Size dependent free vibration analysis of multicrystalline nanoplates by considering surface effects as well as interface region

• The free vibration analysis of a multicrystalline plate of nano thickness by considering the surface effects is presented.
• The fundamental relations of elasticity has been derived for the multicrystalline nanoplate.
• It is shown that an interface region exists between the crystals with distinct orientation.
• The influence of plate thickness, amorphous width, and surface elasticity over the natural frequency are considered..
• It is proved that the natural frequency of multicrystalline nanoplates is strongly size-dependent.

This paper, in line with the previous study [23], is concerned with the finite element implementation of nanoplates. However, in this contribution free vibration responses of multicrystalline nanoplates by considering surface effects are presented. Nanomaterials and nanostructures have been receiving widespread attentions during last decades. This fact is due largely to surprising, peculiar, and impressive mechanical; electrical; and physical behaviors of nanostructures. Currently, nanostructures such as nanoplates are being utilized in the designing and manufacturing Nanoelectromechanical systems (NEMS) and Microelectromechanical systems (MEMS). Furthermore, silicon, thanks to its exceptional mechanical, physical, and electrical properties is extensively employed in the NEMS and MEMS. The mechanical properties and responses of nanoplates are intensely size-dependent, and in contrast to plates with macro dimensions, static and free vibration responses of nanoplates strongly depend on the size of nanoplates. In this study, a rectangular multicrystalline plate with nanothickness; arbitrary geometry, and boundary conditions is analyzed. Each crystal of the nanoplate is assumed to be anisotropic, and a prominent point that must be taken into consideration is the interface region, which exists between every two crystals. The free vibration responses of nanoplate such as natural frequency are considered, and the influence of size, surface effects, interface region, and various boundary conditions over natural frequency of the nanoplate is considered. Due to the fact that geometry of the multicrystalline nanoplate is not straightforward to be dealt with the governing equations, the finite element method is employed to obtain the results of free vibration response. Moreover, we succeed to employ ANSYS software in order to attain the free vibration responses of multicrystalline nanoplates. In addition, the present finite element method results, the code of which is generated in MATLAB, are compared with those obtained from ANSYS software, and the correlation of the results is quite remarkable.