Abstract In this work, the state -space nonlocal strain gradient theory is used for vibration analysis of magneto thermo piezoelectric functionally graded material (FGM) nanobeam. An FGM constituent properties stated by using power law relations. The refined higher order beam and Hamilton’s principle have been to obtain motion equations. Besides, governing equations nanobeam are extracted devel...

Abstract In this work, the bending behavior of nanoplates subjected to both sinusoidal and uniform loads in hygrothermal environment is investigated. The present plate theory based on classical laminated thin with strain gradient effect take into account nonlocality nanostructures. equilibrium equations have been carried out by using principle virtual works a system partial differential sixth o...

in this paper, the stability characteristics of single-walled carbon nanotubes (swcnts) under the action of axial load are investigated. to this end, a nonlocal flügge shell model is developed to accommodate the small length scale effects. the analytical rayleigh-ritz method with beam functions is applied to the variational statement derived from the flügge-type buckling equations. molecular dy...

The equations of motion and bending of Euler-Bernoulli beam are formulated using the nonlocal elasticity theory for cantilever microtubules (MTs). The method of differential quadrature (DQ) has been used for numerical modeling. The size effect is taken into consideration using the Eringen’s non-local elasticity theory. Frequencies and deflections of MTs are obtained. Numerical results are prese...

In the present study the free vibration analysis of the functionally graded rectangular nanoplates is investigated. The nonlocal elasticity theory based on the exponential shear deformation theory has been used to obtain the natural frequencies of the nanoplate. In exponential shear deformation theory an exponential functions are used in terms of thickness coordinate to include the effect of tr...

A method is proposed herein to build beam equations for materials featuring higher-grade elasticity. As it based on the minimization of constitutive equation gap, static admissibility conditions are taken into account so that naturally converges usual resulting from Cauchy elasticity when dimensions large enough. The exemplified, Euler–Bernoulli beams, first-strain gradient and second-strain el...