Extension and Experimental Verification of an Efficient Re-analysis Method for Modified Nonlinear Structures

Design changes often occur during engineering applications. Although there are numerous methods to implement these changes and efficiently calculate dynamic responses of modified linear systems, modification methods applicable to nonlinear systems are few in number. Considering the cost of re-analysis of modified large-scale nonlinear system models, the development of nonlinear modification methods has major importance. A numerically efficient approach has been developed for the re-analysis of a modified nonlinear system using frequency response function (FRFs) of the original system and the mass, stiffness, and damping properties of the modification. However, this method is applicable if the nonlinearity is confined to a single nonlinear element between a linear structure and ground. In recent research, the authors of this chapter proposed a structural modification method applicable to systems with multiple local nonlinearities distributed at different points on the structure and validated the method on lumped systems that exhibit conservative nonlinearities. This method utilizes the response-controlled stepped-sine testing (RCT) to determine quasi-linear FRFs of the original nonlinear system. These quasi-linear FRFs allow the implementation of an efficient re-analysis method previously developed for linear systems to accurately estimate frequency responses of nonlinear systems modified with linear elements. The current study demonstrates the applicability of the method to nonlinear systems exhibiting nonconservative nonlinearities and severe modification (causing a considerably high shift in the natural frequency) by employing a numerical example. The method is also verified by using a real experiment.