A technique for the reduction of dynamic degrees of freedom. - Archer, Graham C. (Earthquake engineering & structural dynamics.)
This paper presents a variation on the component mode technique for the dynamic substructuring of large scale structural analysis of building and bridge frames. The principal innovation of the proposed method of dynamic reduction is that the resulting mass matrix of the reduced substructures remains diagonal. As in the component mode technique, the reduction is accomplished by transforming the degrees of freedom in the substructure using boundary shapes and internal shapes. The diagonal mass matrix is achieved by orthogonalization of the boundary shapes to the internal shapes. The diagonal mass matrix is achieved by orthogonalization of the boundary shapes to the internal shapes and a selective row by row summation of the mass matrix into the diagonal entry (where off diagonal terms are unavoidable). To aid in recovering the accuracy of the rigid body inertias that is lost in the diagonalization process, additional pseudo rigid body mode shapes are proposed.