Transient analysis of nonlinear elastic impact between two rods

The problem of longitudinal collision of rod with free ends and rod with one end free and other end built-in was considered. The problem may be treated as an integrated vibration system, so the nonlinear elastic impact problem was converted into as the problem of conventional dynamic response analysis of the system under initial velocity of disturbance. The basic equations, boundary conditions and initial conditions of the problem were given. The analytical solutions without contact deformation and with linear elastic contact deformation were derived. For the problem with nonlinear contact deformation, the method of linearization based on Hertz's contact principle and algorithm were given. The numerical results have shown that the method is feasible and correct, with which the nonlinear structural feature for natural frequency variation with time was taken into account.