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

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