Structural eigenfrequency optimization based on local sub-domain "frequencies"

The engineering approach of fully stressed design is a practical tool with a theoretical foundation. The analog approach to structural eigenfrequency optimization is presented here with its theoretical foundation. A numerical redesign procedure is proposed and illustrated with examples.For the ideal case, an optimality criterion is fulfilled if the design have the same sub-domain ”frequency” (local Rayleigh quotient). Sensitivity analysis shows an important relation between squared system eigenfrequency and squared local sub-domain frequency for a given eigenmode. Higher order eigenfrequencies may also be controlled in this manner.The presented examples are based on 2D finite element models with the use of subspace iteration for analysis and a recursive design procedure based on the derived optimality condition. The design that maximize a frequency depend on the total amount of available material and on a necessary interpolation as illustrated by different design cases.