An inverse strategy for relocation of eigenfrequencies in structural design. Part I: first order approximate solutions

This paper proposes an inverse strategy for relocation of structural natural frequencies using first order formulation and solution algorithm. In the proposed method a sensitivity analysis of the systems eigenvalues with respect to material or geometrical parameters of the structure is conducted initially. The required parameter variation to achieve a desired frequency shift for the structure is then computed. The proposed technique incorporates the design constraints or objective functions in the system equations in such a way that a square system of equations is always preserved. The formulations are general and applicable to all finite element structures because the sensitivity analysis is based on the stiffness and mass matrices regardless of the type of elements used. An algorithm suitable for implementation of the technique for practical purposes is developed. The accuracies of the proposed methods are tested conducting several case studies and the results are validated against exact solutions.