Spectral basis theory for the identification of structural dynamic systems

Abstract

This paper presents the theoretical formulation of a technique for determining the mathematical model of structural dynamic systems. This technique utilizes the fact that the forced responses of a structure can be decomposed into linear combinations of sets of frequency-dependent functions. The orthonormatized forms of these functions, along with the associated transformation matrices, are used to obtain the unique pseudoinverse of the matrix of forced responses, which satisfies all the required Moore-Penrose conditions. Variations of this scheme can be used to determine: 1) the damping matrix, when the mass and stiffness matrices are known; 2) the complex stiffness matrix, when the mass matrix is known; 3) the mass matrix, when the stiffness matrix is known; and 4) the reduced-order mass and stiffness matrices, when the larger-order matrices are known. Discussed are problems of redundancy and overtruncation of dynamic models and possible methods of avoiding them.