Differential quadrature element model updating of frame structures

Abstract

The following study deals with improving the vibration model of structures obtained by the differential quadrature element method. To this end, first, an initial model of the structure is constructed using the differential quadrature element method in which the values of several physical parameters are unknown. Then, an optimization problem is defined to find the optimum values of the design parameters. In fact, the aim is to minimize an objective function that consists of the weighted sum of the squared errors between the modal parameters (i.e. the natural frequencies, the mode shapes, and the damping ratios) of the differential quadrature element and the experimental models. To solve the optimization problem, a robust evolutionary algorithm, namely the artificial bee colony, is utilized. To verify the effectiveness of the presented approach, the experimental data obtained from the modal testing of a plane frame are utilized to update its differential quadrature element model. The results show that the updating process is successfully performed utilizing artificial bee colony, and the updated differential quadrature element model better represents the vibration behavior of the real structure. Besides, the sensitivities of the eigenvalues of the model with respect to the design parameters are also evaluated to demonstrate the effect of changing the design parameters in the modal parameters of the model.