Optimum transmission of extensional waves through a non-uniform viscoelastic junction between elastic bars

摘要

Reflection, transmission and dissipation of the energy of an incident extensional wave at a viscoelastic junction between two uniform and collineaR elastic bars are considered. The junction consists of N uniform segments with the same transit time for a wave front. The optimum incident wave of given duration which maximizes the energy transmission is determined by finding the eigenvector associated with the largest eigenvalue of a matrix. The optimum waves are unique, which they are not for elastic junctions. Numerical results for optimum and rectangular waves are obtained for four different junctions, of standard linear solid type, with one or three segments between elastic bars with equal or different characteristic impedances. The optimum waves are characterized by having symmetry or antisymmetry, by having alternating or constant sign, and by showing abrupt changes or being smooth. Symmetry, constancy of sign arid smoothness are all promoted by increasing values of a damping coefficient which characterizes the material.