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Transient response of porous inhomogeneous nanobeams due to various impulsive loads based on nonlocal strain gradient elasticity

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Abstract

Transient vibration responses of a porosity-dependent functionally graded nanobeam under different impulsive loadings have been investigated in the context of non-local strain gradient theory. Three impulse loads of rectangular-type, linear-type and sine-type have been applied to top surface of nanobeam. Two porosity distribution types known as even and uneven are discussed. Governing equations of the nanobeam are solved via inverse Laplace transform approach to express the dynamic deflections. One can see that the transient response of nano-size beams is influenced by the type and location of pulse load, porosities volume fractions, porosities distributions, non-local and strain gradient coefficients.

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References

  • Atmane, H.A., Tounsi, A., Bernard, F.: Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations. Int. J. Mech. Mater. Des. 13(1), 71–84 (2017)

    Article  Google Scholar 

  • Attia, M.A., Mahmoud, F.F.: Analysis of viscoelastic Bernoulli–Euler nanobeams incorporating nonlocal and microstructure effects. Int. J. Mech. Mater. Des. 13(3), 385–406 (2017)

    Article  Google Scholar 

  • Barati, M.R., Faleh, N.M., Zenkour, A.M.: Dynamic response of nanobeams subjected to moving nanoparticles and hygro-thermal environments based on nonlocal strain gradient theory. Mech. Adv. Mater. Struct. 1–9 (2018)

  • Barati, M.R., Shahverdi, H., Zenkour, A.M.: Electro-mechanical vibration of smart piezoelectric FG plates with porosities according to a refined four-variable theory. Mech. Adv. Mater. Struct. 24(12), 987–998 (2017)

    Article  Google Scholar 

  • Bourada, M., Kaci, A., Houari, M.S.A., Tounsi, A.: A new simple shear and normal deformations theory for functionally graded beams. Steel Compos. Struct. 18(2), 409–423 (2015)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R.: Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory. J. Therm. Stresses 39(12), 1560–1571 (2016a)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R.: A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures. Int. J. Eng. Sci. 107, 183–196 (2016b)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R.: Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory. Compos. Struct. 159, 433–444 (2017a)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R.: A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams. Compos. Struct. 159, 174–182 (2017b)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R.: Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory. Compos. Struct. 166, 256–267 (2017c)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R.: Longitudinal varying elastic foundation effects on vibration behavior of axially graded nanobeams via nonlocal strain gradient elasticity theory. Mech. Adv. Mater. Struct. 25(11), 953–963 (2018a)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R.: Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory. Mech. Adv. Mater. Struct. 25(4), 350–359 (2018b)

    Article  Google Scholar 

  • Ebrahimi, F., Mokhtari, M.: Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method. J. Braz. Soc. Mech. Sci. Eng. 37(4), 1435–1444 (2015)

    Article  Google Scholar 

  • Ebrahimi, F., Salari, E.: Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams. Mech. Adv. Mater. Struct. 23(12), 1379–1397 (2016)

    Article  Google Scholar 

  • Ebrahimi, F., Barati, M.R., Dabbagh, A.: A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates. Int. J. Eng. Sci. 107, 169–182 (2016)

    Article  Google Scholar 

  • Eltaher, M.A., Emam, S.A., Mahmoud, F.F.: Free vibration analysis of functionally graded size-dependent nanobeams. Appl. Math. Comput. 218(14), 7406–7420 (2012)

    MathSciNet  MATH  Google Scholar 

  • Eltaher, M.A., Agwa, M.A., Mahmoud, F.F.: Nanobeam sensor for measuring a zeptogram mass. Int. J. Mech. Mater. Des. 12(2), 211–221 (2016)

    Article  Google Scholar 

  • Ghadiri, M., Hosseini, S.H.S., Shafiei, N.: A power series for vibration of a rotating nanobeam with considering thermal effect. Mech. Adv. Mater. Struct. 23(12), 1414–1420 (2016)

    Article  Google Scholar 

  • Ghayesh, M.H., Farajpour, A.: Nonlinear coupled mechanics of nanotubes incorporating both nonlocal and strain gradient effects. Mech. Adv. Mater. Struct. 1–10 (2018)

  • Houari, M.S.A., Bessaim, A., Bernard, F., Tounsi, A., Mahmoud, S.R.: Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter. Steel Compos. Struct. 28(1), 13–24 (2018)

    Google Scholar 

  • Ke, L.L., Wang, Y.S., Wang, Z.D.: Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory. Compos. Struct. 94(6), 2038–2047 (2012)

    Article  Google Scholar 

  • Lam, D.C., Yang, F., Chong, A.C.M., Wang, J., Tong, P.: Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51(8), 1477–1508 (2003)

    Article  Google Scholar 

  • Li, L., Hu, Y.: Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int. J. Eng. Sci. 97, 84–94 (2015)

    Article  MathSciNet  Google Scholar 

  • Li, X., Li, L., Hu, Y., Ding, Z., Deng, W.: Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory. Compos. Struct. 165, 250–265 (2017)

    Article  Google Scholar 

  • Li, L., Tang, H., Hu, Y.: Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature. Compos. Struct. 184, 1177–1188 (2018)

    Article  Google Scholar 

  • Lu, L., Guo, X., Zhao, J.: Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory. Int. J. Eng. Sci. 116, 12–24 (2017)

    Article  MathSciNet  Google Scholar 

  • Martinez-Criado, G.: Application of micro- and nanobeams for materials science. In: Jaeschke, E., Khan, S., Schneider, J., Hastings, J. (eds.) Synchrotron light sources and free-electron lasers, pp. 1505–1539. Springer, Cham (2016)

    Google Scholar 

  • Qu, Y., Wu, S., Li, H., Meng, G.: Three-dimensional free and transient vibration analysis of composite laminated and sandwich rectangular parallelepipeds: beams, plates and solids. Compos. B Eng. 73, 96–110 (2015)

    Article  Google Scholar 

  • Shafiei, N., Mousavi, A., Ghadiri, M.: On size-dependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams. Int. J. Eng. Sci. 106, 42–56 (2016)

    Article  Google Scholar 

  • 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. Compos. Struct. 203, 614–623 (2018a)

    Article  Google Scholar 

  • She, G.L., Yuan, F.G., Ren, Y.R.: On wave propagation of porous nanotubes. Int. J. Eng. Sci. 130, 62–74 (2018b)

    Article  MathSciNet  Google Scholar 

  • She, G.L., Ren, Y.R., Yuan, F.G., Xiao, W.S.: On vibrations of porous nanotubes. Int. J. Eng. Sci. 125, 23–35 (2018c)

    Article  MathSciNet  Google Scholar 

  • She, G.L., Yuan, F.G., Karami, B., Ren, Y.R., Xiao, W.S.: On nonlinear bending behavior of FG porous curved nanotubes. Int. J. Eng. Sci. 135, 58–74 (2019)

    Article  MathSciNet  Google Scholar 

  • Sidhardh, S., Ray, M.C.: Effect of nonlocal elasticity on the performance of a flexoelectric layer as a distributed actuator of nanobeams. Int. J. Mech. Mater. Des. 14(2), 297–311 (2018)

    Article  Google Scholar 

  • Şimşek, M., Yurtcu, H.H.: Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Compos. Struct. 97, 378–386 (2013)

    Article  Google Scholar 

  • Wang, Y.Q., Zu, J.W.: Vibration characteristics of moving sigmoid functionally graded plates containing porosities. Int. J. Mech. Mater. Des. 14(4), 473–489 (2018)

    Article  Google Scholar 

  • Zemri, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A.: A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Struct. Eng. Mech. 54(4), 693–710 (2015)

    Article  Google Scholar 

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Acknowledgements

The first and second authors would like to thank FPQ (Fidar project Qaem) for providing the fruitful and useful help.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Qatar University, P.O. Box 2713, Doha, Qatar

    Seyed Sajad Mirjavadi & A. M. S. Hamouda

  2. School of Mechanical Engineering, College of Engineering, Sharif University of Technology, Tehran, Iran

    Behzad Mohasel Afshari

  3. Fidar Project Qaem Company, Co. Reg. Number: 459126, Darvazeh Dowlat, Tehran, Iran

    Mohammad Reza Barati

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  1. Seyed Sajad Mirjavadi
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  2. Behzad Mohasel Afshari
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  3. Mohammad Reza Barati
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  4. A. M. S. Hamouda
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Correspondence to Seyed Sajad Mirjavadi.

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Mirjavadi, S.S., Afshari, B.M., Barati, M.R. et al. Transient response of porous inhomogeneous nanobeams due to various impulsive loads based on nonlocal strain gradient elasticity. Int J Mech Mater Des 16, 57–68 (2020). https://doi.org/10.1007/s10999-019-09452-2

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  • DOI: https://doi.org/10.1007/s10999-019-09452-2

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