Variational Methods in a Thin Shell Problem

Variational methods and their applications are considered in the solution of problems involving vibrations of thin shell segments consisting of partly positive and partly negative Gaussian curvature parts. The lower part of the spectrum of these shells when the boundary conditions exclude pure bending is investigated. The results obtained by using the Raleigh-Ritz approximation are compared with those obtained by applying the Shooting Method and it is observed that there is good agreement. Results obtained also indicate that the variational method used in the investigation gave large and less accurate results for the lowest frequency parameter while increasing the number of coordinate elements to two gave more accurate values. However, it is shown that increasing the number of elements has the disadvantage of increasing the computations needed to solve the problem.