Simulation of vibrations of a continuously elastic supported rod with varying boundary conditions under the action of a movable

¹ VSTU, Structural Mechanics Department, 394026, Voronezh, Russia
² MIPT, Computational Mechanics Department, 115184, Moscow, Russia

^* Corresponding author : gridnev_s_y@rambler.ru

Abstract

To simulate the non-linear vibrations of a floating bridge of a continuous system on separate floating supports with additional limiting supports at the ends with a moving load solves the most complicated problem which is the problem of describing the behavior of a span structure. A technique for simulating the vibration of an elastically supported deformable rod with limiting supports at the ends, which is a design scheme of a span structure, under the action of a moving force is developed. A computational algorithm for solving partial differential equations with varying boundary conditions is proposed, which includes boundary conditions in the model equations and does not require the subordination of basis functions to the boundary conditions. During the calculation, the basis remains constant. Piecewise linear basis functions are used to solve the differential equation. The technique is tested using a computational program Matlab, which is implemented when performing numerical studies of the behavior of the dynamic system as a function of the parameter changes. The developed technique is universal for studying the dynamics of a number of constructively non-linear systems.