Vibration of nanoscale plates with surface energy via nonlocal elasticity

The vibration behaviors of simply supported Kirchhoff and Mindlin nanoscale plates with consideration of surface effects are studied using the nonlocal elastic theory. The motion equations of the nanoplates are obtained and the closed form solutions for natural frequency are established using Navier's approach. According to the analysis, the influences of surface energy and nonlocal effect on natural frequency of the nanoplates are very significant. The surface energy increases the natural frequency but the nonlocal parameter decreases the natural frequency. The influence of nonlocal effect becomes increasingly pronounced for higher order vibration modes. On the contrast, the effect of surface energy is important at lower frequencies.