THE FREE-VIBRATION OF CIRCULARLY CYLINDRICAL-SHELL AND PLATE SYSTEMS

A Rayleigh-Ritz approach, previously shown to apply to the free vibration of beam systems and rectangular plate systems, is applied to the free vibrational problem of systems comprised of circularly cylindrical, thin shells and thin annular or circular plates. The approach utilizes the concept of artificial springs which permit the convenient joining together of the components of each system and simplifies the selection of the trial functions for the Rayleigh-Ritz solution; in this work, orthogonal polynomials are used. Several example systems are treated: a cylindrical shell with a circular plate at each end (described in the literature as a drum or a hermetic can), a double cylindrical shell with an annular plate at each end, and a similar system in which the inner cylinder is extended. The approach is shown to yield rapidly convergent and accurate results.