Nanotechnology is a fast growing field of science and technology which deals with the development of materials, structures and devices at the nanoscale. Nanoplates are pivotal branches of nanostructures with vast applications including their usage in making batteries, chemical and biological sensors and also in nanocars and many other applications. Though, few studies have been investigated the behavior of these structures and this shortage of efforts is possibly related to the troubles in their productions. In this regard, understanding the vibration and buckling behaviors of nanoplates is the most important steps to the design of these structures. Due to high dependencies in static and dynamic stability equations, providing an analytical solution for free vibration and buckling of nanoplates is very difficult, so in most studies numerical or semi-numerical methods such as finite element, Rayleigh-Ritz and… are utilized. various recent experimental results have shown that as the size of the structure reduces to compareable to micro/nanoscale, the influences of atomic forces and small scales play a significant role in their mechanical properties. Thus, neglecting these effects in some cases may results in completely incorrect solutions and hence wrong designs. Some methods such as molecular dynamics involve solving a large number of equations, so, they have difficulties in handling systems with large length and time scales. Therfore, modeling of the large systems is left to continuum mechanics approaches. One of the well known continuum mechanics theory that includes small scales effects with acceptable accuracy is the nonlocal theory of Eringen. Using local theory for the small size analysis leads to the over predicting results. In order to capture the small scale effects in nonlocal continuum theory it is assumed that the stress at a point depends on the strain at all points in the domain. This is contrary to the left; TEXT-INDENT: 0cm; MARGIN: 0cm 0cm 0pt; unicode-bidi: embed; DIRECTION: ltr" align=left Keywords : Nanoplate; Nonlocal elasticity; Buckling; Solid disks; Circular annular plates; Sector plates; Finite difference method.
