Mass optimization of non-conservative cantilever beams with internal and external damping

An adjoint variational principle has been developed for a non-conservatively loaded cantilever beam with Kelvin-Voigt internal and linear external damping and is applied to a beam with a linearly distributed tangential load acting along the centerline of the beam. Relative mass optimization for beams of both rectangular and circular crosssections is considered from a graphical standpoint and from the viewpoint of a computer optimization routine with data given and discussed in both instances. In going to a Rosenbrock optimization routine for beams of rectangular cross-section with a minimum tip thickness constraint imposed it was quite clear that mass ratio reductions in the range 14·9 % to 38 % are possible and that the values of internal and external damping appear influential in determining just how much of a mass reduction is possible. Similarly, for beams of circular cross-section a Rosenbrock optimization routine with a minimum tip diameter constraint imposed showed that mass ratio reductions of the order of 27 % are possible.