<div>
	Modeling of nonlocal porous functionally graded nanobeams under moving loads</div>

Ridha A. Ahmed, Wael N. Abdullah, Nadhim M. Faleh, Mamoon A. Al-Jaafari

2025 , VOLUME 25, NUMBER 3 ( may-june )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

Publications

Editor-in-Chief

Nikiforov
Vladimir O.
D.Sc., Prof.

Partners

doi: 10.17586/2226-1494-2025-25-3-498-507

Modeling of nonlocal porous functionally graded nanobeams under moving loads

R. A. Ahmed, W. N. Abdullah, N. M. Faleh, M. A. Al-Jaafari

Read the full article

Article in English

For citation:

Ahmed R.A., Abdullah W.N., Faleh N.M., Al-Jaafari M.A. Modeling of nonlocal porous functionally graded nanobeams under moving loads. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2025, vol. 25, no. 3, pp. 498–507. doi: 10.17586/2226-1494-2025-25-3-498-507

Abstract

This study focuses on the dynamic response of porous functionally graded nanomaterials to moving loads. The analysis was performed using two approaches: the Ritz method with the help of the benefits achieved by employing Chebyshev polynomials in the cosine form and the differential quadrature method with further inverse Laplace transformation. Both approaches utilize the formulation of a nano-thin beam considering an improved higher-order beam model and nonlocal strain gradient theory with two characteristic length scales, referred to as nonlocality and strain gradient length scales. Power-law dependencies steer the constituent designs of pore-graded materials toward pore factors that influence pore volume either with a uniform or non-uniform distribution of pores. Moreover, a variable scale modulus was adopted to further improve accuracy by considering the scale effects for graded nano-thin beams. The first part of the study addresses the equation of motion, which is solved by applying the Ritz technique with Chebyshev polynomials. In the second part, the governing equations for nanobeams are discussed where the differential quadrature method is used to discretise them further, and the inverse Laplace transform is used to obtain the dynamic deflections. The results of the present study elucidate the effects of the moving load speed, nonlocal strain gradient factors, porosity, pore number and distribution, and elastic medium on the dynamic deflection of functionally graded nanobeams.

Keywords: design, material, gradient porous, moving load, nonlocal strain, porous

Acknowledgements. The authors sincerely thank Mustansiriyah University (www.uomustansiriyah.edu.iq) in Baghdad, Iraq, for their invaluable support in advancing this work.

References

Khider A.S., Aalsaud A., Faleh N.M., Abd A.K., Al-Jaafari, M.A.A., Fenjan R.M. A review on dynamic characteristics of nonlocal porous FG nanobeams under moving loads. Steel and Composite Structures, 2024, vol. 50, no. 1, pp. 15–24. https://doi.org/10.12989/scs.2024.50.1.015
Raheef K.M., Ahmed R.A., Nayeeif A.A., Fenjan R.M., Faleh N.M. Analyzing dynamic response of nonlocal strain gradient porous beams under moving load and thermal environment. Geomechanics and Engineering, 2021, vol. 26, no. 1, pp. 89–99. https://doi.org/10.12989/gae.2021.26.1.089
Zeighampour H., Beni Y.T. Cylindrical thin-shell model based on modified strain gradient theory. International Journal of Engineering Science, 2014, vol. 78, pp. 27–47. https://doi.org/10.1016/j.ijengsci.2014.01.004
Li L., Hu Y., Ling L. Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Composite Structures, 2015, vol. 133, pp. 1079–1092. https://doi.org/10.1016/j.compstruct.2015.08.014
Zhang B., He Y., Liu D., Shen L., Lei J. Free vibration analysis of four-unknown shear deformable functionally graded cylindrical microshells based on the strain gradient elasticity theory. Composite Structures, 2015, vol. 119, pp. 578–597. https://doi.org/10.1016/j.compstruct.2014.09.032
Arefi M.,Zenkour A.M. Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory. Materials Research Express, 2016, vol. 3, no. 11, pp. 115704. https://doi.org/10.1088/2053-1591/3/11/115704
Lou J., He L., Wu H., Du J. Pre-buckling and buckling analyses of functionally graded microshells under axial and radial loads based on the modified couple stress theory. Composite Structures, 2016, vol. 142, pp. 226–237. https://doi.org/10.1016/j.compstruct.2016.01.083
Zeighampour H.,Shojaeian M. Buckling analysis of functionally graded sandwich cylindrical micro/nanoshells based on the couple stress theory. Journal of Sandwich Structures & Materials, 2019, vol. 21, no. 3, pp. 917–937. https://doi.org/10.1177/1099636217703912
Farokhi H., Ghayesh M.H. Nonlinear mechanical behaviour of microshells. International Journal of Engineering Science, 2018, vol. 127, pp. 127–144. https://doi.org/10.1016/j.ijengsci.2018.02.009
Martínez-Criado G. Application of micro-and nanobeams for materials science. Synchrotron light sources and free-electron lasers: accelerator physics, instrumentation and science applications, 2016, pp. 1505–1539. https://doi.org/10.1007/978-3-319-14394-1_46
Berrabah H.M., Tounsi A., Semmah A.,Bedia E.A.A. Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams. Structural Engineering and Mechanics, 2013, vol. 48, no. 3, pp. 351–365. https://doi.org/10.12989/sem.2013.48.3.351
Aissani K., Bouiadjra M.B., Ahouel M., Tounsi A. A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium. Structural Engineering and Mechanics, 2015, vol. 55, no. 4, pp. 743–763. https://doi.org/10.12989/sem.2015.55.4.743
Bouderba B., Houari M.S.A., Tounsi A., Mahmoud S.R.Thermal stability of functionally graded sandwich plates using a simple shear deformation theory. Structural Engineering and Mechanics, 2016, vol. 58, no. 3, pp. 397–422. https://doi.org/10.12989/sem.2016.58.3.397
Chikh A., Bakora A., Heireche H., Houari M.S.A., Tounsi A., Bedia E.A.A. Thermo-mechanical postbuckling of symmetric S-FGM plates resting on Pasternak elastic foundations using hyperbolic shear deformation theory. Structural Engineering and Mechanics, 2016, vol. 57, no. 4, pp. 617–639. https://doi.org/10.12989/sem.2016.57.4.617
Yahiaoui M., Tounsi A., Fahsi B., Bouiadjra R.B., Benyoucef S. The role of micromechanical models in the mechanical response of elastic foundation FG sandwich thick beams. Structural Engineering and Mechanics, 2018, vol. 68, no. 1, pp. 53–66. https://doi.org/10.12989/sem.2018.68.1.053
Achouri F., Benyoucef S., Bourada F., Bouiadjra R. B., Tounsi A. Robust quasi 3D computational model for mechanical response of FG thick sandwich plate. Structural Engineering and Mechanics, 2019, vol. 70, no. 5, pp. 571–589. https://doi.org/10.12989/sem.2019.70.5.571
Barati M.R. Vibration analysis of porous FG nanoshells with even and uneven porosity distributions using nonlocal strain gradient elasticity. Acta Mechanica, 2018, vol. 229, no. 3, pp. 1183–1196. https://doi.org/10.1007/s00707-017-2032-z
She G.L., Yuan F.G., Ren Y.R., Liu H.B., Xiao W.S. Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Composite Structures, 2018, vol. 203, pp. 614–623. https://doi.org/10.1016/j.compstruct.2018.07.063
Şimşek, M. Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory. International Journal of Engineering Science, 2010, vol. 48, no. 12, pp. 1721–1732. https://doi.org/10.1016/j.ijengsci.2010.09.027
Abouelregal A.E., Zenkour A.M. Dynamic response of a nanobeam induced by ramp-type heating and subjected to a moving load. Microsystem Technologies, 2017, vol. 23, no. 12, pp. 5911–5920. https://doi.org/10.1007/s00542-017-3365-1
Shahsavari D., Karami B., Janghorban M., Li L. Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment. Materials Research Express, 2017, vol. 4, no. 8, pp. 085013. https://doi.org/10.1088/2053-1591/aa7d89
Zhang Q., Liu H. On the dynamic response of porous functionally graded microbeam under moving load.International Journal of Engineering Science, 2020, vol. 153, pp. 103317. https://doi.org/10.1016/j.ijengsci.2020.103317
Liu H., Zhang Q., Ma J. Thermo-mechanical dynamics of two-dimensional FG microbeam subjected to a moving harmonic load. Acta Astronautica, 2021, vol. 178, pp. 681–692. https://doi.org/10.1016/j.actaastro.2020.09.045
Menasria A., Kaci A., Bousahla A.A., Bourada F., Tounsi A., Benrahou K.H., Tounsi, Bedia E.A.A., Mahmoud S.R. A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions. Steel and Composite Structures, 2020, vol. 36, no. 3, pp. 355–367. http://dx.doi.org/10.12989/scs.2020.36.3.355
Hachemi H., Bousahla A.A., Kaci A., Bourada F., Tounsi A., Benrahou K.H., Tounsi A., Al-Zahrani M.M., Mahmoud S.R. Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position. Steel and Composite Structures, 2021, vol. 39, no. 1, pp. 51–64. http://dx.doi.org/10.12989/scs.2021.39.1.051
Heidari F., Taheri K., Sheybani M., Janghorban M., Tounsi A. On the mechanics of nanocomposites reinforced by wavy/defected/aggregated nanotubes. Steel and Composite Structures, 2021, vol. 38, no. 5, pp. 533–545. http://dx.doi.org/10.12989/scs.2021.38.5.533
Khaniki H.B., Hosseini-Hashemi S. The size-dependent analysis of multilayered microbridge systems under a moving load/mass based on the modified couple stress theory. The European Physical Journal Plus, 2017, vol. 132, no. 5, https://doi.org/10.1140/epjp/i2017-11466-0
Eringen A.C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. Journal of Applied Physics, 1983, vol. 54, no. 9, pp. 4703–4710. https://doi.org/10.1063/1.332803
Ebrahimi F., Barati M.R., Zenkour A.M. A new nonlocal elasticity theory with graded nonlocality for thermo-mechanical vibration of FG nanobeams via a nonlocal third-order shear deformation theory. Mechanics of Advanced Materials and Structures. 2018, vol. 25, no. 6, pp. 512–522. https://doi.org/10.1080/15376494.2017.1285458

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License