Transmission Matrices for Vibration and Their Relation to Admittance and Impedance

Abstract

The character of transmission matrices is explored for application to the vibration of multiterminal elements which obey reciprocity. The concept of a rectangular transmission matrix is introduced and its limitations discussed. Interrelationships among the transmission, admittance, and impedance matrix descriptions of an element are presented. The approach is applied to a system consisting of a source, a transmission element, and a load, with a multiplicity of interconnections between the three elements. The results apply to linear elements from any field (e.g., structural, electrical, acoustic) and also to elements of mixed type (e.g., electromechanical). The Nomenclature and examples apply specifically to structural elements.