Hamilton’s principle and the derivation of shell theories to approximate vibrations of bounded elastic shells
Abstract
The exact elastodynamic calculations for the motions of bounded elastic shells can be quite consumptive of both computer time and resources. As an alternative, the so‐called shell theories simplify and speed up these calculations by making various dynamic assumptions about the motion of the shell surface when subjected to disturbances. This is typically done using variational considerations in which energy is minimized when various constraints are imposed. Exploitation of the technique using various assumptions gives rise to several shell theories. The resulting expressions are then used to calculate resonances over a frequency range and compared with the exact results. The various approximations are then ranked in order of their agreement to the exact results. Limitations of each of the methods are then outlined as well as those of shell methods in general. [Work supported by ONR/NOARL and by ONT Postdoctoral Fellowship Program.]
