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

This paper extends the first order formulations presented in Part I to second order methods for relocation of structural natural frequencies from their initial design values to new modified frequencies. The method is based on an inverse formulation and solution algorithm of the eigenvalue problem. Using the second order Taylorʹs expansion series, the required parameter variation to achieve a desired natural frequency shift for the structure is computed through second order differential or binomial equations. The proposed technique can also incorporate the design constraints or objective functions in the system equations. The formulations are quite generic and applicable to all finite element structures. The accuracy of the proposed methods is tested by conducting several case studies, the results of which demonstrate the validity of the technique for a wide range of practical problems.