Curves are presented for determining the fundamental frequency and several higher harmonics for cantilever beams linearly tapered in the vertical or the horizontal plane or tapered in both planes simultaneously (double taper); both the single-tapered and the double-tapered beams are treated with free end, end mass, and end support. These curves have been selected from papers previously published by the authors in order to provide data in a form suitable for design application. They are reproduced with permission from Sandia Corporation, Albuquerque, N. M., and from the Acoustical Society of America.

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