calibration. The obtained results were compared to the results based on classic Kelvin-Voight damping model.