Acoustic Vibration of Hexagonal Nanoparticles with Damping and Imperfect Interface Effects

In this paper, acoustic vibration of hexagonal nanoparticles is investigated. In terms of the spherical system of vector functions, the first-order differential equation with constant coefficients for a layered sphere is obtained via variable transformation and mass conservation. The propagation matrix method is then used to obtain the vibration equation in the multilayered system. Further utilizing a new root-searching algorithm, the present solution is first compared to the existing solution for a uniform and isotropic sphere. It is shown that, by increasing the sublayer number, the present solution approaches the exact one. After validating the formulation and program, we investigate the acoustic vibration characteristics in nanoparticles. These include the effects of material anisotropy, damping, and core-shell imperfect interface on the vibration frequency and modal shapes of the displacements and tractions.