Optimization of structures with frequency and mode shape constraints

In this paper an application of structural optimization to the design of structures with constraints in frequency and mode shape is presented. The objective is to obtain an optimum design making adequate changes in the structure to modify its dynamic characteristics. The method is based on an iterative process of optimization that includes structural analysis by the Finite Element Method (FEM), sensitivity analysis, and optimization techniques. An efficient and accurate method is used to calculate the sensitivities of the dynamic behaviour of the structure. The sensitivity analysis is accomplished using a semi‐analytical procedure based on the Nelson method. A Sequential Linear Programming (SLP) algorithm is used to solve the optimization problem. In the minimization process the convergence is assured even in a short number of iterations. The validation of the method is also shown by means of two examples of application.