Finite Element Frequency Optimization of Cantilever Beam by Design Parameters of Supporting Position and Rigidity

An optimization design of natural frequencies of a cantilever beam with rigid or elastic supporting springs is studied. The structure modification is optimized for a given set of the change of the eigenvalues of the frequencies. Design parameters are the position and rigidity of the supporting springs. An iterative calculation to obtain the objective expectations is carried out by means of a sensitivity analysis of the finite element solution and a Lagrange function to seek the objective structure as near to the baseline structure as possible. Useful results are obtained for a calculation method of the sensitivity, a treating method of the running-out support from the end of the cantilever, a restriction method of the change of the design parameters which brings a good convergency, and so on.