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...

In this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. This strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. From the best knowledge of author, it is the first time that this theory is used for investigating wave pro...

in this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. this strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. from the best knowledge of author, it is the first time that this theory is used for investigating wave pro...

Strain gradient elasticity and nonlocal are two enhanced elastic theories intensively used over the last fifty years to explain static dynamic phenomena that classical fails do. The theory has a clear differentiation from case by considering stresses at point of continuum as an integral defined in treated body. On other hand, strain is characterized non-classical because considers both potentia...

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano-...

For classical elasticity, the constitutive equations (Hooke’s law) have the same functional form for both homogeneous and nonhomogeneous materials. However, for straingradient elasticity, such is not the case. This paper shows that for strain-gradient elasticity with volumetric and surface energy (Casal’s continuum), extra terms appear in the constitutive equations which are associated with the...

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...

   The main purpose of the present investigation is to analyze more comprehensively the size-dependent nonlinear free vibration response of multilayer functionally graded graphene platelet-reinforced composite (GPLRC) nanobeams. As a consequence, both of the hardening stiffness and softening stiffness of size effect are taken into consideration by implementation of the nonlocal str...

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 forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...