Analysis of geometric dispersion effect of impact-induced transient waves in composite rod using dynamic substructure method

Abstract

Wave propagation in a composite rod is encountered in many contact-impact events. During the travelling of the impact-induced waves along the rod, geometric dispersion is possible when the diameter of the rod is of the same order as the wavelength. The aim of this paper is to develop an efficient method, namely dynamic substructure method to analyze the geometric dispersion of the waves in the problem of the finite-length composite rod coaxially struck by a moving rigid mass. For analyzing the geometric dispersion, a new rod element is presented through taking the lateral kinetic energy of the rod into account. The transient dynamic equation expressed by the reduced modal coordinates is derived by the Lagrange equation and the fixed-interface mode synthesis method. An adhesive contact model is used to account for contact constraint. The applications of the proposed method are demonstrated using 1) compress trapezoidal impulse and 2) impact-induced waves propagate in the large-diameter rod. In order to validate the feasibility of the proposed method, the comparison is also presented between the LS-DYNA3D solutions and the substructure solutions. It indicates that the proposed method is sufficiently accurate to compute the time history of contact force and to describe the geometric dispersion characteristics such as the attenuation of the amplitude of wavefront and the increasing of rise time. The error of the 2nd peak value of the contact force Fc2 is less than 5.0%, while the time cost of the proposed method are only 1.8% of those of the LS-DYNA3D program. Furthermore, numerical results show that the geometric dispersion results in “succession collisions” phenomenon become more complicated, and it experiences three times of the transitions from contact to separation.