Variational Methods and the Derivation of Shell Theories to ApproximateVibrations of Bounded Elastic Shells

摘要

The calculation of vibrations, and in particular, resonances from bounded elasticshells can be quite tedious and time consuming when using the exact elastodynamic equations. Thus, a popular approach has been to employ various dynamic assumptions about the motion of the shell surface when subjected to disturbances. This can be done using variational considerations in which energy is minimized when various constraints are imposed. We exploit the technique using various assumptions which give rise to several shell theories. We can use the resulting expressions to calculate resonances over a frequency range and compare then with the exact results. We may then rank the various approximations in order of their agreement to the exact results. Limitations of each of the methods can then be outlined as well as those of shell methods in general.... Acoustic scattering, Shallow water, Waveguide propagation.