Abstract: This paper presents a new free-interface method of component mode synthesis for linear systems with arbitrary viscous damping.The left and right projection matrices described by state-variable vectors are first introduced for components with rigid-body freedom.The operator function of projection matrices for state displacement and state force is proved, and then the state residual flexibility matrix and the state residual inertia-relief attachment mode are defined and employed.The results of three examples demonstrate that the method proposed in this paper leads to very accurate system eigenvalues and high mode-synthesis efficiency

Key words: viscously damped systems, component mode synthesis, projection matrix