Co-Ordinates Which Uncouple the Equations of Motion of Damped Linear Dynamic Systems

Abstract Orthogonality relations between the eigenvectors of damped linear dynamic systems with lumped parameters are derived; and from these relations co-ordinates are found in terms of which uncoupled equations of motion can be written. Methods are developed for determining transient stresses in terms of these co-ordinates. The present treatment is extended to systems involving transient damping and to continuous systems.