Optimum design of structures with frequency response constraints using a 3-point function approximation

摘要

An efficient technique is presented for optimum design of structures with both naturalfrequency and complex frequency response constraints. The main idea is to reduce the numberof dynamic analysis by introducing high quality approximations. Eigenvalues are approximatedusing the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvaluesand frequency responses. A three point approximation is developed to approximate the functionsunder consideration. After the substitution of the approximate functions into the original optimizationproblem, 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 problemsunder consideration repeated eigenvalues occur. Thus the sensitivities are evaluated for repeatedeigenvalues.