As the typical systems of nano structures, nanotubes can be widely applied in mechanical electronics, mechanical manufacture and other fields at nano scales. The superior dynamical properties of nanotubes have become a hot topic. Furthermore, there are always complicated conditions for practical engineering (e.g. initial stress/strain, temperature change for external environment and the interaction between the structure and elastic matrix). Then, it is important to establish the proper model and apply the effective analysis method. By using the nonlocal continuum method, this paper reviews the recent progress of dynamical properties of micro structures at nano scales. The discussion is focused on dynamical behaviors of nanotubes, including vibration, wave propagation and fluid-structure interaction, etc. At last, conclusions and prospects in future studies are discussed.
In this paper,the elastic wave propagation in atwo-dimensional piezoelectric phononic crystal is studiedby considering the mechanic-electric coupling.The gener-alized eigenvalue equation is obtained by the relation of themechanic and electric fields as well as the Bloch-Floquet the-orem.The band structures of both the in-plane and anti-planemodes are calculated for a rectangular lattice by the plane-wave expansion method.The effects of the lattice constantratio and the piezoelectricity with different filling fractionsare analyzed.The results show that the largest gap width isnot always obtained for a square lattice.In some situations,a rectangular lattice may generate larger gaps.The band gapcharacteristics are influenced obviously by the piezoelectric-ity with the larger lattice constant ratios and the filling frac-tions.
