Optimization methods with structural dynamics applications

Two efficient and numerically exact methods for the analysis and computation of derivatives and extremum points of variable coefficients differential eigenvalue problems are presented. The methods are applied to optimize the shape of a nonuniform beam such that its fundamental natural frequency is a maximum; One of the methods consists of deriving an analytical expression for the rate of change of the eigenvalue with respect to a free parameter of the variable coefficients differential eigenvalue problem. The expression is then set to zero to analyze the extremum point or is used within an iteration scheme to drive the eigenvalue to its maximum or minimum value. The second method is a ''one-shot'' method which augments the original and differentiated systems by trivial equations for the rates of change of free parameters and solves the resulting nonlinear system subject to the original and differentiated boundary conditions as well as the associated normalization conditions. Copyright (C) 1996 Elsevier Science Ltd.