High frequency vibrations and wave propagation in elastic shells: Variational-asymptotic approach

Two-dimensional equations are derived for high-frequency vibrations of linear elastic shells. The derivation is based on the variational asymptotic analysis of the three-dimensional action functional. This guarantees the exactness of the derived equations for the classical and thickness branches of vibrations in the long-wave range. A best short-wave extrapolation is chosen so as to reach the qualitative. agreement with the three-dimensional theory in the short-wave range. Comparisons are made with the similar results of the three-dimensional theory. 0 1997 Elsevier Science Ltd.