^{1}, Yue-Sheng Wang

^{1}and Chuanzeng Zhang

^{2}

^{1}Beijing Jiaotong University.

^{2}University of Siegen.

In recent years, the acoustic devices toward to miniaturization and components of those in micro-/nanometer length scale received considerable attention due to the rapid development of the information technology. When investigate the mechanical functionality of the advanced materials, the significant influence of surface/interface energy and stresses which resulted from high surface-to-volume ratio can not be neglected, and most properties of the nanosized materials and structures have been demonstrated are size-dependent, thus the surface/interface effects must be taken into account. In this case, the classical continuum theory is replaced by the theory of surface elasticity, which can be validated by atomic simulations.

As well known, Phononic Crystals (PNCs) which drawing attention in worldwide in the last decades are a kind of artificial periodic structures. The distinguishing feature of PNCs that exhibiting the band gaps where the elastic waves can not propagate results in potential applications in acoustic filters, noise suppression, vibration isolation, design of new acoustic devices and so on. Recently the fabrications and investigations of phononic crystals in nanoscale have been demonstrated and the so-called hypersonic phononic crystals provide a new pathway to explore the applications in acoustio-optic modulation, electron-phonon engineering, heat management, etc. It has been indicated that considering the surface/interface effects is necessary for studying the wave propagation properties of nanosized PNCs.

Up to now, two numerical methods were used to calculate the band structures of nanosized phononic crystals with considering the surface/interface effects. One is the method based on Dirichlet-to Neumann (DtN) map, which was extended by Zhen et al to investigate transverse waves propagating in 2D nanosized PNCs composed of circular voids/inclusions and discuss the surface/interface effects in detail; the other is the Multiple Scattering Theory (MST) method used by Liu et al to calculate the band structures of 2D nanosized PNCs. Here in the present paper, we will extend the DtN-map method to explore mixed in-plane wave modes propagating in 2D nanosized phononic crystals in square and triangular lattices with taking into account the surface/interface effects. The surface/interface model developed by Gurtin and Murdoch is employed. We consider three systems: nanosized vacuum cylindrical holes embedded in an aluminium matrix; nanosized aluminium cylinders embedded in a tungsten matrix; and the one that nanosized tungsten cylinders embedded in an aluminium matrix. The results show that the surface/interface effects make obvious deviation of band structures and have more significant influences on the band structures for the soft-inclusion system than for the stiff-inclusion system.