Optimum design of cantilevered columns under the combined action of conservative and nonconservative loads: Part II: The damped case

Stability optimization of cantilevered columns subjected to both conservative and nonconservative loads is studied. Internal and external damping is taken into account. The optimization problem of volume minimization by constant critical load is solved numerically by using finite elements and sequential linear optimization. It is shown that this problem is equivalent to maximization of the critical load by constant volume when stability is lost through (i) a simple or a double zero eigenvalue, λ=0, and (ii) one pair of simple, complex conjugate eigenvalues, λ=±i Im λ. The instability mechanisms of the optimal columns depend on the mutual magnitude of the two force components. Simultaneous divergence and flutter may occur. The optimum design changes smoothly with changing nonconservativeness of the load, although different instability mechanisms are active.