Paradigm for natural frequency of an un-cracked simply supported beam and its application to single-edged and multi-edged cracked beam

In this research paper, a theoretical method of analysis of the first natural frequency of an un-cracked simply supported beam in bending mode is presented. The formula of a paradigm is used to determine the natural frequency of an un-cracked beam. The converged natural frequency formula of a paradigm is then extended to a single edged and multi-edged cracked simply supported beam to evaluate their natural frequency. The main attraction of the proposed method is that it gives one more significant way to the researchers to determine the natural frequency of cracked beams. The limited fatigue strength, defects like corrosion, corrosion-erosion, and corrosion fatigue in the beam are the main causes of formation of edged cracks in beams. Hence the evaluation of natural frequency of cracked beams and its use in the inverse problem is of utmost importance to do the condition monitoring of the structures by the vibration methods.