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

Abstract

In this work, double-layer beams are being researched using Rzhanitsyn’s theory of composite rods. One of the fundamental propositions of this theory is that multiple layers of such bars are connected by absolutely rigid cross links and elastically-pliable shear links. The concentrated forces and partially-constant distributed loads which are changing in time according to the harmonious law are taken into account as the external influence. The method of direct numerical integration of the equations of motion in time is used to solve the problem of the forced oscillations of the beam. The difference equations of the serial approximations method are used to approximate partial spatial coordinate derivatives. The results of the calculation of the beam under the vibrational influence got with different intervals of spatial and temporal coordinates have been given as the illustration of the suggested method.Above-stated method might interest the specialists in the field of the analysis of building constructions because of the universality of Rzhanitsyn’s theory of built-up bars which finds application in calculation of multilayer wooden constructions, perforated metal beams, multilayer reinforced-concrete beams with different elasticity modulus, in modelling the crack formation processes, in calculation of multi-storey buildings’ frames.