一种超材料梁对机械波振动吸收的模拟研究

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-弹簧振子关键词：超材料梁负有效质量负有效刚度机械波

Simulation of a metamaterial beam for mechanical wave absorption

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.