On the quasi-diagonalization and uncoupling of damped circulatory multi-degree-of-freedom systems

The decomposition of linear multi-degree-of-freedom systems with damping, circulatory, and potential forces is considered through a real linear coordinate transformation generated by an orthogonal matrix. Criteria are derived that establish the conditions under which such a transformation exists, allowing these systems to be decomposed into independent, uncoupled subsystems, each with a maximum dimension of two. These criteria are expressed in terms of the properties of systems? coefficient matrices. Several numerical examples are provided to demonstrate the analytical results.