Damage detection of structures using modal strain energy with Guyan reduction method

The subject of structural health monitoring and damage identification of structures at the earliest possible stage has been a noteworthy topic for researchers in the last years. Modal strain energy (MSE) based index is one of the efficient methods which are commonly used for detecting damage in structures. It is also more effective and economical to employ some methods for reducing the degrees of freedom in large-scale structures having a large number of degrees of freedom. The purpose of this study is to identify structural damage via an index based on MSE and reconstructed mode shapes. The Guyan reduction method (GRM) is utilized here to reconstruct the mode shapes. Therefore, in the first step by employing GRM, mode shapes in slave degrees of freedom are estimated by those of master degrees of freedom. In the second step, the modal strain energy based index (MSEBI) is used to find the location of damaged elements. In order to assess the efficiency of the method, two standard examples are considered. Damage is identified with considering complete mode shapes and reconstructed mode shapes, and the results are compared together. The outcomes show that the combination of MSE and GRM can be useful for the structural damage detection, when considering the noise.