一种超材料梁对机械波振动吸收的模拟研究  

Simulation of a metamaterial beam for mechanical wave absorption

作　　者：林国昌[1] 孙宏伟[1] 谭惠丰[1] 杜星文[1] 

机构地区：[1]哈尔滨工业大学复合材料与结构研究所,哈尔滨150001

出　　处：《物理学报》2011年第3期354-360,共7页Acta Physica Sinica

基　　金：国家高技术研究发展计划(批准号:2008AA12A205)资助的课题~~

摘　　要：本文设计了一种能够对机械波进行吸收的超材料梁,超材料梁由若干质量-弹簧微结构系统和一根各向同性梁构成.通过对两种不同结构的质量-弹簧系统的分析,从理论上解释了"负有效质量"和"负有效刚度".根据Hamilton原理,导出了超材料梁的代表性胞元的控制方程.通过数值模拟分析了两种不同结构的有限超材料梁对机械波的吸收性能,一种是弹性系数线性变化的质量-弹簧系统在有限梁内均匀分布,另一种是由固有频率线性变化的弹簧-阻尼器子系统构成四个相同吸收器子群在有限梁内均匀分布.模拟结果表明,进入梁中的机械波与质量-弹簧振子构成的吸收器系统发生了共振,对机械波起到了理想的吸收,从而验证了本文提出的超材料梁对机械波吸收的有效性.In this paper,we present a metamaterial beam consisting of a uniform isotropic beam with many small mass-spring systems serving as mechanical wave absorbers. Based on the analysis of two different mass-spring systems,negative effective mass and negative effective stiffness are explained theoretically. The governing equations of a unit cell of a metamaterial beam are derived using the Hamilton’s principle. The mechanical wave absorbabilities of the following two different finite metamaterial beams are analyzed by numerical simulation：one is the bean in which mass-spring systems with linearly varying elastic coefficients are uniformly distributed,and the other is the bean in which four identical absorber subgroups composed of spring-damper subsystems with linearly varying natural frequenciesare uniformly distributed. The results reveal that the mechanical wave transmitted in the metamaterial beam is absorbed by resonating with spring-mass absorbers, which verifies the effectivity of the proposed metamaterial beam on mechanical wave absorption.

关 键 词：超材料梁 负有效质量 负有效刚度 机械波 

分 类 号：TB535.1[理学—物理]