A Novel Approach for Local Structural Modification of Nonlinear Structures

Abstract

Structural modification methods provide powerful tools to calculate the dynamic behavior of a modified structure from that of the original one. In general, either the modal properties or responses of the original structure are used to calculate the responses of the modified system. These methods reduce the computational efforts drastically compared to a complete system re-analysis, especially when the modification is local. However, such methods do not apply to nonlinear systems due to response-dependent nature of the frequency response functions (FRFs). One of these methods for linear systems, called the “matrix inversion method,” uses the FRFs of the original structure and the spatial properties of the modification to estimate the FRFs of the modified system. Recently, a new method utilizing the response-controlled step-sine testing (RCT) approach was proposed for obtaining the quasi-linear FRFs and response-dependent modal properties of nonlinear structural systems. Full-duality between the quasi-linear constant amplitude FRFs and the nonlinear constant force FRFs was shown around the nonlinear structure’s resonance frequencies. In this chapter, a novel structural modification approach is proposed, which utilizes the matrix inversion method (so far used to modify only linear systems) and the RCT-based quasi-linear FRFs of the nonlinear structure. This approach enables obtaining the modified structure’s quasi-linear FRFs, similar to the linear system structural modification problem. Combining the matrix inversion method for linear systems with the RCT approach enables the efficient calculation of receptances of structures with local nonlinearities placed around response-controlled degree of freedom, or when the modifications are such that the mode shapes do not change significantly, even if the nonlinearity is distributed.