Abstract
This paper provides simple, yet accurate, estimates of the fundamental natural frequencies of vibration of simply supported and clamped polar orthotropic circular plates with and without internal (central) point supports. Such estimates are obtained by means of Rayleigh’s method coupled with the deflection functions for the corresponding statically loaded systems. As will be seen, the present formulation, which generalizes an earlier work dealing with plates composed of isotropic materials, yields compact, closed-form expressions, enabling the ready calculation of (approximate) natural frequencies for arbitrary values of the elastic constants. Furthermore, remarkable simplifications in the derivations for, and form of, some of these expressions are achieved through the application of a computerized symbolic algebra system.
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