Surface Effects On The Buckling And Vibration Behaviors Of Nanoplates

Plate-like nanostructures are widely applied in microelectromechanicalsystem (MEMS), nanoelectromechanical system (NEMS), biochemical sensors,mass sensors, and electrical filters, due to their high sensitivity and high naturalfrequency. With the increasing ratio of surface area to bulk, surface effects playan important role in the mechanical behavior of nanostructures. It is necessaryand urgent to correctly understand the static and dynamic behaviors ofnanoplates. In this paper, the buckling and vibration behaviors of Kirchhoff andMindlin nanoscale plates with consideration of surface effects are studied byusing the nonlocal elastic theory. The postbuckling and nonlinear vibration ofnanoplates is also studied. The closed-form of buckling force and frequency ofnonlocal nanoplates is obtained. The Galerkin’s method is employed to obtain theapproximate postbuckling load and nonlinear period of nanoplates. From thenumerical results, it can be seen the following phenomenon.The critical buckling force of the nonlocal nanoplate increases withdecreasing nonlocal parameter. The positive surface elasticity and positivesurface stress will increase the critical buckling load of the plate but the negativeones will decrease the critical buckling load. The reduction of critical bucklingforce by shear deformation becomes significant as the thickness of the plateincreases.The positive surface elasticity and positive surface stress will increase thenatural frequency of the plate but the negative ones will decrease the naturalfrequency. It is also found that the effect of surface energy is important at lowerfrequencies. However, the nonlocal parameter decreases the natural frequencyand its influence on the natural frequency becomes increasingly pronounced forhigher order vibration modes. The shear deformation reduces the naturalfrequency significantly for higher order vibration modes.The influence of surface effects on the postbuckling load of nanoplate ismore significant when the thickness of the plate decreases. More importantly, theinfluence of the surface effects on the postbuckling load reduces if the amplitudeof deflection increases. The shear deformation reduces the postbuckling load of the plate significantly when the thickness of the plate increases and theamplitude of deflection decrease.The influence of surface effects on the normalized period of nanoscaleplates becomes increasingly significant when the thickness of the plate decreases.More importantly, the influence of the surface effects on the normalizedvibration period reduces if the initial amplitude of the vibration increases. Theshear deformation increases the normalized vibration period.