Abstract
Using simple beam theory, solutions are given for the
vibration of beams having rectangular cross section with
(a) linear depth and any power width variation, (b) quadratic
depth and any power width variation, (c) cubic depth
and any power width variation, and (d) constant depth and
exponential width variation. Beams of elliptical and
circular cross section are also investigated. Several cases
of cantilever beams are given in detail. The vibration of
compound beams is investigated. Several cases of free
double wedges with various width variations are discussed.
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