Exact Decoupling of Non-Classically Damped Matrix Second-Order Linear Mechanical Systems

Matrix second-order damped linear dynamic systems are frequently encountered in mechanical, structural, civil, aerospace engineering, and related fields. This class of systems is also obtained by approximating dynamics of systems described by partial differential equations (distributed parameter systems). There are many papers in the engineering literature on analysis and control of matrix second-order linear damped systems. They provide either approximate (simplified) analytical results or accurate numerical results (usually computationally involved). In this paper, we show how to decouple exactly a matrix second-order linear system into scalar second-order subsystems and study exactly the corresponding system dynamics at the subsystem level using simple analytical tools. Conditions are established under which the presented procedure is applicable. An example is included to demonstrate the efficiency of the proposed technique.