System identification and experimental modal analysis of a frame structure

In this paper, an effective method for performing the experimental modal analysis of structural systems is developed. The proposed methodology is corroborated by analytical considerations and is verified experimentally. The identification method developed in this paper is based on time-domain system identification numerical techniques. The case study considered in this work is a frame structure that can be modeled as a two-story shear building system. A preliminary mechanical model of the two-story shear building system is developed by using a lumped parameter approach. Subsequently, a more realistic second-order model of the frame structure is obtained directly from input-output experimental data. To this end, a numerical procedure based on the combination of the Observer/Kalman Filter Identification Method (OKID) with the Eigensystem Realization Algorithm (ERA) is employed for determining the sequence of system Markov parameters. In particular, the fundamental matrices that characterize the state-space representation of a general linear time-invariant dynamical system are obtained from the identified system Markov parameters. In addition to the identified first-order state space model, a second-order mechanical model of the frame structure is experimentally obtained employing a methodology for constructing mechanical models from identified state-space representations. More importantly, considering the assumption of proportional damping, an effective method based on a simple least-square approach is used for calculating an improved estimation of the identified damping coefficients. The experimental modal parameters found by using the proposed methodology are consistent with those predicted by using the analytical approach based on the simplified lumped parameter model. Furthermore, the mechanical model identified employing the approach discussed in this paper is used for developing an actively controlled inertial-based vibration absorber based on the Linear Quadratic Gaussian (LQG) control and estimation method. The numerical and experimental results found in this investigation confirmed the effectiveness of the methodology developed in the paper.