A Vibration Analysis of a Cylinder with Slits

The free vibrations of an elastic cylinder with open slits are analyzed with the Rayleigh-Ritz method. The analytical procedure is based on the formulation in cylindrical coordinates with the three-dimensional linear elasticity. For the formulation and calculation of kinetic and strain energies, the cylinder is divided into upper and lower parts with the depth of the slit. Using the Rayleigh-Ritz method, the eigenvalue equation is obtained for the two parts with different displacements in Chebyshev polynomials. Utilizing the displacement continuity conditions at the interface between, the eigenvalue equations for the cylinder is obtained. A convergence check and comparison with the FEM results demonstrate the validity and accuracy of the present method.