FRF Based Structural Modification of a Mechanical System by Adding Masses and Utilizing the Grey Wolf Optimization Technique

Abstract

Resonance and anti-resonance frequencies are important parameters that determine the dynamic behavior of mechanical systems. Changes in these parameters, which depend on the system's physical properties such as mass and stiffness, also affect the system's dynamic behavior. Finding the necessary structural modifications to adjust the resonance and anti-resonance frequencies of a system to the desired values is a study area of inverse structural modification. In this study, an inverse structural modification method for one and multi-rank modifications is presented. With the presented method some resonance or anti-resonance frequencies of mechanical systems can be shifted to prescribed values by calculating the necessary modifications. The presented method is based on Sherman-Morrison (SM) formula and uses the frequency response functions (FRF) of the original system directly. For one modification an exact solution is obtained on the other hand for two or more modifications some nonlinear set of equations has to be solved. A meta-heuristic optimization technique known as Grey Wolf Optimizer (GWO) is applied for the solution of the nonlinear equations. The method is applied to a six-degrees-of-freedom mass-spring system. Some resonance and anti-resonance frequencies in the frequency bandwidth of the system are selected as target frequencies. The necessary modification masses are calculated to match these frequencies. After applying the calculated masses to the system the target frequencies are obtained successfully.