We prove short-time existence of smooth solutions for a class of nonlinear, and generally spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh waves in elasticity.

Free vibration characteristics of polymer composite plates reinforced by graphene nanosheets employing the Eringen nonlocal elasticity theory were investigated. Theoretical formulations are derived based on Hamilton’s principle implementing linear orthotropic constitutive equations of lamina while the behavior of nanostructure points affected by all other nonlocal points is also taken into acco...

The damping vibration characteristics of magneto-electro-viscoelastic (MEV) nanobeam resting on viscoelastic foundation based on nonlocal strain gradient elasticity theory (NSGT) is studied in this article. For this purpose, by considering the effects of Winkler-Pasternak, the viscoelastic medium consists of linear and viscous layers. with respect to the displacement field in accordance with th...

In epitaxial growth on vicinal surfaces, elasticity effects give rise to step bunching instability and some self-organization phenomena, which are widely believed to be important in the fabrication of nanostructures. It is challenging to model and analyze these phenomena due to the nonlocal effects and interactions between different length scales. In this paper, we study a discrete model for ep...

Nonlinear bending of shear deformable nanobeams subject to a temperature field is investigated in this paper based on von Kármán type nonlinearity and nonlocal elasticity theory. By using the variational principle approach, new higher-order governing differential equations and the corresponding higher-order boundary conditions both in the transverse and axial directions are derived and discusse...

The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin’s gradient elasticity. We consider simple but rigorous versions of Mindlin’s first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislo...

The possibility is investigated that a nonlocal formulation of gauge theories may provide an alternative mechanism for the generation of mass. For this purpose, a path-integral approach is used, with gauge-averaging term leading to an invertible integro-differential operator on field disturbances and to a mass term in the semiclassical Lagrangian. It is therefore shown that suitable choices of ...

This paper is concerned with the surface and small scale effects on transverse vibration of a viscoelastic single-layered graphene sheet (SLGS) subjected to an in-plane magnetic field. The SLGS is surrounded by an elastic medium which is simulated as Visco-Pasternak foundation. In order to investigate the small scale effects, the nonlocal elasticity theory is employed due to its simplicity and ...

Using differential quadrature method (DQM), this study investigated pull-in instability of beam-type nano-switches under the effects of small-scale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nano-switches, electrostatic forces served as the driving force, and von-Karman type nonlinear strain was used to examine nonlinear geometric effects. To de...