Plates have wide applications in areas such as; modern construction engineering, aerospace and aeronautical industries, aircraft construction, shipbuilding and the components of nuclear power plants. It is therefore very important that the static and dynamic behavior of plates when subjected to different loading conditions be clearly understood so that they may be safely used in these industrial applications. The present study is concerned with the free vibration and buckling analysis of a horizontal rectangular plate on elastic foundations, either immersed in fluid or floating on its free surface. The governing equations for a thin rectangular plate are analytically derived based on the justify; LINE-HEIGHT: normal; MARGIN: 0cm 0cm 0pt; mso-layout-grid-align: none" Also, in recent years Nanomaterials are among the most important topics discussed in the scientific community due to their unique mechanical, chemical, thermal, and electrical properties since the invention of carbon nanotubes (CNTs). Therefore, the exact knowledge of the physical and mechanical properties and their effect on production efficiency and ability to applications is necessary. Thus, the buckling and vibration analysis of single-layered graphene sheet and doubled-layered nanoplate is studied based on Eringen’s nonlocal elasticity theory under thermal loading coupled with fluid by using CLPT and HSDT theory. The van der Waals (vdW) forces between two layers are taken into account based on the Lennard–Jones model. Results indicate that the small scale parameter, elastic medium and temperature change have significant effects on the dimensionless natural frequency and critical fluid velocity. Natural frequencies of the plate are presented in graphical forms for different temperature change, aspect ratio, fluid level, stiffness parameter and fluid velocity for different boundary conditions. It is demonstrated that some properties of vibrations of double-layered nanoplates are dependent on the change of temperature. Keywords: Rectangular plates, Buckling analysis, Vibrational frequencies, Solid - Fluid Interaction, Graphene nanosheets.
