摘要
周期结构是构建自然界和人类工程结构的一种重要形式,平移对称性引起的Bloch调制作用赋予其独特的能带结构和丰富的时/频域动力学特性,为弹性波/声波传播调控、新型声功能器件设计、振动与噪声控制等提供了新思路.非线性效应可以突破线性理论框架的束缚,能够增强甚至拓展人工周期结构的功能.但非线性周期系统在单胞结构设计和建模分析方面存在诸多困难,也面临时空平移对称性破缺、非线性响应特性及机理复杂等深层次科学难题,给非线性周期结构动力学设计与实际应用带来挑战.针对上述问题,学者们融合力学、声学、材料学和能带物理等多学科研究方法开展了一些卓有成效的研究,本文旨在及时总结非线性周期结构动力学和波动调控领域的重要研究进展,梳理研究中存在的不足之处和关键难题,凝聚力量,促进该领域的深入发展.首先,归纳了力学周期结构非线性效应来源、单胞结构设计方法、非线性周期结构动力学建模与分析方法;之后,综述了非线性周期结构在通带、带隙和能量局域束缚等方面的主要特性,着重介绍了非线性导致的能带频移、模式耦合、低频宽带拓展和带隙内波动模式局域束缚等丰富动力学现象,梳理了非线性周期结构在波调控装置和减振降噪设计方面的一些应用探索.最后,针对现有研究存在的一些不足和关键难题,展望了未来理论研究和应用探索亟需关注的若干发展方向.
Periodic structures are an important form of constructing structures in natural and human engineering.The Bloch modulation caused by translational symmetry gives them unique band structures and rich time/frequency domain dynamic characteristics,providing new avenues for elastic/acoustic wave propagation regulation,novel wave-based functional device design,vibration and noise control,etc.Nonlinear effects can break through the constraints of linear theoretical frameworks and can enhance or even expand the functions of artificial periodic structures.However,nonlinear periodic systems have many difficulties in unit cell design and modeling analysis.They also face key scientific problems such as the broken of space-time invariance,the complexity of nonlinear response characteristics and mechanisms,which brings challenge to the dynamic design and practical application of nonlinear periodic structures.In response to the above problems,scholars have carried out some fruitful research by integrating multidisciplinary research methods in fileds such as mechanics,acoustics,materials science and band physics.This article aims to timely summarize the important research progress concerning about wave dynamics and control in nonlinear periodic structures,sort out the shortcomings and key problems,gather strength and promote the in-depth development of this field.First,the sources of nonlinear effects of periodic structures,unit cell structure design methods,and nonlinear dynamics modeling and analysis methods are summarized.Then,the main characteristics of nonlinear periodic structures in terms of passband,bandgap,and local energy confinement are reviewed,and the rich dynamic phenomena such as amplitude-induced band shift,wave mode coupling,low-frequency broadband bandgap,and spatial confinement of wave modes in the bandgap caused by nonlinearity are introduced.Some application explorations of nonlinear periodic structures in wave control devices,vibration and noise reduction are sorted out.Finally,in view of some shortcomings and key problems in existing research,several development directions that need special attention in future theoretical research and application exploration are prospected.
作者
高鹏林
龚凌云
王国旭
罗宇
朱俊喆
高昊
马海斌
瞿叶高
GAO Penglin;GONG Lingyun;WANG Guoxu;LUO Yu;ZHU Junzhe;GAO Hao;MA Haibin;QU;Yegao(State Key Laboratory of Mechanical System and Vibration,School of Mechanical Engineering,Shanghai Jiao Tong University,Shanghai 20024,China;Institute of Vibration,Shock and Noise,Shanghai Jiao Tong University,Shanghai 200240,China)
出处
《力学进展》
北大核心
2025年第3期567-641,共75页
Advances in Mechanics
关键词
非线性周期结构
动力学设计
非线性振动
振动控制
波动调控
nonlinear periodic structure
dynamic design
nonlinear vibration
vibration control
wave control
作者简介
高鹏林,上海交通大学机械与动力工程学院副教授,博士生导师.主要研究方向为人工周期结构动力学与振动噪声控制,在《Physical Reviews Letters》《Nature Communications》《Journal of Sound and Vibration》等学术期刊发表论文30余篇,入选上海市浦江人才计划、上海市海外高层次青年人才,获上海市力学学会优秀青年学者一等奖;瞿叶高,教授,上海交通大学科研院副院长、前沿创新研究院院长,机械系统与振动全国重点实验室副主任.主要从事非线性动力学设计及振动与声波操控研究.主持国家杰出青年科学基金以及基金委重大项目课题、叶企孙基金重点项目等.获教育部自然科学奖一等奖、上海市科技进步一等奖、中国力学学会青年科技奖、中国振动工程学会青年科技奖等奖励.担任《Applied Acoustics》副主编以及多个国内外期刊编委.兼任中国力学学会理性力学和力学中的数学方法专业委员会委员,中国振动工程学会副秘书长、非线性振动专业委员会副主任等.E-mail:quyegao@sjtu.edu.cn。
