Effect of moving load on dynamics of nanoscale Timoshenko CNTs embedded in elastic media based on doublet mechanics theory

Alaa A. Abdelrahman,Rabab A. Shanab,Ismail Esen,Mohamed A Eltaher 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.44 No.2

This manuscript illustrates the dynamic response of nanoscale carbon nanotubes (CNTs) embedded in an elastic media under moving load using doublet mechanics theory, which not considered before. CNTs are modelled by Timoshenko beam theory (TBT) and a bottom to up modelling nano-mechanics is simulated by doublet mechanics theory to capture the size effect of CNTs. To explore the influence of the CNTs configurations on the dynamic behaviour, both armchair and zigzag configurations are considered. The governing equations of motion and the associated boundary conditions are obtained using the Hamiltonian principle. The Navier solution methodology is applied to obtain the solutions for both orientations. Free vibration and forced response under moving loads are considered. The accuracy of the developed procedure is verified by comparing the obtained results with available previous algorithms and good agreement is observed. Parametric studies are conducted to demonstrate effects of doublet length scale, CNTs configurations, moving load velocities as well as the elastic media parameters on the dynamic behaviours of CNTs. The developed procedure is supportive in the design and manufacturing of MEMS/NEMS made from CNTs.

Free and forced analysis of perforated beams

Alaa A. Abdelrahman,Mohamed A. Eltaher,Abdallah M. Kabeel,Azza M. Abdraboh,Asmaa A. Hendi 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.31 No.5

This article presents a unified mathematical model to investigate free and forced vibration responses of perforated thin and thick beams. Analytical models of the equivalent geometrical and material characteristics for regularly squared perforated beam are developed. Because of the shear deformation regime increasing in perforated structures, the investigation of dynamical behaviors of these structures becomes more complicated and effects of rotary inertia and shear deformation should be considered. So, both Euler-Bernoulli and Timoshenko beam theories are proposed for thin and short (thick) beams, respectively. Mathematical closed forms for the eigenvalues and the corresponding eigenvectors as well as the forced vibration time response are derived. The validity of the developed analytical procedure is verified by comparing the obtained results with both analytical and numerical analyses and good agreement is detected. Numerical studies are presented to illustrate effects of beam slenderness ratio, filling ratio, as well as the number of holes on the dynamic behavior of perforated beams. The obtained results and concluding remarks are helpful in mechanical design and industrial applications of large devices and small systems (MEMS) based on perforated structure.

On bending analysis of perforated microbeams including the microstructure effects

Alaa A. Abdelrahman,Hanaa E. Abd El Mottaleb,Mohamed A Eltaher 국제구조공학회 2020 Structural Engineering and Mechanics, An Int'l Jou Vol.76 No.6

This article presents a nonclassical size dependent model based on the modified couple stress theory to study and analyze the bending behavior of perforated microbeams under different loading patterns. Modified equivalent material and geometrical parameters for perforated beam are presented. The modified couple stress theory with one material length scale parameter is adopted to incorporate the microstructure effect into the governing equations of perforated beam structure. The governing equilibrium equations of the perforated Timoshenko as well as the perforated Euler Bernoulli are developed based on the potential energy minimization principle. The Poisson’s effect is included in the governing equilibrium equations. Regular square perforation configuration is considered. Based on Fourier series expansion, closed forms for the bending deflection and the rotational displacements are obtained for simply supported perforated microbeams. The proposed methodology is validated and compared with the available results in the literature and an excellent agreement is detected. Numerical results demonstrated the applicability of the proposed methodology to investigate the bending behavior of regularly squared perforated beams incorporating microstructure effect under different excitation patterns. The obtained results are significantly important for the design and production of perforated microbeam structures.

Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory

Alaa A. Abdelrahman,Ismail Esen,Cevat Özarpa,Ramy Shaltout,Mohamed A Eltaher,Amr E. Assie 국제구조공학회 2021 Smart Structures and Systems, An International Jou Vol.28 No.4

The goal of this manuscript is to develop a nonclassical size dependent model to study and analyze the dynamic behaviour of the perforated Reddy nanobeam under moving load including the length scale and microstructure effects, that not considered before. The kinematic assumption of the third order shear deformation beam theory in conjunction with modified continuum constitutive equation of nonlocal strain gradient (NLSG) elasticity are proposed to derive the equation of motion of nanobeam included size scale (nonlocal) and microstructure (strain gradient) effects. Mathematical expressions for the equivalent geometrical parameters due to the perforation process of regular squared pattern are developed. Based on the virtual work principle, the governing equations of motion of perforated Reddy nanobeams are derived. Based on Navier's approach, an analytical solution procedure is developed to obtain free and forced vibration response under moving load. The developed methodology is verified and checked with previous works. Impacts of perforation, moving load velocity, microstructure parameter and nonlocal size scale effects on the dynamic and vibration responses of perforated Reddy nanobeam structures have been investigated in a wide context. The obtained results are supportive for the design of MEMS/NEMS structures such as frequency filters, resonators, relay switches, accelerometers, and mass flow sensors, with perforation.

Bending behavior of squared cutout nanobeams incorporating surface stress effects

Mohamed A Eltaher,Alaa A. Abdelrahman 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.36 No.2

In nanosized structures as the surface area to the bulk volume ratio increases the classical continuum mechanics approaches fails to investigate the mechanical behavior of such structures. In perforated nanobeam structures, more decrease in the bulk volume is obtained due to perforation process thus nonclassical continuum approaches should be employed for reliable investigation of the mechanical behavior these structures. This article introduces an analytical methodology to investigate the size dependent, surface energy, and perforation impacts on the nonclassical bending behavior of regularly squared cutout nanobeam structures for the first time. To do this, geometrical model for both bulk and surface characteristics is developed for regularly squared perforated nanobeams. Based on the proposed geometrical model, the nonclassical Gurtin-Murdoch surface elasticity model is adopted and modified to incorporate the surface energy effects in perforated nanobeams. To investigate the effect of shear deformation associated with cutout process, both Euler-Bernoulli and Timoshenko beams theories are developed. Mathematical model for perforated nanobeam structure including surface energy effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Closed forms for the nonclassical bending and rotational displacements are derived for both theories considering all classical and nonclassical kinematics and kinetics boundary conditions. Additionally, both uniformly distributed and concentrated loads are considered. The developed methodology is verified and compared with the available results and an excellent agreement is noticed. Both classical and nonclassical bending profiles for both thin and thick perforated nanobeams are investigated. Numerical results are obtained to illustrate effects of beam filling ratio, the number of hole rows through the cross section, surface material characteristics, beam slenderness ratio as well as the boundary and loading conditions on the non-classical bending behavior of perforated nanobeams in the presence of surface effects. It is found that, the surface residual stress has more significant effect on the bending deflection compared with the corresponding effect of the surface elasticity, Es. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams.

On forced and free vibrations of cutout squared beams

Khalid H. Almitani,Alaa A. Abdelrahman,Mohamed A. Eltaher 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.32 No.5

Perforation and cutouts of structures are compulsory in some modern applications such as in heat exchangers, nuclear power plants, filtration and microeletromicanical system (MEMS). This perforation complicates dynamic analyses of these structures. Thus, this work tends to introduce semi-analytical model capable of investigating the dynamic performance of perforated beam structure under free and forced conditions, for the first time. Closed forms for the equivalent geometrical and material characteristics of the regular square perforated beam regular square, are presented. The governing dynamical equation of motion is derived based on Euler-Bernoulli kinematic displacement. Closed forms for resonant frequencies, corresponding Eigen-mode functions and forced vibration time responses are derived. The proposed analytical procedure is proved and compared with both analytical and numerical analyses and good agreement is noticed. Parametric studies are conducted to illustrate effects of filling ratio and the number of holes on the free vibration characteristic, and forced vibration response of perforated beams. The obtained results are supportive in mechanical design of large devices and small systems (MEMS) based on perforated structure.

Stability of perforated nanobeams incorporating surface energy effects

Khalid H. Almitani,Alaa A. Abdelrahman,Mohamed A. Eltaher 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.35 No.4

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

Static analysis of cutout microstructures incorporating the microstructure and surface effects

Mashhour A. Alazwari,Alaa A. Abdelrahman,Ahmed Wagih,Mohamed A Eltaher,Hanaa E. Abd-El-Mottaleb 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.38 No.5

This article develops a nonclassical model to analyze bending response of squared perforated microbeams considering the coupled effect of microstructure and surface stress under different loading and boundary conditions, those are not be studied before. The corresponding material and geometrical characteristics of regularly squared perforated beams relative to fully filled beam are obtained analytically. The modified couple stress and the modified Gurtin-Murdoch surface elasticity models are adopted to incorporate the microstructure as well as the surface energy effects. The differential equations of equilibrium including the Poisson’s effect are derived based on minimum potential energy. Exact closed form solution is obtained for bending behavior of the proposed model considering the classical and nonclassical boundary conditions for both uniformly distributed and concentrated loads. The proposed model is verified with results available in the literature. Influences of the microstructure length scale parameter, surface energy, beam thickness, boundary and loading conditions on the bending behavior of perforated microbeams are investigated. It is observed that microstructure and surface parameters are vital in investigation of the bending behavior of perforated microbeams. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams that commonly used in nanoactuators, nanoswitches, MEMS and NEMS systems.

On bending of cutout nanobeams based on nonlocal strain gradient elasticity theory

Mashhour A. Alazwari,Mohamed A Eltaher,Alaa A. Abdelrahman 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.43 No.6

This article aims to investigate the size dependent bending behavior of perforated nanobeams incorporating the nonlocal and the microstructure effects based on the nonlocal strain gradient elasticity theory (NSGET). Shear deformation effect due to cutout process is studied by using Timoshenko beams theory. Closed formulas for the equivalent geometrical characteristics of regularly squared cutout shape are derived. The governing equations of motion considering the nonlocal and microstructure effects are derived in comprehensive procedure and nonclassical boundary conditions are presented. Analytical solution for the governing equations of motion is derived. The derived non-classical analytical solutions are verified by comparing the obtained results with the available results in the literature and good agreement is observed. Numerical results are obtained and discussed. Parametric studies are conducted to explore effects of perforation characteristics, the nonclassical material parameters, beam slenderness ratio as well as the boundary and loading conditions on the non-classical transverse bending behavior of cutout nanobeams. Results obtained are supportive for the design, analysis and manufacturing of such nanosized structural system.

Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermo-magnetic fields and moving load

Alazwari, Mashhour A.,Esen, Ismail,Abdelrahman, Alaa A.,Abdraboh, Azza M.,Eltaher, Mohamed A. Techno-Press 2022 Advances in nano research Vol.12 No.3

Dynamic behavior of temperature-dependent Reddy functionally graded (RFG) nanobeam subjected to thermomagnetic effects under the action of moving point load is carried out in the present work. Both symmetric and sigmoid functionally graded material distributions throughout the beam thickness are considered. To consider the significance of strain-stress gradient field, a material length scale parameter (LSP) is introduced while the significance of nonlocal elastic stress field is considered by introducing a nonlocal parameter (NP). In the framework of the nonlocal strain gradient theory (NSGT), the dynamic equations of motion are derived through Hamilton's principle. Navier approach is employed to solve the resulting equations of motion of the functionally graded (FG) nanoscale beam. The developed model is verified and compared with the available previous results and good agreement is observed. Effects of through-thickness variation of FG material distribution, beam aspect ratio, temperature variation, and magnetic field as well as the size-dependent parameters on the dynamic behavior are investigated. Introduction of the magnetic effect creates a hardening effect; therefore, higher values of natural frequencies are obtained while smaller values of the transverse deflections are produced. The obtained results can be useful as reference solutions for future dynamic and control analysis of FG nanobeams reinforced nanocomposites under thermomagnetic effects.