The paper presents a method for analyzing complex structures by dividing them into substructures. This approach uses basic mass and stiffness matrices for each substructure, along with compatibility conditions at their boundaries. Two types of generalized coordinates are employed: boundary generalized coordinates for displacements and rotations at substructure boundaries, and substructure normal-mode generalized coordinates for free vibration modes. The method allows for the reduction of the total number of degrees of freedom while maintaining accurate dynamic behavior. Substructure boundaries may have any degree of redundancy, and the method incorporates a Rayleigh-Ritz procedure for this reduction. The paper also discusses the definition of substructure modes and the use of coordinate transformation matrices to derive system mass and stiffness matrices. The method is applied to a cantilever plate example, where the results are compared with those from a full finite-element analysis. The results show that the substructure coupling method provides accurate mode shapes and frequencies, even when the substructure boundary is not aligned with the symmetry line of the full structure. The method simplifies the treatment of rigid-body modes by eliminating the distinction between statically determinate and indeterminate boundary reactions, allowing all boundary modes to be treated uniformly. This approach leads to more efficient formulation, compact presentation, and simplified computer programming.The paper presents a method for analyzing complex structures by dividing them into substructures. This approach uses basic mass and stiffness matrices for each substructure, along with compatibility conditions at their boundaries. Two types of generalized coordinates are employed: boundary generalized coordinates for displacements and rotations at substructure boundaries, and substructure normal-mode generalized coordinates for free vibration modes. The method allows for the reduction of the total number of degrees of freedom while maintaining accurate dynamic behavior. Substructure boundaries may have any degree of redundancy, and the method incorporates a Rayleigh-Ritz procedure for this reduction. The paper also discusses the definition of substructure modes and the use of coordinate transformation matrices to derive system mass and stiffness matrices. The method is applied to a cantilever plate example, where the results are compared with those from a full finite-element analysis. The results show that the substructure coupling method provides accurate mode shapes and frequencies, even when the substructure boundary is not aligned with the symmetry line of the full structure. The method simplifies the treatment of rigid-body modes by eliminating the distinction between statically determinate and indeterminate boundary reactions, allowing all boundary modes to be treated uniformly. This approach leads to more efficient formulation, compact presentation, and simplified computer programming.