Reliability of Dynamically Measured Flexibility Matrix on Damage Detection of Frame Structures

Abstract

The use of dynamically measured flexibility matrix to indicate and locate damage is reported in many studies. However their focus is mostly on structures like beams or slabs that each node has one degree of freedom and all DOFs are in the same direction. For a structure with degrees of freedoms in three directions e.g. frame structures, both modal testing and damage detection become more complicated. It is because each DOF in the stiffness matrix is influenced by all the members connected to it. When it comes to flexibility matrix, another problem arises. Since flexibility matrix is more global, damage does not only affect the related DOFs, but others too. This article aims to address these problems in order to develop a reliable damage detection method for frame structures. The modal parameters of a four story frame structure are calculated for intact and damage cases. Changes in the flexibility matrix were analyzed for different damage scenarios when the damage member is known. It was suggested that there are some patterns that relate DOFs and members which can be used to locate the damage member. Introduction Review of Damage Detection MethodsVibration-based damage detection methods are vastly used to identify and locate probable damages through different types of structures. The basic principle is simple; once damage appears in the structure, it changes the structure's stiffness matrix, which accordingly affects the modal behaviour of the structure. Therefore major changes in modal parameters of the structure may perhaps be understood as existence of damage.The simplest modal parameter that can be used for damage detection purposes is natural frequency. But the sensitivity of frequency shifts to minor damages is relatively low which requires more accurate measurements [1,2]. Salawu [3] stated that the advantages of using natural frequencies are its simplicity in both modal analysis and detection algorithm. Friswell, et al. [4] used frequency shifts of the first n modes for undamaged structure and some proposed damage scenarios. Then they calculated the ratios of all frequency shifts between undamaged and each damaged scenarios. To detect the probable damage in a candidate structure, the same ratios were computed and checked if it lies in any of the damage classes.Other modal parameter that can be used for damage detection purposes is mode shape. Fox [5] used the modal assurance criteria (MAC) to determine the relations between the mode shapes of undamaged and damaged structures. They suggested the MAC based on measurement points close to a node point is a more sensitive indicator of changes in the mode shape caused by damage. One of the most reported detection methods based on mode shapes uses modal strain energy as an indicator to represent damage. Modal strain energy was developed by Stubbs et al. [6] and was successfully applied to onedimensional beam type structures for damage localization. However its application for two and three-dimensional frame type structures was not as promising. Yang and...