Size dependent forced vibration of nanoplates with consideration of surface effects

A variational size-dependent model for electrostatically actuated NEMS incorporating nonlinearities and Casimir force

“…Based on the Bernoulli-Euler beam assumption, the bending strain energy (Eq. (1)), with strain gradient incorporated, is expressed by [18] 22 23 12 23 00 (14) in which…”

“…Moreover, the nonlocal theory predicts a "softening effect", which is inconsistent with the "stiffening effect" observed in experiments. For surface energy theory, it is considered that the surface properties cannot be overlooked in the study of nanostructures and nanomaterials due to the large value of surface to volume ratios at that scale [14]. Although it is applied to study the size dependent behaviors, it is had to admit that the fundamental properties are not only relative to the surface part but also relative to the internal part because the characteristic length is in the bulk such as the grain size or atomic lattice spacing.…”

A review on the mechanics of nanostructures

“…However, stiffness hardening has been observed in some small-scale structures, especially at higher lengths. This stiffness hardening can be estimated incorporating surface effects [75][76][77][78][79][80] or strain gradients [52,53,[81][82][83][84][85][86]. For example, it was found that the pure nonlocal plate model cannot completely predict the buckling instability of circular graphene sheets subject to axisymmetric radial loading [87] by employing MD simulations.…”

Hygrothermal vibration of orthotropic double-layered graphene sheets embedded in an elastic medium using the two-variable plate theory

“…Thermal vibration analysis of orthotropic nanoplates based on nonlocal continuum mechanics was studied by Satish et al [14] using two variable refined plate theory. Based on a generalized form of Kirchhoff plate model, an analytical method has been presented by Assadi [15] to study the size dependent forced vibration of rectangular nanoplates under general external loading. The elastic buckling and vibration characteristics of isotropic and orthotropic nanoplates have been investigated by Analooei et al [16] employing finite strip method.…”