Optimal tapering of a conservative system of the second kind

This Lecture deals with the problem of the optimal tapering of a conservative system of the second kind, namely the generalized Pfluger column.The conservative systems of the second kind are truly non-selfadjoint and nonconservative systems in a classical sense, but self-adjoint in a generalized sense.These systems buckle by divergence and possess a generalized conservation theorem and a generalized Rayleigh quotient.Optimization problems for the generalized Pfluger column with pinned-pinned or sliding ends, subjected to distributed compressive follower forces are considered.It is shown that by means of a special transformation of independent variables, the problem is reduced to a classical conservative bifurcation problem for the column loaded by the axially distributed load.The optimal solutions for some load distributions are found in closed form and isoperimetric inequality is established