In this paper mathematical formulation for buckling analysis of a column and vibrationanalysis of a beam is presented. The beam and the column is assumed to be non-uniform and cracked.Using calculus of variations, the problem is expressed as an optimization problem. A technique ofoptimization is used for analysis of buckling load. Considering the similarity between the governingequation for buc...

The present paper deals with the concept of antiresonance in multiple cracked beams and application for multi-crack identification. First, governing equations antiresonant frequency are conducted used both computing frequencies versus crack parameters measuring-loading colocation identifying cracks by measured frequencies. Then, a procedure is proposed identification cantilever beam based on so...

BACKGROUND The purpose of this study was to analyze the characteristics of cracked teeth and to evaluate pulp status according to periodontal probing depth (PPD). METHODS A total of 182 cracked teeth were included. The location and type of the cracked teeth, age and gender of the patients, restoration type, pulp status, PPD, and radiographic findings were analyzed. RESULTS Mandibular second...