OPTIMIZATION OF BOUNDARY-CONDITIONS FOR MAXIMUM FUNDAMENTAL-FREQUENCYOF VIBRATING STRUCTURES

A sensitivity formula of eigenvalues with respect to the change of bou ndary conditions is derived using the material derivative concept base d on a variational formulation. The change of boundary conditions is d escribed with the introduction of the tangential component of the desi gn velocity field used in shape design. Simply supported and partially welded plates are taken as numerical examples to check the accuracy o f the sensitivity formula. The sensitivites of the distinct and multip le eigenvalues calculated by the formulas are compared with those calc ulated by finite differences. Optimal support locations are then deter mined by use of a gradient-based optimization method. It is shown that a crossing of eigenvalues can occur in the solution process.