Nonlocal stress-strain gradient vibration analysis of heterogeneous double-layered plates under hygro-thermal and linearly varying in-plane loads

This paper develops a nonlocal strain gradient plate model for vibration analysis of double-layered graded nanoplates under linearly variable in-plane mechanical loads in hygro-thermal environments. For more accurate analysis of nanoplates, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. The double-layered nanoplate is modeled via a four-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient nanoplate on elastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations. Effects of different factors such as in-plane loading, load factor, nonlocal parameter, length scale parameter, moisture percentage rise, temperature rise, elastic foundation, and boundary conditions on vibration characteristics of a double-layered nanoplate have been examined.