Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

linear dynamic response of simply supported nanobeams subjected to a variable axial force is assessed by galerkin numerical approach. constitutive behavior is described by three functional forms of elastic energy densities enclosing nonlocal and strain gradient effects and their combination. linear stationary dynamics of nanobeams is modulated by an axial force which controls the global stiffne...

Classical effective descriptions of heterogeneous materials fail to capture the influence of the spatial scale of the heterogeneity on the overall response of components. This influence may become important when the scale at which the effective continuum fields vary approaches that of the microstructure of the material and may then give rise to size effects and other deviations from the classic...

A new driving mechanism for direction-controlled motion of nano-scale objects is proposed, based on a model of stretching a graphene strip linked to a rigid base with linear springs of identical stiffness. We find that the potential energy difference induced by the strain gradient field in the graphene strip substrate can generate sufficient force to overcome the static and kinetic friction for...

A critical examination is made of two classes of strain gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quantities expressed in terms of increments of strains and their gradients, whereas the other class employs incremental relationships between all stress quantities and the increments of strains and their g...

We study the consensus decentralized optimization problem where objective function is average of $n$ agents private non-convex cost functions; moreover, can only communicate to their neighbors on a given network topology. The stochastic learning setting considered in this paper each agent access noisy estimate its gradient. ...