The cracks if not detected in time leads to catastrophic failure. As a result techniques of detection and analysis of effect of cracks on the behavior of structures became important in the last six decades. Crack has a paramount effect on the dynamic characteristics, buckling load and dynamic stability of structures. Analysis of cracked members and damage detection are important issues in Civil, Mechanical and Aerospace engineering. In the first decade of the twenty first century the investigation on the cracked members gained more weights. The present author derived a golden derivative of...