一维立方非线性刚度周期结构色散特性研究  

Study on Dispersion Characteristics of One-Dimensional Cubic Nonlinear Stiffness Periodic Structures

作　　者：左昂 徐艳龙 陈宁[1] 张梦佳 谷迎松[1] 杨智春[1] Zuo Ang;Xu Yanlong;Chen Ning;Zhang Mengjia;Gu Yingsong;Yang Zhichun(Northwestern Polytechnical University,Xi’an 710072,China;State Key Laboratory for Strength and Vibration of Mechanical Structures,Xi'an 710049,China)

机构地区：[1]西北工业大学,陕西西安710072 [2]复杂服役环境重大装备结构强度与寿命全国重点实验室,陕西西安710049

出　　处：《航空科学技术》2024年第6期63-70,共8页Aeronautical Science & Technology

基　　金：航空科学基金(20161553016);广东省基础与应用基础研究基金(2022A1515011497);西安交通大学复杂服役环境重大装备结构强度与寿命全国重点实验室开放课题基金(SV2023-KF-19)。

摘　　要：研究立方非线性刚度单胞阵列形成一维周期结构后的色散特性,对飞机壁板振动控制的研究具有一定的促进作用。首先构建一维线性刚度周期结构的动力学模型,基于布洛赫理论(Bloch theorem)推导了其色散方程,并对其色散特性和弹性波传播现象进行分析。进而建立含立方非线性刚度单胞的一维周期结构的动力学模型,利用摄动法推导该周期结构的色散方程,分析非线性刚度的软、硬和激励振幅对其色散特性以及弹性波传播产生的影响。最后考虑到飞行器壁板复杂工作环境,避免摄动法仅适用于弱非线性的局限性,给出含立方非线性刚度一维周期结构色散关系的谐波平衡法的求解过程,对比两种方法的求解结果。本文为利用非线性周期结构对飞行器壁板进行振动控制的进一步研究奠定基础,对非线性声子晶体低频减振研究也具有一定的促进作用。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 lowfrequency damping of nonlinear phononic crystals.

关 键 词：周期结构 色散特性 摄动法 谐波平衡法 非线性 

分 类 号：V223[航空宇航科学与技术—飞行器设计]