Efficient Optimum Design of Steructures With Reqency Response Consteraint Using High Quality Approximation

An efficient technique is presented for optimum design of structures with both natural frequency and complex frequency response constraints. The main ideals to reduce the number of dynamic analysis by introducing high quality approximation. Eigenvalues are approximated using the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvalues and frequency responses. A two point approximation is used to approximate the functions under consideration. After the substitution of the approximate functions into the original optimization problem, the dynamic analysis of the structure is not necessary in the specified move limits. The sensitivities of the eigenvalues and eigenvectors are calculated analytically. In the problems under consideration repeated eigenvalues occur. Thus the sensitivities are evaluated for repeated eigenvalues.