Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models

Emad E. Ghandourh,Azza M. Abdraboh 국제구조공학회 2020 Steel and Composite Structures, An International J Vol.36 No.3

This article presented a nanoscale modified continuum model to investigate the free vibration of functionally graded (FG) porous nanobeam by using finite element method. The main novelty of this manuscript is presenting effects of four different porosity models on vibration behaviors of nonlocal nanobeam structure including size effect, that not be discussed before The proposed porosity models are, uniform porosity distribution, symmetric with mid-plane, bottom surface distribution and top surface distribution. The nano-scale effect is included in modified model by using the differential nonlocal continuum theory of Eringen that adding the length scale into the constitutive equations as a material parameter constant. The graded material is distributed through the beam thickness by a generalized power law function. The beam is simply supported, and it is assumed to be thin. Therefore, the kinematic assumptions of Euler-Bernoulli beam theory are held. The mathematical model is solved numerically using the finite element method. Results demonstrate effects of porosity type, material gradation, and nanoscale parameters on the free vibration of nanobeam. The proposed model is effective in vibration analysis of NEMS structure manufactured by porous functionally graded materials.

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.

Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model

Ghandourah, Emad E.,Ahmed, Hitham M.,Eltaher, Mohamed A.,Attia, Mohamed A.,Abdraboh, Azza M. Techno-Press 2021 Advances in nano research Vol.11 No.4

This paper explores the size-dependent vibration response of porous functionally graded (FG) micro/nanobeams based on an integrated nonlocal-couple stress continuum model (NLCS). The mutual effect of the microstructure local rotation and nonlocality are modelled using the modified couple stress theory and Eringen nonlocal elasticity theory, respectively, into the classical Euler-Bernoulli beam model. All the material properties of the bulk continuum including the microstructure material length scale parameter (MLSP) are assumed to be graded along the thickness according to a power law. For the first time, the effect of the porosity and voids on the modulus of elasticity and MLSP is taken as a ratio of the mass density with porosity-to-that without porosity. Accounting for the physical neutral axis concept and generalized elasticity theory, Hamilton's principle is utilized to formulate the equations of motion and boundary conditions for the FG porous micro/nanobeams. The analytical solution using Navier method is applied to solve the governing equations and obtain the results. The impact of different parameters such as the gradation index, porosity pattern, porosity parameter, nonlocal parameter, and MLSP on the free vibration characteristics of simply supported FG nanobeams are presented discussed in detail. The current model is efficient in many applications used porous FGM, such as aerospace, nuclear, power plane sheller, and marine structures.

Mechanical behaviors of piezoelectric nonlocal nanobeam with cutouts

Mohamed A. Eltaher,Fatema-Alzahraa Omar,Azza M. Abdraboh,Waleed S. Abdalla,Amal E. Alshorbagy 국제구조공학회 2020 Smart Structures and Systems, An International Jou Vol.25 No.2

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.

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.

Experimental and numerical FEM of woven GFRP composites during drilling

Mohamed S. Abd-Elwahed,Usama A. Khashaba,Khaled I. Ahmed,Mohamed A. Eltaher,Ismael Najjar,Ammar Melaibari,Azza M. Abdraboh 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.80 No.5

This paper investigates experimentally and numerically the influence of drilling process on the mechanical and thermomechanical behaviors of woven glass fiber reinforced polymer (GFRP) composite plate. Through the experimental analysis, a CNC machine with cemented carbide drill (point angles =118° and 6 mm diameter) was used to drill a woven GFRP laminated squared plate with a length of 36.6 mm and different thicknesses. A produced temperature during drilling “heat affected zone (HAZ)” was measured by two different procedures using thermal IR camera and thermocouples. A thrust force and cutting torque were measured by a Kistler 9272 dynamometer. The delamination factors were evaluated by the image processing technique. Finite element model (FEM) has been developed by using LS-Dyna to simulate the drilling processing and validate the thrust force and torque with those obtained by experimental technique. It is found that, the present finite element model has the capability to predict the force and torque efficiently at various drilling conditions. Numerical parametric analysis is presented to illustrate the influences of the speeding up, coefficient of friction, element type, and mass scaling effects on the calculated thrust force, torque and calculation’s cost. It is found that, the cutting time can be adjusted by drilling parameters (feed, speed, and specimen thickness) to control the induced temperature and thus, the force, torque and delamination factor in drilling GFRP composites. The delamination of woven GFRP is accompanied with edge chipping, spalling, and uncut fibers.