Analysis and computation of the vibration spectrum of the shallow circular cylindrical shell with rectangular domain

An asymptotic method of Bolotin, for the computation of eigenvalues of self-adjoint problems on rectangular domains, is extended to the shallow shell equations for the vibrating circular cylindrical shell. These same eigenfrequencies are then computed using the Legendre-tau spectral method. The asymptotic and numerical results are seen to be in good agreement and, as expected, approach those of the flat plate as the curvature tends to zero.