General theory of vibration of damped linear dynamic systems

Abstract

The usual treatment of linearly damped lumped parameter systems assumes that the system equations may be transformed to a symmetrical set of equations. This assumption is justified in passive systems. However, in many problems of interest to aeronautical and electrical engineers the system equations cannot be transformed to a symmetric set of equations. One case in point is the analysis of an aircraft wing under flutter conditions. That non-symmetric systems are physically realizable will be understood when one remembers that it is possible to build any non-symmetric system using an active analog computer. It is the purpose of this report to give a comprehensive analysis of lumped parameter linearly damped second order vibrating systems having symmetric or non-symmetric matrices.