Dynamics of longitudinal impact in uniform and composite rods with effects of various support conditions

Abstract

A finite element formulation is developed in this paper to analyze impact-induced waves in a rod collide with a striking mass. The formulation is established based on St. Venant's contact theory. Effects of mass ratios and boundary conditions, whether fixed, free, or elastic, are investigated. Both uniform rods and composite rods are considered. A shortcoming in traditional finite element models is to consider the rod and the struck mass as separate identities that gives inaccurate results for the discontinuity at the arrival of the impact wave. Instead, the proposed model considers the rod and the struck mass as one system that gives extremely accurate corresponding results. Wave propagation, transmission, and reflection from the constraint end and at the discontinuous interface are thoroughly analyzed. Succession collision that may occur between the struck mass and the rod is also investigated. Whenever it is possible, the finite element results are compared with analytical solutions. The analytical solutions are obtained with either the direct mode superposition method (DMSM) or wave theory. The proposed model can be used to model many systems that are subjected to longitudinal impact loadings and for crack detection. The model has the potential to be extended to perform simulation and analysis for many practical applications, like nanostructures under impact loads.

Keywords

• Wave propagation
• Impact mechanics
• Longitudinal vibration
• Composite structure
• Superposition method
• Newmark integration method