A novel mixed nonlocal elasticity theory for thermoelastic vibration of nanoplates

This paper develops a nonlocal theory of elasticity for the thermoelastic vibration of nanoplates. A mixed variational formula based upon Hamilton's principle is extended to deal with nanoplates. The present nonlocal first-order shear deformation theory does not need any shear correction factors. Equations of motion and boundary conditions are obtained simultaneously through the mixed variational formula. Governing equations of a mixed nonlocal smart nanoplate are obtained and their solutions are given. The accuracy of the present results is investigated through many comparison examples in the literature. The influences of different factors such as nonlocal parameter, aspect ratio, side-to-thickness ratio, and mode numbers on the natural vibration characteristics of nanoplates are studied.