Crack Detection in Plate-Like Structures Using Modal Strain Energy Method considering Various Boundary Conditions

Among vibration-based damage detection methods, one of the effective approaches for damage localization is the modal strain
energy method. In this paper, the modal strain energy method is developed for damage detection in plate-like structures with
various boundary conditions. Firstly, the theory of the modal strain energy method is briefly outlined. In order to overcome the
limitation of measuring points, a central difference method is newly employed to compute the partial differential terms in the
modal strain energy formula. Finite element analysis is conducted on an aluminum thin plate to obtain the mode shapes before
and after the occurrence of damage. Feasibility of the proposed method is verified by investigating plates with different types of
boundary conditions. A damage index is presented to identify the location and extent of crack in the plate-like structures. &e
analytical results show that the proposed method accurately identifies the crack in the plate structure with various types of
boundary conditions by using appropriate mode shapes and damage threshold.