Research Problem About Impact Contact Between Timoshenko Beam And Rigidity Rod

This paper has researched various problems about impact contact between linear elasticity beams of Timoshenko model and rigidity rods; and the problems about transverse impact contact between linear elasticity beams of Timoshenko model and rigidity rods have been solved. The Laplace transformation is the main method used in this paper, and lastly by using Durbin numerical inversion method, Timoshenko beams have been solved under various restriction conditions. Concretely, firstly with Timoshenko beams, the fundamental formulae of solutions of dynamical equations, boundary conditions and initial conditions have been transformed by Laplace transformation. Secondly, in the Laplace regions , we gain the analytical solutions of impact forces at the impact contact points, shear and maximum inverse stress of beams. Then, by using Durbin numerical inverse method, we gain the numerical solutions of Timoshenko beams under various restriction conditions. Moreover, the graphs about impact forces at the impact contact points, shear and maximum inverse stress of beams can be obtained too. Lastly, we obtain the relationship between velocity and mass of rigidity rods and impact force, and contrasting graph about impact forces at the impact contact points, shear and maximum inverse stress under various restriction conditions. When we deal with impact contact conditions, because rods are rigidity, considering rods as our researching objects could simplify our solving process a lot. Otherwise, the problems about non-rigidity rods are out of the scope of this paper. In this paper, we made an elementary discussion how we can use Laplace transformation to study linear elasticity Timoshenko beams. However, in practice, high-speed collisions are not elasticity problems, and many plastic conditions need to be taken into consideration. Actually, under high-speed collision conditions, considering plastic deformations in processes of dealing with effects of impact forces will accord with actual situations more precisely, and these problems are open to more researches.