A numerical algorithm for solving a two-layered composite beam subjected to vibrational loads

The article proposes the development of a numerical method for calculating multilayer beams, based on the theory of composite rods by A.R. Rzhanitsyn. The modification of this theory is to simplify the calculation model for a determined class of structures. It is considered multilayer beams composed of same layers of rectangular cross section, with the same physical and mechanical characteristics. The stiffness of all connecting seams is taken equal. In the research the hypothesis of a functional relationship between shear forces in the seams of the structure is taken. This allows the authors to significantly reduce the dimension of the system of resolving differential equations, from n + 2 equations to three for any finite number of layers. Where n -is the number of seams, and, accordingly, the number of shear forces to find in the seams according to the A.R Rzhanitsyn model, n + 1 is the number of layers. A comparison of three models of the above dependence is given. The numerical methodology is based on the approximation of differential equations by difference equations of the method of successive approximations (MSA). This methodology has proven itself well in the calculation of beams, plates, shells for the action of static loads, in calculations in a dynamic setting and for stability, on an elastic foundation. Including multilayer beams and plates. It allows to take into account the finite discontinuities of the load parameters, stiffness parameters of the structure and foundation. The described methodology can find application in the practice of design organizations and enter the educational courses of higher educational institutions of the construction profile.

show abstract