Abstract
A three-dimensional vibration study is presented using the three-dimensional theory developed by Chaoet al. [34–39] for a variety of simply supported shallow spherical, cylindrical, plate, and saddle (hyberbolic) panels in rectangular planform. A complete survey and comparison of existing literature have been made with excellent lowest frequencies via a 3-D augmented energy variational approach. In all of these shell configurations, natural frequencies are noted to decrease in the above-mentioned order according to minimum total potential energy in the natural state.
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