• Advances in nano research
• /
• v.7 no.4
• /
• pp.223-231
• /
• 2019

In this article the frequency response of magneto-flexo-electric rotary porous (MFERP) nanobeams subjected to thermal loads has been investigated through nonlocal strain gradient elasticity theory. A quasi-3D beam model beam theory is used for the expositions of the displacement components. With the aid of Hamilton's principle, the governing equations of MFERP nanobeams are obtained. Further, administrating an analytical solution the frequency problem of MFERP nanobeams are solved. In addition the numerical examples are also provided to evaluate the effect of nonlocal strain gradient parameter, hygro thermo environment, flexoelectric effect, in-plane magnet field, volume fraction of porosity and angular velocity on the dimensionless eigen frequency.

• Advances in nano research
• /
• v.7 no.5
• /
• pp.351-364
• /
• 2019

In this work, dynamic behavior of functionally graded (FG) porous nano-beams is studied based on nonlocal nth-order shear deformation theory which takes into the effect of shear deformation without considering shear correction factors. It has been observed that during the manufacture of "functionally graded materials" (FGMs), micro-voids and porosities can occur inside the material. Thus, in this work, the investigation of the dynamic analysis of FG beams taking into account the influence of these imperfections is established. Material characteristics of the FG beam are supposed to be vary continuously within thickness direction according to a "power-law scheme" which is modified to approximate material characteristics for considering the influence of porosities. A comparative study with the known results in the literature confirms the accuracy and efficiency of the current nonlocal nth-order shear deformation theory.

• Structural Monitoring and Maintenance
• /
• v.6 no.2
• /
• pp.147-159
• /
• 2019

In present article, a size-dependent refined thick beam element has been established based upon nonlocal elasticity theory. Next, it is used to explore vibration response of porous metal foam nanobeams on elastic medium. The established beam element introduces ten degrees of freedom. Different porosity distributions called uniform, symmetric and asymmetric will be employed. Herein, introduced thick beam element contains shear deformations without using correction factors. Convergence and verification studies of obtained results from finite element method are also provided. The impacts of nonlocality factor, foundation factors, shear deformation, slenderness ratio, porosity kinds and porosity factor on vibration frequencies of metal foam nano-sized beams have been explored.

• Advances in nano research
• /
• v.7 no.6
• /
• pp.379-390
• /
• 2019

Putting emphasis on the effect of existence of porosity in the functionally graded materials (FGMs) on the dynamic responses of waves scattered in FG nanobeams resulted in implementation of a novel porosity-based homogenization method for FGMs and show its applicability in a wave propagation problem in the presence of axial pre-load for the first time. In the employed porosity-dependent method, the coupling between density and Young's moduli is included to consider for the effective moduli of the FG nanobeam by the means of a more reliable homogenization technique. The beam-type element will be modeled via the classical theory of beams, namely Euler-Bernoulli beam theory. Also, the dynamic form of the principle of virtual work will be extended for such nanobeams to derive the motion equations. Applying the nonlocal constitutive equations of Eringen on the obtained motion equations will be resulted in derivation of the nanobeam's governing equations. Depicted results reveal that the dispersion responses of FG nanobeams will be decreased as the porosity volume fraction is increased which must be noticed by the designers of advanced nanosize devices who are interested in employment of wave dispersion approach in continuous systems for specific goals.

• Advances in materials Research
• /
• v.6 no.1
• /
• pp.45-63
• /
• 2017

In this article, static deflection and buckling of functionally graded (FG) nanoscale beams made of porous material are carried out based on the nonlocal Timoshenko beam model which captures the small scale influences. The exact position of neutral axis is fixed, to eliminate the stretching and bending coupling due to the unsymmetrical material change along the FG nanobeams thickness. The material properties of FG beam are graded through the thickness on the basis of the power-law form, which is modified to approximate the material properties with two models of porosity phases. By employing Hamilton's principle, the nonlocal governing equations of FG nanobeams are obtained and solved analytically for simply-supported boundary conditions via the Navier-type procedure. Numerical results for deflection and buckling of FG nanoscale beams are presented and validated with those existing in the literature. The influences of small scale parameter, power law index, porosity distribution and slenderness ratio on the static and stability responses of the FG nanobeams are all explored.

• Steel and Composite Structures
• /
• v.42 no.6
• /
• pp.805-826
• /
• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.