双周期声子晶体梁弯曲振动带隙特性分析  

Study on Bending Vibration Band Gap Characteristics of a Double Periodic Phononic Crystal Beam

作　　者：冯青松[1] 杨舟 梁玉雄 陆建飞[2] 雷晓燕[1] FENG Qingsong;YANG Zhou;LIANG Yuxiong;LU Jianfei;LEI Xiaoyan(Engineering Research Center of Railway Environment Vibration and Noise of the Ministry of Education,East China Jiaotong University,Nanchang 330013,China;School of Civil Engineering and Mechnics,Jiangsu University,Zhenjiang 212013,Jiangsu,China)

机构地区：[1]华东交通大学铁路环境振动与噪声教育部工程研究中心,南昌330013 [2]江苏大学土木工程与力学学院,江苏镇江212013

出　　处：《噪声与振动控制》2020年第3期1-7,32,共8页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(51878277,51668020,51368020)。

摘　　要：提出一种双周期五组元声子晶体梁结构,用以研究弯曲波的带隙特性。在无限结构条件下,将其等效为铁木辛柯梁,利用传递矩阵法推导、计算其能带结构,并与简单二组元声子晶体梁结构的带隙进行对比分析,结果表明内部周期的存在主要影响带隙的宽度。在有限结构条件下,利用有限元法研究双周期五组元声子晶体梁的振动传递特性,证明理论推导的正确性,并得到双周期五组元声子晶体梁的弯曲波衰减特性。结果表明,双周期五组元声子晶体梁可以看作是一种滤波器,弯曲波沿波传播方向在禁带中逐渐衰减,而在通带中传播不衰减。最后讨论参数对带隙的影响,研究发现内部周期的存在能够解决低频与宽频相悖的问题,通过改变内部周期数,能够成功产生低频、宽频带隙,可为低频减振降噪设计提供新的思路。A double-periodic phononic crystal beam structure with five elements is proposed to study the bandgap characteristic of the bending wave.Under the condition of infinite structure,this structure is equivalent to a Timoshenko beam.Its energy band structure is calculated and derived by the transmission matrix method,and compared with the band gap of the crystal beam structure with simple two elements.The results show that the existence of the internal period mainly affects the width of the band gap.Under the condition of finite structure,the vibration transfer characteristics of the doubleperiod five-element crystal beam are studied by finite element method.The correctness of theoretical derivation is proved.And the bending wave attenuation characteristics of the double-period five-element crystal beam are obtained.The results show that the double-period five-element crystal beam can be regarded as a filter,and the bending wave decays gradually in the propagation direction of the wave,while the wave propagation does not decay in the passband.Finally,the influence of parameters on the band gap is discussed.It is found that the existence of the internal period can solve the contradiction problem between low frequency and broadband frequency.Changing the number of internal cycles can successfully produce low-frequency and broadband frequency band gaps,which provides a new idea for low-frequency vibration and noise reduction.

关 键 词：振动与波 双周期声子晶体梁 弯曲波带隙 铁木辛柯梁 传递矩阵法 振动传递特性 

分 类 号：TU311.3[建筑科学—结构工程] TU352.1