Dynamics of a Solid Moving Along an Elastic Base with Contact at Two Points of Support

This article presents the dynamics of motion of a body moving along an elastic beam. The aim of the work is mathematical modeling of the dynamics of the “rigid body - elastic beam” system taking into account the force interaction of these bodies at a two points of contact. Based on the Euler-Bernoulli beam theory and general theorems of dynamics, the equations of motion of the system “rigid body - elastic beam” in partial derivatives are constructed. Using the Bubnov-Galerkin method, ordinary differential equations are obtained for the weight coefficients of the approximate solution of the equation in partial derivatives. Based on the results of numerical integration of ordinary differential equations, the dependences of the deflection and rotation angle of the cross section of the elastic beam on time are obtained. Unlike previously used models, the developed model allows one to take into account the influence of the force action of a moving rigid body on the bending of the elastic beam. The results of the work can be used in the design and manufacture of new transport systems.