Dynamic Model of Beam Deformation With Consider Nonlocal In Time Elastic Properties of the Material

In this paper, the problem of numerical dynamic calculation of a beam made of composite material with a developed internal structure is considered.  The elastic properties are assumed to be nonlocal in time. A short review of the existing methods for mathematical modeling of the dynamic behavior of elements with a developed internal structure was carried out. A non-local in time model of dynamic deformation of a bending beam is constructed. Since the finite element analysis (FEA) is the most demanded numerical method for mechanical systems analysis, a non-local dynamic deformation model is integrated into the algorithm of this method. The equilibrium equation of the structure in motion is solved by an explicit scheme. The damping matrix is obtained from the condition of stationarity of the total deformation energy of a moving mechanical system. A one-dimensional non-local in time model was implemented in the MATLAB software package.