Analytical Solution of Free Vibration Characteristics of Partially Circumferential Cracked Cylindrical Shell

Free vibration characteristics of a cylindrical shell of finite length containing a partial peripheral crack are studied. An analytical solution method is proposed to evaluate the natural frequency of the cracked cylindrical shell structures. The governing equations of motion are based on classical shell theory and are simplified by Love’s theory. The bending rigidity equivalent to the shell (D) expressed by exponential function is calculated taking into account the effect of the crack. The influence of the crack length, crack depth, crack location, are investigated on the vibratory characteristics under simply supported (SS-SS) at each end boundary condition. Natural frequencies were obtained by solving general equations using “MATLAB” program. The results obtained from the proposed method were confirmed by comparing them with the results obtained from the literature. The results showed that the natural frequency decreases as the crack length, and depth decreased. also, the natural frequency decrease when the crack locates at the mid of the longitudinal line of the shell more than if it were in other locations. The results obtained by this work have a very good agreements with those been found by literatures.