一维立方非线性刚度周期结构色散特性研究OA

The study of the dispersion characteristics of periodic structures formed by cubic nonlinear stiffness unit cell arrays,which has a certain promoting effect on the research of aircraft panel vibration control.Firstly,the dynamic model of one-dimensional linear stiffness periodic structure is constructed,and its dispersion equation is derived based on Bloch theory.Its dispersion characteristics and wave propagation are analyzed.Then the dynamic model of the periodic structure with cubic nonlinear stiffness unit cells is established,and the dispersion equation of the periodic structure is derived by using the perturbation approach.Finally,considering the complex working environment of aircraft panels and the limitation that the perturbation approach is only applicable to weak nonlinearity,the solution process of harmonic balance method for periodic structures with cubic nonlinear stiffness dispersion relation is given,and the solution results of the two methods are compared.This paper lays the foundation for further research on vibration control of aircraft wall panels using nonlinear periodic structures,and also contributes to the research on low-frequency damping of nonlinear phononic crystals.