Studia Geotechnica et Mechanica (Mar 2025)
Identification of mass, damping and stiffness matrices of multi degree of freedom system subjected to kinematic excitations
Abstract
This paper presents theoretical considerations relating to the possibility of fully identifying the parameters of a numerical model describing a building structure. An input–output method with system momentum change is proposed for this purpose, thanks to which the basic matrices describing the system were identified, that is, the mass matrix M, the damping matrix C and the stiffness matrix K. The proposed way of system identification is based on the knowledge of the vibration excitation (the input signal) and the structure’s dynamic response (the output signal) to the applied excitation, and the analyses are performed in the time domain. The reverse problem defined in this way consists of determining the coefficients of matrices M, C and K at any discrete point of time. In the case when the vibrations of the system are excited by kinematic excitation (ground motion), in order for the inverse problem to be solvable, either knowledge of the mass matrix or a known modification of the system masses is required. This is due to the representation of excitation forces, which in the case of kinematic excitation contains a mass matrix in their full description. This paper presents a method based on an inertial modification, that is, adding known masses to the analysed system, which entails a change in system momentum. The addition of known masses to the system being identified results in the introduction of additional known forces into the system. In this way, a heterogenous linear algebraic system of equations is obtained in the reverse problem and the coefficients of the particular matrices M, C and K are calculated from this system of equations. Moreover, considering the fact that the input signal and the output signal are known in many time points, the proposed procedure leads to a set of systems of equations.
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