Analysis of solutions of specified dynamic equations of beam bending on the example of investigation of the transverse forces evolution
The paper deals with investigating the disturbed region of the beam during a suddenly applied load on the border (the problem of suddenly applied bending moment). Structural dynamics is de- scribed by the new specified one-dimensional dynamic equations of the beam bending. These equations were derived based on a rigorous mathematical algorithm (so-called non-minimal simplification of three-dimensional dynamic equations of elasticity theory).The resulting equations have allowed to explore the layer- thickness averaged three-dimensional picture of the disturbance propagation by constructing graphs of respective solutions for the59Восточно-Европейский журнал передовых технологий 1/7 ( 73 ) 2015transverse forces. The results are in good agreement with the elastic- ity theory, in particular, the wave-front velocities coincide with the velocities according to elasticity theory problems. At the same time, all boundary conditions are defined in the same way as in the known problems of strength of materials.