Analysis of Locally Nonlinear Two Dimensional Periodic Structures Using NOFRFs

The analysis of locally nonlinear two dimensional (2D) periodic structures is studied using the concept of nonlinear output frequency response functions (NOFRFs). NOFRFs are a series of one-dimensional functions of frequency, which allow the analysis of nonlinear systems to be implemented in a manner similar to the analysis of linear system in the frequency domain. By inspecting the relationships between the NOFRFs of unit cell in the locally nonlinear two dimensional periodic structures, a series of properties about the NOFRFs of the nonlinear system are derived. The correctness of these properties is demonstrated by numerical studies. These properties obtained in this paper are of significance to the frequency response analysis for nonlinear 2D periodic structures. One important potential application of these properties is the location of damage in 2D periodic structures, which make system behave locally nonlinearity.