Optimal structural dynamics modificationb using frequency response function synthesis and its applications

Abstract

A frequency response function (FRF) based structural optimization method is presented. The design object is to improve its natural frequencies to make the system dynamic characteristics better. Structural dynamics modification (SDM) has been widely used for improvements of built-in structures. However, the optimum design obtained by SDM differs from the true optimal solution when large modal changes are happened. In this study, a substructure-coupling concept is used to get system dynamic equation in order to cover its use to large modal changes, thus large-scale optimum modification is obtained. FRF matrix of baseline structure and those of modification structures are coupled at the connection points by using force equilibrium and geometric compatibility constraints. Modified eigenvalue is found exactly by determinant search of characteristic equation. Error analysis of eigenvalue determination is also performed when FRF errors are involved and major factors of eigenvalue determination errors are analyzed. Design modification is performed through eigenvalue sensitivity analysis. The optimal structural modification is calculated by combining eigenvalue sensitivities and eigenvalue reanalysis technique iteratively. Proposed method is applied to well-known structural modification problems such as beam stiffener modification and optimal support selections. Structure shape optimization is also treated. In other way, an analytical approach is presented to derive exact mass and stiffness modifications which specifythe system natural frequency and mode shape. In applications, special attention is given to the case where baseline structure has some unidentified structural parameters to enlighten the advantage of the proposed method. The results of applications indicate that the proposed method can provide an accurate optimal structural change just based on measured FRFs without any kind of numerical models.``