The fundamental frequency of vibration of beams and plates elastically restrained against rotation at the supports and carrying finite masses is determined in the present paper using the optimized Rayleigh methodology. The analysis takes into account the effect of both translational and rotational inertias. In the case of simply supported vibrating plates a lower bound for the frequency coefficient is obtained by means of an extension of Dunkerley's method. © 1987 Academic Press Limited.
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