Vibrational analysis of a simply supported beam with crack

Abstract

Vibrational analysis of simply supported beam was investigated using an analytical method, called the perturbation method. The beam was modelled as a single degree of freedom system for simplicity and application of the physics laws into this mathematical model. The stiffness function was modelled as a time varying function due to the breathing characteristics of the crack. The governing equation of motion was found using the d Alembert's principle along with all the lumped parameters. Solving this equation lead to another equation called Mathieu equation. This Mathieu equation was solved using lindstedt method and the solution of which led to the solution of the governing equation of motion. This method is called as the perturbation method, by which the displacement equation was found analytically and theoretically. The damping ratio of the cracked beam was also found as a function of geometrical dimensions, mechanical properties and crack parameters