on the distribution of nonlinear effects in locally nonlinear one-dimensional chain type structures

nonlinear effect is a typical phenomenon for nonlinear systems, which is characterized as the energy of the system input transferred from the frequency modes in the input to the output frequency locations, which are either below or above the input frequency band. the present work is devoted to investigating the distribution of nonlinear effects in one-dimensional chain type structures with local nonlinearity in which only one or few components are of nonlinear property. the results reveal that the positions of both the nonlinear components and the external input play crucial roles in determining the distribution of nonlinear effects in the locally nonlinear structures, and provide a new insight into the complex dynamic of nonlinear systems in frequency domain. the results are of great significance to the analysis, design and control of the mechanical systems whose few components are of nonlinear property.