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Öğe Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load(Taylor & Francis Inc, 2023) Abdelrahman, Alaa A.; Esen, Ismail; Daikh, Ahmed Amin; Eltaher, Mohamed A.In the context of nonclassical continuum mechanics, the nonlocal strain gradient theory is employed to develop a nonclassical size dependent model to investigate the dynamic behavior of a CNTs reinforced composite beam resting on two parameters elastic foundations under a moving load. The governing dynamic equations of motion are derived based on third-order shear deformation theory using Hamilton's principle. An analytical solution methodology is developed using Navier's procedure is developed to derive the analytical solution for the equations of motion. The developed methodology is checked and compared. Parametric studies are conducted to demonstrate the applicability of the developed procedure to investigate the dynamic behavior of CNTs beams under moving load. Effects of the elastic foundation parameters, volume fraction, CNTs configuration, the nonclassical parameters, and the moving load velocity parameter on the dynamic behavior of CNTs beams under moving load are investigated and analyzed. The obtained results are supportive for design and manufacturing of composite CNTs beams.Öğe Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermo-magnetic fields and moving load(Techno-Press, 2022) Alazwari, Mashhour A.; Esen, Ismail; Abdelrahman, Alaa A.; Abdraboh, Azza M.; Eltaher, Mohamed A.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.Öğe Dynamic response of FG porous nanobeams subjected thermal and magnetic fields under moving load(Techno-Press, 2022) Esen, Ismail; Alazwari, Mashhour A.; Eltaher, Mohamed A.; Abdelrahman, Alaa A.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.Öğe Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load(Springer Heidelberg, 2021) Esen, Ismail; Daikh, Ahmed Amin; Eltaher, Mohamed A.In this study, the dynamic behavior of composite beams reinforced by carbon nanotubes (CNTs) exposed to a mass moving is investigated. By considering the external potential energy due to the applied moving mass, the equations of motion of the CNT-reinforced beam are obtained using Hamilton's principle by combining Reddy's third-order shear deformation theory and nonlocal strain gradient theory. Three types of aligned CNT-reinforced beams are considered, namely uniformly distributed CNT beams (UD-CNT) and functionally graded CNT beams type ? (FG?-CNT), and type X (FGX-CNT). Navier's procedure is applied to obtain the closed-form solutions of simply supported CNT-reinforced beams. Verification of the present solution with previous works is presented. A detailed parametric analysis is carried out to highlight the impact of moving load velocity, nonlocal parameter, material scale parameter, total volume fraction and CNTs distribution patterns on the midspan deflections of CNTs-reinforced composite beams. The proposed model is useful in the designing and analyzing of MEMS/NEMS, nanosensor, and nanoactuator manufactured from CNTs.Öğe Dynamic vibration response of functionally graded porous nanoplates in thermal and magnetic fields under moving load(Techno-Press, 2023) Esen, Ismail; Alazwari, Mashhour A.; Almitani, Khalid H.; Eltaher, Mohamed A.; Abdelrahman, A.In the context of nonclassical nonlocal strain gradient elasticity, this article studies the free and forced responses of functionally graded material (FGM) porous nanoplates exposed to thermal and magnetic fields under a moving load. The developed mathematical model includes shear deformation, size-scale, miscorstructure influences in the framework of higher order shear deformation theory (HSDT) and nonlocal strain gradient theory (NSGT), respectively. To explore the porosity effect, the study considers four different porosity models across the thickness: uniform, symmetrical, asymmetric bottom, and asymmetric top distributions. The system of quations of motion of the FGM porous nanoplate, including the effects of thermal load, Lorentz force, due to the magnetic field and moving load, are derived using the Hamilton's principle, and then solved analytically by employing the Navier method. For the free and forced responses of the nanoplate, the effects of nonlocal elasticity, strain gradient elasticity, temperature rise, magnetic field intensity, porosity volume fraction, and porosity distribution are analyzed. It is found that the forced vibrations of FGM porous nanoplates under thermal and live loads can be damped by applying a directed magnetic field.Öğe Dynamics analysis of timoshenko perforated microbeams under moving loads(Springer, 2022) Esen, Ismail; Abdelrahman, Alaa A.; Eltaher, Mohamed A.This paper aims to present a modified continuum mathematical model capable on investigation of dynamic behavior and response of perforated microbeam under the effect of moving mass/load for the first time. A size-dependent finite element model with non-classical shape function is exploited to solve the mathematical model and obtain the dynamic response of perforated Timoshenko microbeams under moving loads. To that end, first, equivalent material and geometrical parameters for perforated beam are developed, based on the regular squared perforation configuration. Second, both the stiffness and mass property matrices including the microstructure effect based on modified couple stress theory and Timoshenko first-order shear beam theory are derived for two-node finite element using new shape function. After that, the interaction between the load and beam is modeed and unified with the equation of motion of the beam incorporating mass inertia effects of moving load. The developed procedure is validated and compared. Effects of perforation parameters, moving load velocities, inertia of mass, and the microstructure size parameter on the dynamic response of perforated microbeam structures have been investigated in a wide context. The achieved results are helpful for the design and production of MEMS structures such as frequency filters, resonators, relay switches, accelerometers and mass flow sensors, with perforation.Öğe Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory(Techno-Press, 2021) Abdelrahman, Alaa A.; Esen, Ismail; Ozarpa, Cevat; Shaltout, Ramy; Eltaher, Mohamed A.; Assie, Amr E.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.Öğe Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory(Elsevier Science Inc, 2021) Abdelrahman, Alaa A.; Esen, Ismail; Ozarpa, Cevat; Eltaher, Mohamed A.In the present manuscript, based on the nonlocal strain gradient theory, a nonclassical dynamic finite element model is developed to study and analyze the dynamic behavior of perforated nanobeam structures under moving mass/load. In the context of nonclassical continuum mechanics and Timoshenko beam theory, dynamic equations of motion of perforated nanobeams are derived including both size scale (nonlocal) and microstructure (strain gradient) effects. The modification of the geometrical parameters due to the perforation process is included in the equations of motion for squared holes arranged in the arrayed form. The effect of the moving mass (the inertia, Coriolis and centripetal forces, and the gravity force) or moving load are included in the proposed model. To remove shear locking problem in slender nanobeams, finite element model on nonclassical shape function basis is developed. Elements stiffness and mass matrices and force vector including the nonlocal and strain gradient effects are derived. The proposed model is verified and checked with previous works. Impacts of perforation, mass/load velocities, inertia of mass, microstructure parameter and nonlocal size scale effects on the dynamic and vibration responses of perforated nanobeam structures have been investigated in a wide context. The following model is beneficial for the design of MEMS/NEMS structures such as frequency filters, resonators, relay switches, accelerometers, and mass flow sensors, with perforation. (c) 2021 Elsevier Inc. All rights reserved.Öğe Effect of moving load on dynamics of nanoscale Timoshenko CNTs embedded in elastic media based on doublet mechanics theory(Techno-Press, 2022) Abdelrahman, Alaa A.; Shanab, Rabab A.; Esen, Ismail; Eltaher, Mohamed A.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.Öğe Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields(Springer, 2022) Esen, Ismail; Abdelrhmaan, Alaa A.; Eltaher, Mohamed A.Due to the increasing usage of nanostructures in nanotechnology and nanodevice, the following article aims to investigate the free vibration and buckling behaviours of a Timoshenko functionally graded nanobeam under to thermal and magnetic environment. The nanoscale and microstructure effects of FG nanobeam are included to classical mechanics using nonlocal strain gradient theory. The gradation of material properties throughout the beam thickness is described by power-law function. The material properties are assumed to be temperature dependent. Considering the thermal and Lorentz forces, the equations of motion of the functionally graded Timoshenko nanobeam are obtained using the strain gradient and nonlocal elasticity theories. The transverse Lorentz force induced by the horizontal magnetic field vector is derived using Maxwell's equations. External compressive axial and transverse point loads are included in the formulation and the motion equations are solved using a Navier-type approach. The effects nonlocal size scale, and strain gradient microstructure influence, thermal loadings and magnetic field intensities on the free vibration, transverse bending and buckling behaviours of the functionally graded nanobeam are presented. The following model can be used as benchmark to analyse the nanobeam structure under thermomagnetic field using a finite element or any other numerical method.Öğe Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment(Elsevier Sci Ltd, 2021) Esen, Ismail; Ozarpa, Cevat; Eltaher, Mohamed A.A mathematical model is developed, though this article, to investigate a vibrational behaviour of functionally graded (FG) cracked microbeam rested on elastic foundation and exposed to thermal and magnetic fields. The model includes a size scale effect and temperature dependent material properties, for the first time. The crack is modelled as a rotating spring, that is connecting the two parts of the microbeam at the crack's position. The equation of motion of the FG microbeam is obtained by using the Euler-Bernoulli beam theory for kinematic assumption and nonlocal elasticity theory for size- dependency effects. The transverse Lorentz force induced from the magnetic field is derived using Maxwell's equations. By adding the effects of thermal loading and foundation parameters on the cracked micro beam, the motion equation of the entire system is obtained using the Hamilton's principle and then solved with a Navier type solution method. Eight constraints equations are used to derived the frequency equation, which are boundary conditions at the end points and the displacement, slope, bending moment and transverse force continuity in the section where the crack is located. The resulting system of equations is solved sequentially, and natural frequencies and vibration modes of the cracked microbeam are obtained. The model is verified with previous published work. Numerical results are presented to illustrate influences of temperature, material composition, foundation parameters and magnetic field on the dynamics of the cracked FG microbeam.Öğe On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load(Springer Heidelberg, 2021) Esen, Ismail; Abdelrahman, Alaa A.; Eltaher, Mohamed A.In the framework of nonlocal strain gradient theory, a size-dependent symmetric and sigmoid functionally graded (FG) Timoshenko beam model is developed to study and analyze the free vibration and dynamic response under moving load, for the first time. To incorporate the size-dependent effect, the nonlocal strain gradient theory is adopted. The Hamilton principle is employed to drive the dynamic equations of motion and the associated boundary conditions. Based on Navier's approach, an analytical solution methodology for free and forced vibration problems is developed. The developed methodology is verified by comparing the obtained results with the available resources and good agreement is observed. Numerical results are obtained and discussed. Effects of the material gradation index, nonlocal parameter, microstructure length scale parameter, and the nondimensional velocity parameter of the moving load on the dynamic behavior are investigated. It is found that these variables significantly affect the dynamic behavior of the functionally graded nanobeams, and they could be adjusted to control this behavior. Obtained results are supportive of the design and control of such types of structural components.Öğe On vibrations of functionally graded carbon nanotube (FGCNT) nanoplates under moving load(Techno-Press, 2024) Abdelrahman, Alaa A.; Esen, Ismail; Tharwan, Mohammed Y.; Assie, Amr; Eltaher, Mohamed A.This article develops a nonclassical size dependent nanoplate model to study the dynamic response of functionally graded carbon nanotube (FGCNT) nanoplates under a moving load. Both nonlocal and microstructure effects are incorporated through the nonlocal strain gradient elasticity theory. To investigate the effect of reinforcement orientation of CNT, four different configurations are studied and analysed. The FGM gradation thorough the thickness direction is simulated using the power law. In the context of the first order shear deformation theory, the dynamic equations of motion and the associated boundary conditions are derived by Hamilton's principle. An analytical solution of the dynamic equations of motion is derived based on the Navier methodology. The proposed model is verified and compared with the available results in the literature and good agreement is found. The numerical results show that the dynamic performance of FGCNT nanoplates could be governed by the reinforcement pattern and volume fraction in addition to the non -classical parameters and the moving load dimensionless parameter. Obtained results are reassuring in design and analysis of nanoplates reinforced with CNTs.Öğe Vibration response of symmetric and sigmoid functionally graded beam rested on elastic foundation under moving point mass(Taylor & Francis Inc, 2023) Esen, Ismail; Eltaher, Mohamed A.; Abdelrahman, Alaa A.This article investigates dynamic responses of symmetric and sigmoid FG Timoshenko beam rested on elastic foundation and subjected to moving mass. The gradation is described by symmetrical and sigmoidal law functions. The Hamilton principle is exploited to derive the system equations of motion. Finite element has been developed to convert the partial differential equations to ordinary equations in time domain, those will be solved incrementally by Newmark method. The model is verified. Parametric studies are presented to investigate influences of gradation type, gradation index, elastic foundation stiffnesses, inertia, and variable velocity of the moving mass on the dynamic response.Öğe Vibration response of Timoshenko perforated microbeams under load and thermal environment(Elsevier Science Inc, 2021) Abdelrahman, Alaa A.; Esen, Ismail; Eltaher, Mohamed A.This article presents a dynamic finite elements procedure capable of analyzing the dynamic behavior of perforated Timoshenko microbeams in thermal environment and subjected to moving mass for the first time. An analytical geometrical model is presented to incorporate the perforation effect into the governing equations. The microstructure size dependent effect is incorporated based on the modified couple stress theory. Based on the presented geometrical model, the dynamic equations of motion including the interaction terms of the mass inertia are derived from the exact differential of the displacement functions of the beam relative to the mass contact point. To investigate the temperature effect on the dynamic behavior, thermal loading with different temperature rise profiles are considered. Thermal stresses, due to thermal loads are converted to mechanical stresses and then the thermal rigidity matrix is combined with the stiffness matrix of the beam. The dynamic finite element equations of motion are derived including the thermal effect. The system equations are solved numerically by using implicit time integration method due to its stability. The proposed numerical procedure is checked by comparing the obtained results with the available solutions and good agreement is observed. Effects of perforation parameters, thermal loading profile, moving mass characteristics, as well as the moving speed on the dynamic behavior of perforated microbeams are studied. The obtained results are helpful in the design and manufacturing of perforated microbeams structural systems. (c) 2021 Elsevier Inc. All rights reserved.
