A modified differential equation for bending vibrations of an exponentially tapered beam under rotation is derived and an upper bound for the natural (ω2) frequency of the nth mode of vibration has been determined. A shape function is used to determine the theoretical frequency equation of bending vibrations. The shape function used in obtaining the solution satisfies geometrical as well as the dynamical boundary conditions of tapered beams that may represent a turbomachinery blade, and therefore the frequency equation obtained in this paper can provide an engineer with some important design information before an expensive prototype turbine blade is made.
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