Abstract
The stability of a rotating pretwisted non-uniform viscoelastic cantilever beam subjected to a tangential force applied at its free end is determined by a method of approximation based on an adjoint variational principle. The coupled equations of motion are derived from a conservation law, the adjoint boundary value problem is introduced, and an approximate stability determinant is developed from the variational principle. The stability determinant is solved numerically for a variety of choices of values for the rotary inertia of the beam, transverse and rotary inertia properties of a mass capping the free end, the rotational speed, and the pretwist angle, and several graphs are presented to show the influence of these parameters upon the value of the critical flutter load.
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