https://northumbria-test.eprints-hosting.org/id/document/265204

A review of continuum mechanics models for size-dependent analysis of beams and plates

A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams

A unified nonlocal strain gradient model for nanobeams and the importance of higher order terms

Abstract A modified functionally graded beam theory based on the neutral axis is exploited to investigate natural frequencies of macro/nanobeams. The location of neutral axis is determined, where material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The FG nanobeam is investigated on the basis of the nonlocal Eringen continuum model. The kinematic assumption of nanobeam is proposed according to Euler–Bernoulli beam theory. The finite element method is used to discretize the model and obtain a numerical approximation of the equation of motion. The verification of the model is obtained by comparing the current results with previously published work. Numerical results are presented to show the significance of neutral axis position, the material distribution profile, and nonlocal effect on the fundamental frequencies of nanobeams.

Determination of neutral axis position and its effect on natural frequenciesof functionally graded macro/nanobeams

Modified nonlocal elasticity theory for functionally graded materials

Static and buckling analysis of functionally graded Timoshenko nanobeams

This manuscript illustrates coupled effects of nonlocal elasticity and surface properties on static and vibration characteristics of piezoelectric nanobeams using thin beam theory. The mechanical a...

Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity

This work presents a modified continuum model to explore and investigate static and vibration behaviors of perforated piezoelectric NEMS structure. The perforated nanostructure is modeled as a thin perforated nanobeam element with Euler.Bernoulli kinematic assumptions. A size scale effect is considered by included a nonlocal constitutive equation of Eringen in differential form. Modifications of geometrical parameters of perforated nanobeams are presented in simplified forms. To satisfy the Maxwell's equation, the distribution of electric potential for the piezoelectric nanobeam model is assumed to be varied as a combination of a cosine and linear functions. Hamilton's principle is exploited to develop mathematical governing equations. Modified numerical finite model is adopted to solve the equation of motion and equilibrium equation. The proposed model is validated with previous respectable work. Numerical investigations are presented to illustrate effects of the number of perforated holes, perforation size, nonlocal parameter, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric nanobeams.

Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts

This manuscript tends to investigate influences of nanoscale and surface energy on a static bending and free vibration of piezoelectric perforated nanobeam structural element, for the first time. Nonlocal differential elasticity theory of Eringen is manipulated to depict the long–range atoms interactions, by imposing length scale parameter. Surface energy dominated in nanoscale structure, is included in the proposed model by using Gurtin–Murdoch model. The coupling effect between nonlocal elasticity and surface energy is included in the proposed model. Constitutive and governing equations of nonlocal-surface perforated Euler–Bernoulli nanobeam are derived by Hamilton’s principle. The distribution of electric potential for the piezoelectric nanobeam model is assumed to vary as a combination of a cosine and linear variation, which satisfies the Maxwell’s equation. The proposed model is solved numerically by using the finite-element method (FEM). The present model is validated by comparing the obtained results with previously published works. The detailed parametric study is presented to examine effects of the number of holes, perforation size, nonlocal parameter, surface energy, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric perforated nanobeams. It is found that the effect of surface stresses becomes more significant as the thickness decreases in the range of nanometers. The effect of number of holes becomes significant in the region 0.2≤ɑ ≤0.8. The current model can be used in design of perforated nano-electro-mechanical systems (PNEMS).

Fatema-Alzahraa Omar

Papers

Static and buckling analysis of functionally graded Timoshenko nanobeams

Bending and vibrational behaviors of piezoelectric nonlocal nanobeam including surface elasticity

Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts

Mechanical analysis of cutout piezoelectric nonlocal nanobeam including surface energy effects