An improved technique of the component-mode synthesis for nonclassically damped systems with the secondorder approximation is proposed in this paper. It is based on free-interface vibration modes and residual attachment modes or residual inertia-relief attachment modes complemented with dynamic effects of the truncated modes. Both nondefective and defective components are considered, and the relationships between them are discussed. A new criterion for the selection of the component vibration modes is developed in the frequency domain. State-level synthesis procedures are naturally employed in the new formulations presented herein. The accuracy and effectiveness of the present synthesis method are demonstrated and are compared with those of the static approach via numerical examples, and also the validity of the modes selection criterion is also proved by these examples. Nomenclature A s , B s = synthesized system matrices C = damping matrix of the component f = external force vector acting on the component I = identity matrix K = stiffness matrix of the component M = mass matrix of the component p = modal coordinate vector T = transformation matrix between independent and dependent modal coordinates x = unknown displacement response vector of the component i = complex eigenvalue of the component = complex spectrum matrix ' i , i = right and left eigenvectors of the component in the state space , = right and left modal matrices in the state space = component mode used for the synthesis d rd , d rd = right and left rigid-body modes in the displacement space Subscripts a = set of residual attachment modes e = set of elastic complex modes ek = set of kept elastic complex modes k = set of kept complex modes r = set of rigid-body modes t = set of truncated complex modes Superscripts = component = component
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