Wave dispersion in viscoelastic FG nanobeams via a novel spatial–temporal nonlocal strain gradient framework

References

• Ebrahimi F, Dabbagh A. Wave propagation analysis of smart nanostructures. 1st ed. Boca Raton (FL): CRC Press; 2019.
   Google Scholar
• Ebrahimi F, Dabbagh A. A novel porosity-based homogenization scheme for propagation of waves in axially-excited FG nanobeams. Adv Nano Res. 2019;7(6):379–390.
   Web of Science ®Google Scholar
• Ebrahimi F, Rastgo A. An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory. Thin-Walled Struct. 2008 2008/12/01/;46(12):1402–1408.
   Web of Science ®Google Scholar
• Ebrahimi F, Rastgoo A. Free vibration analysis of smart annular FGM plates integrated with piezoelectric layers. Smart Mater Struct. 2008;17(1):015044.
   Web of Science ®Google Scholar
• Ebrahimi F, Rastgoo A, Atai AA. A theoretical analysis of smart moderately thick shear deformable annular functionally graded plate. Eur J Mech A Solids. 2009 2009/09/01/;28(5):962–973.
   Web of Science ®Google Scholar
• Li S-R, Su H-D, Cheng C-J. Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment. Appl Math Mech. 2009 2009/08/01;30(8):969–982.
   Web of Science ®Google Scholar
• Kiani Y, Eslami MR. Thermal buckling analysis of functionally graded material beams. Int J Mech Mater Des. 2010 2010/09/01;6(3):229–238.
   Web of Science ®Google Scholar
• Sepiani HA, Rastgoo A, Ebrahimi F, et al. Vibration and buckling analysis of two-layered functionally graded cylindrical shell, considering the effects of transverse shear and rotary inertia. Mater Des. 2010 2010/03/01/;31(3):1063–1069.
   Web of Science ®Google Scholar
• Sun D, Luo S-N. Wave propagation of functionally graded material plates in thermal environments. Ultrasonics. 2011 2011/12/01/;51(8):940–952.
   PubMed Web of Science ®Google Scholar
• Thai H-T, Choi D-H. A refined shear deformation theory for free vibration of functionally graded plates on elastic foundation. Composites Part B. 2012 2012/07/01/;43(5):2335–2347.
   Web of Science ®Google Scholar
• Kiani Y, Eslami MR. An exact solution for thermal buckling of annular FGM plates on an elastic medium. Composites Part B. 2013 2013/02/01/;45(1):101–110.
   Web of Science ®Google Scholar
• Thai H-T, Park T, Choi D-H. An efficient shear deformation theory for vibration of functionally graded plates. Arch Appl Mech. 2013 2013/01/01;83(1):137–149.
   Web of Science ®Google Scholar
• Nejad M Z, Rastgoo A, Hadi A. Exact elasto-plastic analysis of rotating disks made of functionally graded materials. Int J Eng Sci. 2014 2014/12/01/;85:47–57.
   Web of Science ®Google Scholar
• Shahsavari D, Shahsavari M, Li L, et al. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerosp Sci Technol. 2018 2018/01/01/;72:134–149.
   Web of Science ®Google Scholar
• Iijima S. Helical microtubules of graphitic carbon. Nature. 1991 1991/11/01;354(6348):56–58.
   Web of Science ®Google Scholar
• Iijima S, Ichihashi T. Single-shell carbon nanotubes of 1-nm diameter. Nature. 1993 1993/06/01;363(6430):603–605.
   Web of Science ®Google Scholar
• Eringen AC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys. 1983;54(9):4703–4710.
   Web of Science ®Google Scholar
• Wang Y-Z, Li F-M, Kishimoto K. Scale effects on the longitudinal wave propagation in nanoplates. Physica E. 2010 2010/03/01/;42(5):1356–1360.
   Google Scholar
• Civalek Ö, Demir Ç. Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory. Appl Math Model. 2011 2011/05/01/;35(5):2053–2067.
   Web of Science ®Google Scholar
• Arani AG, Amir S, Shajari AR, et al. Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory. Composites Part B. 2012 2012/03/01/;43(2):195–203.
   Web of Science ®Google Scholar
• Reddy JN, El-Borgi S. Eringen’s nonlocal theories of beams accounting for moderate rotations. Int J Eng Sci. 2014 2014/09/01/;82:159–177.
   Web of Science ®Google Scholar
• Zhang LL, Liu JX, Fang XQ, et al. Effects of surface piezoelectricity and nonlocal scale on wave propagation in piezoelectric nanoplates. Eur J Mech A Solids. 2014 2014/07/01/;46:22–29.
   Web of Science ®Google Scholar
• Arani AG, Amir S, Dashti P, et al. Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect. Comput Mater Sci. 2014 2014/04/15/;86:144–154.
   Web of Science ®Google Scholar
• Ebrahimi F, Barati MR. On nonlocal characteristics of curved inhomogeneous euler–Bernoulli nanobeams under different temperature distributions. Appl Phys A. 2016 2016/09/08;122(10):880.
   Web of Science ®Google Scholar
• Ebrahimi F, Shaghaghi GR, Boreiry M. A semi-analytical evaluation of surface and nonlocal effects on buckling and vibrational characteristics of nanotubes with various boundary conditions. Int J Struct Stab Dyn. 2016;16(06):1550023.
   Google Scholar
• Nejad MZ, Hadi A. Eringen’s non-local elasticity theory for bending analysis of bi-directional functionally graded Euler–Bernoulli nano-beams. Int J Eng Sci. 2016 2016/09/01/;106:1–9.
   Web of Science ®Google Scholar
• Nejad MZ, Hadi A. Non-local analysis of free vibration of bi-directional functionally graded euler–Bernoulli nano-beams. Int J Eng Sci. 2016 2016/08/01/;105:1–11.
   Web of Science ®Google Scholar
• Nejad MZ, Hadi A, Rastgoo A. Buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on nonlocal elasticity theory. Int J Eng Sci. 2016 2016/06/01/;103:1–10.
   Web of Science ®Google Scholar
• Ebrahimi F, Barati MR. Size-dependent vibration analysis of viscoelastic nanocrystalline silicon nanobeams with porosities based on a higher order refined beam theory. Compos Struct. 2017 2017/04/15/;166:256–267.
   Web of Science ®Google Scholar
• Ebrahimi F, Shafiei N. Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on reddy’s higher-order shear deformation plate theory. Mech Adv Mater Struct. 2017 2017/07/04;24(9):761–772.
   Web of Science ®Google Scholar
• Norouzzadeh A, Ansari R. Finite element analysis of nano-scale Timoshenko beams using the integral model of nonlocal elasticity. Physica E. 2017 2017/04/01/;88:194–200.
   Google Scholar
• Ebrahimi F, Barati MR. Vibration analysis of size-dependent flexoelectric nanoplates incorporating surface and thermal effects. Mech Adv Mater Struct. 2018 2018/05/19;25(7):611–621.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. On wave dispersion characteristics of double-layered graphene sheets in thermal environments. J Electromagn Waves Appl. 2018 2018/10/13;32(15):1869–1888.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Wave dispersion characteristics of heterogeneous nanoscale beams via a novel porosity-based homogenization scheme. Eur Phys J Plus. 2019 2019/04/16;134(4):157.
   Web of Science ®Google Scholar
• Zarezadeh E, Hosseini V, Hadi A. Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory. Mech Based Des Struct Mach. 2020 2020/07/03;48(4):480–495.
   Web of Science ®Google Scholar
• Fleck NA, Hutchinson JW. A phenomenological theory for strain gradient effects in plasticity. J Mech Phys Solids. 1993 1993/12/01/;41(12):1825–1857.
   Web of Science ®Google Scholar
• Stölken JS, Evans AG. A microbend test method for measuring the plasticity length scale. Acta Mater. 1998 1998/09/01/;46(14):5109–5115.
   Web of Science ®Google Scholar
• Lim CW, Zhang G, Reddy JN. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids. 2015 2015/05/01/;78:298–313.
   Web of Science ®Google Scholar
• Farajpour A, Haeri Yazdi MR, Rastgoo A, et al. A higher-order nonlocal strain gradient plate model for buckling of orthotropic nanoplates in thermal environment. Acta Mech. 2016 2016/07/01;227(7):1849–1867.
   Web of Science ®Google Scholar
• Li L, Li X, Hu Y. Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci. 2016 2016/05/01/;102:77–92.
   Web of Science ®Google Scholar
• Li L, Hu Y. Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci. 2016 2016/10/01/;107:77–97.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Wave propagation analysis of embedded nanoplates based on a nonlocal strain gradient-based surface piezoelectricity theory. Eur Phys J Plus. 2017 2017/11/02;132(11):449.
   Web of Science ®Google Scholar
• Li X, Li L, Hu Y, et al. Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory. Compos Struct. 2017 2017/04/01/;165:250–265.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Effect of humid-thermal environment on wave dispersion characteristics of single-layered graphene sheets. Appl Phys A. 2018 2018/03/13;124(4):301.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates. Eur Phys J Plus. 2018 2018/03/08;133(3):97.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. NSGT-based acoustical wave dispersion characteristics of thermo-magnetically actuated double-nanobeam systems. Struct Eng Mech. 2018;68(6):701–711.
   Web of Science ®Google Scholar
• Hadi A, Zamani Nejad M, Hosseini M. Vibrations of three-dimensionally graded nanobeams. Int J Eng Sci. 2018 2018/07/01/;128:12–23.
   Web of Science ®Google Scholar
• Sahmani S, Aghdam MM. Nonlocal strain gradient shell model for axial buckling and postbuckling analysis of magneto-electro-elastic composite nanoshells. Composites Part B. 2018 2018/01/01/;132:258–274.
   Web of Science ®Google Scholar
• Karami B, Shahsavari D, Janghorban M. On the dynamics of porous doubly-curved nanoshells. Int J Eng Sci. 2019 2019/10/01/;143:39–55.
   Web of Science ®Google Scholar
• Mohammadi M, Hosseini M, Shishesaz M, et al. Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads. Eur J Mech A Solids. 2019 2019/09/01/;77:103793.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Application of the nonlocal strain gradient elasticity on the wave dispersion behaviors of inhomogeneous nanosize beams. Eur Phys J Plus. 2019 2019/03/21;134(3):112.
   Web of Science ®Google Scholar
• She G-L, Yuan F-G, Karami B, et al. On nonlinear bending behavior of FG porous curved nanotubes. Int J Eng Sci. 2019 2019/02/01/;135:58–74.
   Web of Science ®Google Scholar
• Noroozi R, Barati A, Kazemi A, et al. Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity. Adv Nano Res. 2020;8(1):13–24.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Magnetic field effects on thermally affected propagation of acoustical waves in rotary double-nanobeam systems. Waves Random Complex Media. 2021 2021/01/02;31(1):25–45.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A, Rabczuk T. On wave dispersion characteristics of magnetostrictive sandwich nanoplates in thermal environments. Eur J Mech A Solids. 2021 2021/01/01/;85:104130.
   Web of Science ®Google Scholar
• Xu X, Karami B, Shahsavari D. Time-dependent behavior of porous curved nanobeam. Int J Eng Sci. 2021 2021/03/01/;160:103455.
   Web of Science ®Google Scholar
• Brinson HF, Brinson LC. Polymer Engineering Science and viscoelasticity. 2nd ed Boston (MA): Springer; 2015.
   Google Scholar
• Ebrahimi F, Barati MR. A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures. Int J Eng Sci. 2016 2016/10/01/;107:183–196.
   Web of Science ®Google Scholar
• Ebrahimi F, Barati MR. Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory. Compos Struct. 2017 2017/01/01/;159:433–444.
   Web of Science ®Google Scholar
• Shahsavari D, Karami B, Janghorban M, et al. Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment. Mater Res Express. 2017 2017/08/03;4(8):085013.
   Web of Science ®Google Scholar
• Jalaei MH, Ghorbanpour Arani A, Tourang H. On the dynamic stability of viscoelastic graphene sheets. Int J Eng Sci. 2018;132:16–29.
   Web of Science ®Google Scholar
• Karami B, Shahsavari D, Li L. Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory. Physica E. 2018 2018/03/01/;97:317–327.
   Google Scholar
• Zeighampour H, Tadi Beni Y, Botshekanan Dehkordi M. Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory. Thin-Walled Struct. 2018 2018/01/01/;122:378-386.
   Web of Science ®Google Scholar
• Jalaei MH, Civalek . On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. Int J Eng Sci. 2019 2019/10/01/;143:14–32.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Viscoelastic wave propagation analysis of axially motivated double-layered graphene sheets via nonlocal strain gradient theory. Waves Random Complex Media. 2020 2020/01/02;30(1):157–176.
   Web of Science ®Google Scholar
• Ebrahimi F, Hosseini SH S. Double harmonically excited nonlinear vibration of viscoelastic piezoelectric nanoplates subjected to thermo-electro-mechanical forces. J Vib Control. 2020;26(7-8):430–446.
   Web of Science ®Google Scholar
• Li L, Lin R, Ng TY. A fractional nonlocal time-space viscoelasticity theory and its applications in structural dynamics. Appl Math Model. 2020 2020/08/01/;84:116–136.
   Web of Science ®Google Scholar
• Zaoui FZ, Ouinas D, Tounsi A. New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations. Composites Part B. 2019;159:231–247.
   Web of Science ®Google Scholar
• Lai WM, Rubin D, Krempl E. Introduction to continuum mechanics. 4th ed. X: Butterworth-Heinemann; 2009.
   Google Scholar
• Ebrahimi F, Dabbagh A. Mechanics of nanocomposites: homogenization and analysis. 1st ed. Boca Raton, FL: CRC Press; 2020.
   Google Scholar
• Gholipour G, Zhang C, Mousavi AA. Effects of axial load on nonlinear response of RC columns subjected to lateral impact load: ship-pier collision. Eng Fail Anal. 2018 2018/09/01/;91:397–418.
   Web of Science ®Google Scholar
• Zeng S, Zhang C, Wang K, et al. Analysis of delamination of unimorph cantilever piezoelectric energy harvesters. J Intell Mater Syst Struct. 2018;29(9):1875–1883.
   Web of Science ®Google Scholar
• Dabbagh A, Rastgoo A, Ebrahimi F. Finite element vibration analysis of multi-scale hybrid nanocomposite beams via a refined beam theory. Thin-Walled Struct. 2019 2019/07/01/;140:304–317.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. Vibration analysis of graphene oxide powder-/carbon fiber-reinforced multi-scale porous nanocomposite beams: a finite-element study. The European Physical Journal Plus. 2019 2019/05/24;134(5):225.
   Web of Science ®Google Scholar
• Gholipour G, Zhang C, Mousavi AA. Loading rate effects on the responses of simply supported RC beams subjected to the combination of impact and blast loads. Eng Struct. 2019 2019/12/15/;201:109837.
   Web of Science ®Google Scholar
• Zhang C, Gholipour G, Mousavi AA. Nonlinear dynamic behavior of simply-supported RC beams subjected to combined impact-blast loading. Eng Struct. 2019 2019/02/15/;181:124–142.
   Web of Science ®Google Scholar
• Zou G, Wang Y, Xue Q, et al. Buckling analysis of Sandwich Plate Systems with Stiffening Ribs: theoretical. Nume Exp Approaches. Adv Civ Eng. 2019 2019/03/04;2019:8737561.
   Web of Science ®Google Scholar
• Alambeigi K, Mohammadimehr M, Bamdad M, et al. Free and forced vibration analysis of a sandwich beam considering porous core and SMA hybrid composite face layers on Vlasov’s foundation. Acta Mech. 2020 2020/08/01;231(8):3199–3218.
   Web of Science ®Google Scholar
• Abedini M, Mutalib AA, Zhang C, et al. Large deflection behavior effect in reinforced concrete columns exposed to extreme dynamic loads. Front Struct Civ Eng. 2020 2020/04/01;14(2):532–553.
   Web of Science ®Google Scholar
• Ansari E, Setoodeh AR, Rabczuk T. Isogeometric-stepwise vibrational behavior of rotating functionally graded blades with variable thickness at an arbitrary stagger angle subjected to thermal environment. Compos Struct. 2020 2020/07/15/;244:112281.
   Web of Science ®Google Scholar
• Barati A, Hadi A, Zamani Nejad M, et al. On vibration of bi-directional functionally graded nanobeams under magnetic field. Mech Based Des Struct Mach. 2020: 1–18. DOI:10.1080/15397734.2020.1719507.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A, Rastgoo A. Static stability analysis of multi-scale hybrid agglomerated nanocomposite shells. Mech Based Des Struct Mach. 2020: 1–17. DOI:10.1080/15397734.2020.1848585.
   Web of Science ®Google Scholar
• Gholipour G, Zhang C, Mousavi AA. Numerical analysis of axially loaded RC columns subjected to the combination of impact and blast loads. Eng Struct. 2020 2020/09/15/;219:110924.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A, Taheri M. Vibration analysis of porous metal foam plates rested on viscoelastic substrate. Eng Comput. 2020 2020/05/12. DOI:10.1007/s00366-020-01031-w.
   Web of Science ®Google Scholar
• Yarali E, Farajzadeh MA, Noroozi R, et al. Magnetorheological elastomer composites: modeling and dynamic finite element analysis. Compos Struct. 2020 2020/12/15/;254:112881.
   Web of Science ®Google Scholar
• Zhang C, Wang H. Swing vibration control of suspended structures using the Active Rotary Inertia Driver system: theoretical modeling and experimental verification. Struct Control Health Monit. 2020;27(6):e2543.
   Web of Science ®Google Scholar
• Ebrahimi F, Dabbagh A. An analytical solution for static stability of multi-scale hybrid nanocomposite plates. Eng Comput. 2021 2021/01/01;37(1):545–559.
   Web of Science ®Google Scholar
• Dabbagh A, Rastgoo A, Ebrahimi F. Static stability analysis of agglomerated multi-scale hybrid nanocomposites via a refined theory. Eng Comput. 2021 2020/01/19;37(3):2225–2244.
   Web of Science ®Google Scholar
• Amani MA, Ebrahimi F, Dabbagh A, et al. A machine learning-based model for the estimation of the temperature-dependent moduli of graphene oxide reinforced nanocomposites and its application in a thermally affected buckling analysis. Eng Comput. 2021 2020/01/22;37(3):2245–2255.
   Web of Science ®Google Scholar
• Abedini M, Zhang C. Dynamic performance of concrete columns retrofitted with FRP using segment pressure technique. Compos Struct. 2021 2021/03/15/;260:113473.
   Web of Science ®Google Scholar
• Ebrahimi F, Nopour R, Dabbagh A. Effect of viscoelastic properties of polymer and wavy shape of the CNTs on the vibrational behaviors of CNT/glass fiber/polymer plates. Eng Comput. 2021 2021/04/13. DOI:10.1007/s00366-021-01387-7.
   Web of Science ®Google Scholar
• Gao D, Wang S, Zhang M, et al. Experimental and numerical investigation on in-plane impact behaviour of chiral auxetic structure. Compos Struct. 2021 2021/07/01/;267:113922.
   Web of Science ®Google Scholar
• Gao N, Guo X, Deng J, et al. Elastic wave modulation of double-leaf ABH beam embedded mass oscillator. Appl Acoust. 2021 2021/02/01/;173:107694.
   Web of Science ®Google Scholar
• Kutlu A, Dorduncu M, Rabczuk T. A novel mixed finite element formulation based on the refined zigzag theory for the stress analysis of laminated composite plates. Compos Struct. 2021 2021/07/01/;267:113886.
   Web of Science ®Google Scholar
• Thai TQ, Zhuang X, Rabczuk T. A nonlinear geometric couple stress based strain gradient Kirchhoff–Love shell formulation for microscale thin-wall structures. Int J Mech Sci. 2021 2021/04/15/;196:106272.
   Web of Science ®Google Scholar
• Gao N, Wang B, Lu K, et al. Complex band structure and evanescent Bloch wave propagation of periodic nested acoustic black hole phononic structure. Appl Acoust. 2021 2021/06/01/;177:107906.
   Web of Science ®Google Scholar
• Eltaher MA, Emam SA, Mahmoud FF. Free vibration analysis of functionally graded size-dependent nanobeams. Appl Math Comput. 2012 2012/03/15/;218(14):7406–7420.
   Web of Science ®Google Scholar