Mathematical Theorization for Search and Identification of Shallow Cracks Based on Eigenvalue Analysis. : Mathematical Theorization and Stiffness Matrix for Shallow Cracks

Abstract

The purpose of this paper is to specify the positions and the sizes of cracks by a percussive sound. At first, a cracked element in FEM analysis is developed for both a surface crack and an internal crack for obtaining monotone decreasing eigenvalues for all degrees. Next, a converse theorem of Weyl's monotony theorem is constructed in order to inspect the accuracy of the crack elements. A method for searching and identifying various cracks is developed based on an efficient exhaustive search method composed of the hierarchical algorithm using the evaluation function. Finally, the validity of this method is verified from several calculation examples.