Analytic solution for reflection and transmission coefficients of joints in three-dimensional truss-type structural networks

This paper presents an analytic solution method to evaluate transient response of the joints in the truss-type structural networks. The analytic method models the wave propagation along the elastic members connected to the joints and derives the functions for the reflection and transmission coefficients for the structural joints. The coefficients of wave reflection and transmission across the joints are functions of material properties and geometrical parameters of the elements connected to the joint. The present analytic solution considers the effects of abrupt change in material properties as well as the alignment of connected elements on the transmission and reflection coefficients of the joints. The analytic solution method derives the functions for the transmission and reflection coefficients at the connection point of two different coaxial elements as well as the joints in planar and space frame structures.