Nassar H, Chen H, Norris A N, Haberman M R, Huang G L
Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA.
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854-8058, USA.
Proc Math Phys Eng Sci. 2017 Jun;473(2202):20170188. doi: 10.1098/rspa.2017.0188. Epub 2017 Jun 28.
Time-reversal symmetry for elastic wave propagation breaks down in a resonant mass-in-mass lattice whose inner-stiffness is weakly modulated in space and in time in a wave-like fashion. Specifically, one-way wave transmission, conversion and amplification as well as unidirectional wave blocking are demonstrated analytically through an asymptotic analysis based on coupled mode theory and numerically thanks to a series of simulations in harmonic and transient regimes. High-amplitude modulations are then explored in the homogenization limit where a non-standard effective mass operator is recovered and shown to take negative values over unusually large frequency bands. These modulated metamaterials, which exhibit either non-reciprocal behaviours or non-standard effective mass operators, offer promise for applications in the field of elastic wave control in general and in one-way conversion/amplification in particular.
对于弹性波传播而言，时间反演对称性在一种质量嵌套的共振晶格中失效，该晶格的内部刚度以波的形式在空间和时间上受到微弱调制。具体而言，通过基于耦合模理论的渐近分析，以及借助在谐波和瞬态状态下的一系列模拟进行数值计算，证明了单向波传输、转换和放大以及单向波阻挡。然后在均匀化极限下探索高振幅调制，此时恢复了一个非标准的有效质量算符，并表明其在异常宽的频带上取负值。这些表现出非互易行为或非标准有效质量算符的调制超材料，总体上为弹性波控制领域，特别是单向转换/放大领域的应用带来了希望。
