This study investigated the effects of considering surface and nonlocal energy parameters on the buckling analysis of double piezoelectric nanoplate (DPNP) embedded in elastic foundations and thermal environments. Both in-phase and out-of-phase modes of buckling and various boundary conditions are studied and compared with each other. The governing equations were derived by drawing on the principle of virtual work and then solved by employing the finite difference method. Finite difference solution was validated using Navier's method and journal references. A parametric study was also launched in order to investigate the effects of the external electric voltage, nonlocal parameters, different boundary conditions, elastic foundations and thermal environments on the surface effect of DPNP buckling. The obtained numerical results showed that the influence of surface stress on in-phase and out-of-phase modes of buckling of the DPNP was enhanced by augmenting the nonlocal parameters and external electric voltage; on the other hand, it was found to be decreased by increasing elastic foundations and temperature changes. In addition, the value of surface stress effects for the in-phase mode was higher than that of the out-of-phase one.

This survey examines the geometrically nonlinear bending of a doubly clamped nanobeam that is subjected to combined actions of actuator voltage, prestress, and intermolecular force, with the pull-in instability as the primary objective. A nonlocal Euler-Bernoulli beam model, which takes the small scale effect into account, is developed making use of the principle of virtual displacement on the basis of Eringen's nonlocal theory in conjunction with von Kármán assumption. Due to complexity of the resulting equations, a shooting technique is established through taking the applied voltage as an unknown and the central deflection as a control parameter. This treatment has the capability of tackling the nonlinearities from both the large deformation and electrostatic force as well as the intermolecular force and enables the size dependent deflection response to an applied voltage of the nanobeam to be obtained conveniently. Validation is conducted in numerical examples through direct comparisons with existing solutions to confirm the proposed method. Parametric studies are undertaken addressing the impacts of the nonlocal effect, intermolecular force, residual stress, and geometry of the beam on the pull-in behaviors.