Damage identification in skeletal structures: A dynamic stiffness approach
The present work is devoted to investigate ways of identifying cracks in skeletal structures by frequency monitoring. This is a challenging problem as the number of cracks, their severity and location all need to be found. It has been shown that roving bodies with rotary inertia could be used to find the total number of cracks and their locations without any knowledge of their severity. The Dynamic Stiffness Method was chosen due to its capabilities in enabling an exact solution while facilitating addition of new elements such as springs and masses to the structure in the same way as in the approximate Finite Element Method (FEM). Using the Dynamic Stiffness Matrices (DSM), it was possible to derive an interesting and useful relationship between the determinants of the DSM of the following: the original undamaged structure, the cracked structure and the structure with a hinge at the potential crack location. This relationship is a simple equation which gives the determinant of the cracked structure as the sum of the determinant of the undamaged structure multiplied by the rotational stiffness of the beam at the crack and the determinant of a structure with a hinge at the same crack location. Experimental results from literature are used to validate the application of the found features in beam structures and frameworks to identify damages or dynamic properties. A semi-experimental methodology is proposed to treat multi-cracked structures where, as a first step, the roving inertia method is used to identify the number and location of the cracks in a simple way without the need to perform any calculations or theoretical analysis. The theoretical basis of this method is explained using the DSM. Experimental work was carried out on a cantilever beam to verify the applicability of the roving inertia method but no conclusive results were obtained. Further experimental investigations are needed to study the practical feasibility of the method. It is hoped that once the locations of all cracks are identified, the severity of the cracks can be found using the frequency measurements as the determinants of the DSM are linear functions of crack severity.
Damage identification, Dynamic stiffness matrix, Closed-form solution, Inverse methods
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