Natural frequency analysis of a cylindrical shell containing a variably oriented surface crack utilizing Line-Spring model

A new analytical approach for the determination of natural frequencies of a long cylindrical shell containing a variably oriented semi-elliptical surface crack is presented in this paper. Equations of motion for the cracked shell are obtained based on classical shell theories and are simplified using the Donell-Mushtari-Vlasov (DMV) theory. It has been assumed that the crack length is far smaller than the radius of curvature of the shell and line-spring model (LSM) is used in order to calculate crack compliance coefficients which are subsequently to be added into the equations of motion to include crack effects in the problem. An analytical solution has been developed using Hamilton's principle and the results are obtained for the shells considering clamped-clamped (C-C) and simply supported (S-S) boundary conditions at both ends. Results obtained from the proposed model are verified using a finite element model created with ABAQUS and there is an acceptable agreement between analytical and FEM results. Effects of the shell properties such as length, radius and thickness as well as the effects of the crack characteristics such as its length and orientation on the natural frequencies of the cracked shell are analyzed in this study.