The asymptotic analysis of free vibrations of a cylindrical shell joined with annular plates

Low frequencies and vibration modes of a closed circular cylindrical shell joined with annular plates are obtained by means of asymptotic methods. Two types of vibrations, corresponding to narrow and wide plates, are analyzed. If the width of the ring is sufficiently small, then the vibration mode of the stiffened shell is similar to the mode of the shell without rings. For wide plates joined with a cylindrical shell the vibration mode is localized on the surface of the ring, and the cylindrical shell itself does not actually deform. In both cases the solution of a boundary value problem is searched in the form of the sum of slowly varying functions and edge effect integrals. For narrow plates as a first approximation we obtain a problem about vibrations of the beam supported by springs. For wide plates the problem is reduced to a problem about vibrations of a ring plate.