Physique de la Matière Condensée, Ecole Polytechnique, CNRS, 91128 Palaiseau, France.
Phys Rev Lett. 2009 Dec 18;103(25):254301. doi: 10.1103/PhysRevLett.103.254301.
We discover a strong localization of flexural (bi-Laplacian) waves in rigid thin plates. We show that clamping just one point inside such a plate not only perturbs its spectral properties, but essentially divides the plate into two independently vibrating regions. This effect progressively appears when increasing the plate eccentricity. Such a localization is qualitatively and quantitatively different from the results known for the Laplacian waves in domains of irregular boundary. It would allow us to control the confinement of mechanical vibrations in rigid plates and of eddies in the slow Stokes flow.
我们发现，在刚性薄板中，弯曲（双拉普拉斯）波具有很强的局域性。我们表明，在这样的板内仅仅夹持一个点，不仅会干扰其光谱特性，而且实质上会将板分成两个独立振动的区域。当增加板的偏心度时，这种局域化现象会逐渐出现。这种局域化与在不规则边界域中已知的拉普拉斯波的结果在定性和定量上都有所不同。它将允许我们控制刚性板中机械振动和慢斯托克斯流中涡旋的限制。
