Use of the Finite Element Method in the Analysis of Impact-Induced Longitudinal Waves in Constrained Elastic Systems

In rotating elastic rods, dispersions occurs as the result of the finite rotations. By using Fourier method, it can be shown that the impact-induced longitudinal waves no longer travel with the same phase velocities. Furthermore, the speeds of the wave propagation are independent of the impact conditions including the value of the coefficient of restitution. In this investigation the use of the finite element method in the analysis of impact-induced longitudinal waves in rotating elastic rods is examined. The equations of motion are developed using the principle of virtual work in dynamics. Jump discontinuity in the system velocity vector as result of impact is predicted using the generalized impulse momentum equations. The solution obtained using the finite element method is compared with the solution obtained using Fourier method. Numerical results show that there is a good agreement between the solution obtained by using Fourier method and the finite element solution in the analysis of wave motion. However, discrepancies between the two solutions in the analysis of the velocity waves are observed and discussed in this paper.