High Precision Identification Method of Mass and Stiffness Matrix for Shear-Type Frame Test Model

Abstract

In the direct method of identifying the physical parameters of the shear-type frame structures through the frequencies and modes from the experimental modal analysis (EMA), the accuracy of the lumped mass depends on the initial mass, while the identified mass matrix and stiffness matrix are prone to generate some matrix elements without any physical meaning. In this paper, based on the natural frequencies and modes obtained from the EMA, an iterative constrained optimization solution for correcting mass matrix and a least squares solution for the lateral stiffness are proposed. The method takes the total mass of the test model as the constraint condition and develops an iterative correction method for the lumped mass, which is independent of the initial lumped mass. When the measured modes are exact, the iterative solution converges to the exact solution. On this basis, the least squares calculation equation of the lateral stiffness is established according to the natural frequencies and modes. Taking the numerical model of a 3-story steel frame structure as an example, the influence of errors of measured modes on the identification accuracy is investigated. Then, a 2-story steel frame test model is used to identify the mass matrix and stiffness matrix under three different counterweights. Numerical and experimental results show that the proposed method has good accuracy and stability, and the identified mass matrix and stiffness matrix have clear physical significance.