The size-dependent elastic property of rectangular nanobeams （nanowires or nanoplates） induced by the surface elas- ticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 1 O0 nm. It is also found that the theoretical results calculated by a mod- ified core-shell model have more obvious advantages than those by other models （core-shell model and core-surface model） by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers.
Using the plane-wave expansion method, the spin-wave band structures of two-dimensional magnonic crystals consisting of square arrays of different shape scatterers are calculated numerically, and the effects of rotating rectangle and hexagon scaterers on the gaps are studied, respectively. The results show that the gaps can be substantially opened and tuned by rotating the scatterers. This approach should be helpful in designing magnonic crystals with desired gaps.
