Size dependent free vibration analysis of 2D-functionally graded curved nanobeam by meshless method

References

• S. Mukherjee and N.R. Aluru, Applications in micro- and nano-electromechanical systems, Eng. Anal. Bound. Elem., vol. 30, no. 11, p. 909, 2006. DOI: 10.1016/j.enganabound.2006.07.001.
   Web of Science ®Google Scholar
• A. Peschot, C. Qian, and T.J.K. Liu, Nanoelectromechanical switches for low-power digital computing, Micromachines, vol. 6, no. 8, pp. 1046–1065, 2015. DOI: 10.3390/mi6081046.
   Web of Science ®Google Scholar
• A.K. Singh, A. Das, and P. Kumar, Nanobiosensors and their applications. In: Nanotechnology, Jenny Stanford Publishing, New York, pp. 249–288, 2021.
   Google Scholar
• S. Saravanan, E.K. Nangai, S.V. Ajantha, and S. Sankar, Recent developments in nanomaterial applications. In: Nanomaterials and Nanocomposites, CRC Press, Boca Raton, pp. 3–15, 2021.
   Google Scholar
• M.A. Roudbari, T.D. Jorshari, C. Lü, R. Ansari, A.Z. Kouzani, and M. Amabili, A review of size-dependent continuum mechanics models for micro-and nano-structures, Thin-Walled Struct., vol. 170, p. 108562, 2022. DOI: 10.1016/j.tws.2021.108562.
   Web of Science ®Google Scholar
• R.D. Mindlin and N.N. Eshel, On first strain-gradient theories in linear elasticity, Int. J. Solids Struct., vol. 4, no. 1, pp. 109–124, 1968. DOI: 10.1016/0020-7683(68)90036-X.
   Google Scholar
• L. Lu, X. Guo, and J. Zhao, Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory, Int. J. Eng. Sci., vol. 116, pp. 12–24, 2017. DOI: 10.1016/j.ijengsci.2017.03.006.
   Web of Science ®Google Scholar
• R.A. Toupin, Theories of elasticity with couple-stress, Arch. Ration. Mech. Anal., vol. 17, no. 2, pp. 85–112, 1964. DOI: 10.1007/BF00253050.
   Web of Science ®Google Scholar
• S.K. Park and X.L. Gao, Bernoulli–Euler beam model based on a modified couple stress theory, J. Micromech. Microeng., vol. 16, no. 11, pp. 2355–2359, 2006. DOI: 10.1088/0960-1317/16/11/015.
   Web of Science ®Google Scholar
• A.C. Eringen, Nonlocal polar elastic continua, Int. J. Eng. Sci., vol. 10, no. 1, pp. 1–16, 1972. DOI: 10.1016/0020-7225(72)90070-5.
   Web of Science ®Google Scholar
• A.C. Eringen and J.L. Wegner, Nonlocal continuum field theories, Appl. Mech. Rev., vol. 56, no. 2, pp. B20–B22, 2003. DOI: 10.1115/1.1553434.
   Google Scholar
• M.A. Eltaher, S.A. Emam, and F.F. Mahmoud, Free vibration analysis of functionally graded size-dependent nanobeams, Appl. Math. Comput., vol. 218, no. 14, pp. 7406–7420, 2012. DOI: 10.1016/j.amc.2011.12.090.
   Web of Science ®Google Scholar
• M. Şimşek, Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory, Compos. B: Eng., vol. 56, pp. 621–628, 2014. DOI: 10.1016/j.compositesb.2013.08.082.
   Web of Science ®Google Scholar
• F. Bakhtiari-Nejad and M. Nazemizadeh, Size-dependent dynamic modeling and vibration analysis of mems/nems-based nanomechanical beam based on the nonlocal elasticity theory, Acta Mech., vol. 227, no. 5, pp. 1363–1379, 2016. DOI: 10.1007/s00707-015-1556-3.
   Web of Science ®Google Scholar
• B. Karami and M. Janghorban, A new size-dependent shear deformation theory for free vibration analysis of functionally graded/anisotropic nanobeams, Thin-Walled Struct., vol. 143, p. 106227, 2019. DOI: 10.1016/j.tws.2019.106227.
   Web of Science ®Google Scholar
• A. Babaei, A. Rahmani, and I. Ahmadi, Transverse vibration analysis of nonlocal beams with various slenderness ratios, undergoing thermal stress, Arch. Mech. Eng., vol. 66, pp. 5–24, 2019.
   Web of Science ®Google Scholar
• B. Uzun, M.Ö. Yaylı, and B. Deliktaş, Free vibration of FG nanobeam using a finite-element method, Micro Nano Lett., vol. 15, no. 1, pp. 35–40, 2020. DOI: 10.1049/mnl.2019.0273.
   Web of Science ®Google Scholar
• E.R. Estabragh and G.H. Baradaran, Large amplitude free vibration analysis of nanobeams based on modified couple stress theory, Int. J. Struct. Stab. Dyn., vol. 21, no. 9, p. 2150129, 2021. DOI: 10.1142/S0219455421501297.
   Google Scholar
• J. Sladek, V. Sladek, M. Xu, and Q. Deng, A cantilever beam analysis with flexomagnetic effect, Meccanica, vol. 56, no. 9, pp. 2281–2292, 2021. DOI: 10.1007/s11012-021-01357-9.
   Web of Science ®Google Scholar
• I. Esen, A.A. Abdelrhmaan, and M.A. Eltaher, Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields, Eng. Comput., vol. 38, pp. 3463–3482, 2021. DOI: 10.1007/s00366-021-01389-5.
   Web of Science ®Google Scholar
• R. Lal and C. Dangi, Dynamic analysis of bi-directional functionally graded Timoshenko nanobeam on the basis of Eringen’s nonlocal theory incorporating the surface effect, Appl. Math. Comput., vol. 395, p. 125857, 2021. DOI: 10.1016/j.amc.2020.125857.
   Web of Science ®Google Scholar
• M. Najafi and I. Ahmadi, A nonlocal layerwise theory for free vibration analysis of nanobeams with various boundary conditions on Winkler–Pasternak foundation, Steel Compos. Struct., vol. 40, no. 1, pp. 101–119, 2021.
   Web of Science ®Google Scholar
• M. Najafi and I. Ahmadi, Nonlocal layerwise theory for bending, buckling and vibration analysis of functionally graded nanobeams, Eng. Comput., 2022. DOI: 10.1007/s00366-022-01605-w.
   Web of Science ®Google Scholar
• M. Soltani, F. Atoufi, F. Mohri, R. Dimitri, and F. Tornabene, Nonlocal elasticity theory for lateral stability analysis of tapered thin-walled nanobeams with axially varying materials, Thin-Walled Struct., vol. 159, p. 107268, 2021. DOI: 10.1016/j.tws.2020.107268.
   Web of Science ®Google Scholar
• Y.P. Liu and J.N. Reddy, A nonlocal curved beam model based on a modified couple stress theory, Int. J. Struct. Stab. Dyn., vol. 11, no. 3, pp. 495–512, 2011. DOI: 10.1142/S0219455411004233.
   Web of Science ®Google Scholar
• H. Kananipour, M. Ahmadi, and H. Chavoshi, Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams, Lat. Am. J. Solids Struct., vol. 11, no. 5, pp. 848–853, 2014. DOI: 10.1590/S1679-78252014000500007.
   Web of Science ®Google Scholar
• S.A.H. Hosseini and O. Rahmani, Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model, Appl. Phys. A, vol. 122, no. 3, p. 169, 2016. DOI: 10.1007/s00339-016-9696-4.
   Web of Science ®Google Scholar
• E. Tufekci, S.A. Aya, and O. Oldac, In-plane static analysis of nonlocal curved beams with varying curvature and cross-section, Int. J. Appl. Mech., vol. 8, no. 1, p. 1650010, 2016. DOI: 10.1142/S1758825116500101.
   Web of Science ®Google Scholar
• M. Ganapathi and O. Polit, Dynamic characteristics of curved nanobeams using nonlocal higher-order curved beam theory, Physica E, vol. 91, pp. 190–202, 2017. DOI: 10.1016/j.physe.2017.04.012.
   Google Scholar
• S.A. Aya and E. Tufekci, Modeling and analysis of out-of-plane behavior of curved nanobeams based on nonlocal elasticity, Compos. B: Eng., vol. 119, pp. 184–195, 2017. DOI: 10.1016/j.compositesb.2017.03.050.
   Web of Science ®Google Scholar
• M. Rezaiee-Pajand and N. Rajabzadeh-Safaei, Nonlocal static analysis of a functionally graded material curved nanobeam, Mech. Adv. Mater. Struct., vol. 25, no. 7, pp. 539–547, 2018. DOI: 10.1080/15376494.2017.1285463.
   Web of Science ®Google Scholar
• F. Ebrahimi, M. Daman, and A. Jafari, Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment, Smart Struct. Syst., vol. 20, pp. 709–728, 2017.
   Web of Science ®Google Scholar
• M. Ganapathi, T. Merzouki, and O. Polit, Vibration study of curved nanobeams based on nonlocal higher-order shear deformation theory using finite element approach, Compos. Struct., vol. 184, pp. 821–838, 2018. DOI: 10.1016/j.compstruct.2017.10.066.
   Web of Science ®Google Scholar
• F. Ebrahimi and M.R. Barati, Vibration analysis of piezoelectrically actuated curved nanosize FG beams via a nonlocal strain-electric field gradient theory, Mech. Adv. Mater. Struct., vol. 25, no. 4, pp. 350–359, 2018. DOI: 10.1080/15376494.2016.1255830.
   Web of Science ®Google Scholar
• M. Arefi, M. Pourjamshidian, and A.G. Arani, Free vibration analysis of a piezoelectric curved sandwich nano-beam with FG-CNTRCs face-sheets based on various high-order shear deformation and nonlocal elasticity theories, Eur. Phys. J. Plus, vol. 133, no. 5, p. 193, 2018. DOI: 10.1140/epjp/i2018-12015-1.
   Web of Science ®Google Scholar
• O. Polit, T. Merzouki, and M. Ganapathi, Elastic stability of curved nanobeam based on higher-order shear deformation theory and nonlocal analysis by finite element approach, Finite Elem. Anal. Des., vol. 146, pp. 1–15, 2018. DOI: 10.1016/j.finel.2018.04.002.
   Web of Science ®Google Scholar
• M. Arefi and A.M. Zenkour, Thermal stress and deformation analysis of a size-dependent curved nanobeam based on sinusoidal shear deformation theory, Alex. Eng. J., vol. 57, no. 3, pp. 2177–2185, 2018. DOI: 10.1016/j.aej.2017.07.003.
   Web of Science ®Google Scholar
• M. Ganapathi and O. Polit, A nonlocal higher-order model including thickness stretching effect for bending and buckling of curved nanobeams, Appl. Math. Model., vol. 57, pp. 121–141, 2018. DOI: 10.1016/j.apm.2017.12.025.
   Web of Science ®Google Scholar
• M.N. Allam and A.F. Radwan, Nonlocal strain gradient theory for bending, buckling, and vibration of viscoelastic functionally graded curved nanobeam embedded in an elastic medium, Adv. Mech. Eng., vol. 11, no. 4, p. 168781401983706, 2019. DOI: 10.1177/1687814019837067.
   Web of Science ®Google Scholar
• F. Ebrahimi, M.R. Barati, and V. Mahesh, Dynamic modeling of smart magneto-electro-elastic curved nanobeams, Adv. Nano Res., vol. 7, no. 3, p. 145, 2019.
   Web of Science ®Google Scholar
• T. Merzouki, M. Ganapathi, and O. Polit, A nonlocal higher-order curved beam finite model including thickness stretching effect for bending analysis of curved nanobeams, Mech. Adv. Mater. Struct., vol. 26, no. 7, pp. 614–630, 2019. DOI: 10.1080/15376494.2017.1410903.
   Web of Science ®Google Scholar
• R. Barretta, F.M. de Sciarra, and M.S. Vaccaro, On nonlocal mechanics of curved elastic beams, Int. J. Eng. Sci., vol. 144, p. 103140, 2019. DOI: 10.1016/j.ijengsci.2019.103140.
   Web of Science ®Google Scholar
• P. Zhang, H. Qing, and C.‐F. Gao, Analytical solutions of static bending of curved Timoshenko microbeams using Eringen’s two‐phase local/nonlocal integral model, ZAMM‐J. Appl. Math. Mech./Z. Angew. Math. Mech., vol. 100, no. 7, p. e201900207, 2020.
   Web of Science ®Google Scholar
• P. Zhang and H. Qing, Buckling analysis of curved sandwich microbeams made of functionally graded materials via the stress-driven nonlocal integral model, Mech. Adv. Mater. Struct., vol. 29, no. 9, pp. 1211–1228, 2022. DOI: 10.1080/15376494.2020.1811926.
   Web of Science ®Google Scholar
• P. Zhang and H. Qing, Exact solutions for size-dependent bending of Timoshenko curved beams based on a modified nonlocal strain gradient model, Acta Mech., vol. 231, no. 12, pp. 5251–5276, 2020. DOI: 10.1007/s00707-020-02815-3.
   Web of Science ®Google Scholar
• G.L. She, H.B. Liu, and B. Karami, On resonance behavior of porous FG curved nanobeams, Steel Compos. Struct., vol. 36, no. 2, pp. 179–186, 2020.
   Web of Science ®Google Scholar
• D. Sarthak, G. Prateek, R. Vasudevan, O. Polit, and M. Ganapathi, Dynamic buckling of classical/non-classical curved beams by nonlocal nonlinear finite element accounting for size dependent effect and using higher-order shear flexible model, Int. J. Non-Linear Mech., vol. 125, p. 103536, 2020. DOI: 10.1016/j.ijnonlinmec.2020.103536.
   Web of Science ®Google Scholar
• A.M. Zenkour and A.F. Radwan, A compressive study for porous FG curved nanobeam under various boundary conditions via a nonlocal strain gradient theory, Eur. Phys. J. Plus, vol. 136, no. 2, pp. 1–16, 2021. DOI: 10.1140/epjp/s13360-021-01238-w.
   Web of Science ®Google Scholar
• N. Zhang, S. Zheng, and D. Chen, Size-dependent static bending, free vibration and buckling analysis of curved flexomagnetic nanobeams, Meccanica, vol. 57, pp. 1–14, 2022. DOI: 10.1007/s11012-022-01506-8.
   Web of Science ®Google Scholar
• C.M.C. Roque, A.J.M. Ferreira, and J.N. Reddy, Analysis of Timoshenko nanobeams with a nonlocal formulation and meshless method, Int. J. Eng. Sci., vol. 49, no. 9, pp. 976–984, 2011. DOI: 10.1016/j.ijengsci.2011.05.010.
   Web of Science ®Google Scholar
• Y. Tian, C. Zhang, and Y. Sun, The application of mesh-free method in the numerical simulation of beams with the size effect, Math. Probl. Eng., vol. 2014, pp. 1–6, 2014. DOI: 10.1155/2014/590271.
   Google Scholar
• M.C. Ray, Mesh free model of nanobeam integrated with a flexoelectric actuator layer, Compos. Struct., vol. 159, pp. 63–71, 2017. DOI: 10.1016/j.compstruct.2016.09.011.
   Web of Science ®Google Scholar
• L. Wang, X. He, Y. Sun, and K.M. Liew, A mesh-free vibration analysis of strain gradient nano-beams, Eng. Anal. Bound. Elem., vol. 84, pp. 231–236, 2017. DOI: 10.1016/j.enganabound.2017.09.001.
   Web of Science ®Google Scholar
• S. Sidhardh and M.C. Ray, Element-free Galerkin model of nano-beams considering strain gradient elasticity, Acta Mech., vol. 229, no. 7, pp. 2765–2786, 2018. DOI: 10.1007/s00707-018-2139-x.
   Web of Science ®Google Scholar
• M.H. Ghadiri Rad, F. Shahabian, and S.M. Hosseini, Nonlocal geometrically nonlinear dynamic analysis of nanobeam using a meshless method, Steel Compos. Struct., vol. 32, no. 3, pp. 293–304, 2019.
   Web of Science ®Google Scholar
• M. Rezaiee-Pajand and M. Mokhtari, A novel meshless particle method for nonlocal analysis of two-directional functionally graded nanobeams, J. Braz. Soc. Mech. Sci. Eng., vol. 41, no. 7, pp. 1–23, 2019. DOI: 10.1007/s40430-019-1799-3.
   Web of Science ®Google Scholar
• Isa Ahmadi, Vibration analysis of 2D-functionally graded nanobeams using the nonlocal theory and meshless method, Eng. Anal. Bound. Elem., vol. 124, pp. 142–154, 2021. DOI: 10.1016/j.enganabound.2020.12.010.
   Web of Science ®Google Scholar
• G.L. She, H.B. Liu, and B. Karami, Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets, Thin-Walled Struct., vol. 160, p. 107407, 2021. DOI: 10.1016/j.tws.2020.107407.
   Web of Science ®Google Scholar
• G. Prateek, D. Sarthak, R. Vasudevan, M. Haboussi, and M. Ganapathi, Large amplitude free vibration analysis of isotropic curved nano/microbeams using a nonlocal sinusoidal shear deformation theory-based finite element method, Int. J. Struct. Stab. Dyn., vol. 21, no. 5, p. 2150074, 2021. DOI: 10.1142/S0219455421500747.
   Google Scholar
• I. Ahmadi, Free vibration of multiple-nanobeam system with nonlocal Timoshenko beam theory for various boundary conditions, Eng. Anal. Bound. Elem., vol. 143, pp. 719–739, 2022. DOI: 10.1016/j.enganabound.2022.07.011.
   Web of Science ®Google Scholar
• A. Karamanli and T.P. Vo, Finite element model for free vibration analysis of curved zigzag nanobeams, Compos. Struct., vol. 282, p. 115097, 2022. DOI: 10.1016/j.compstruct.2021.115097.
   Web of Science ®Google Scholar
• G.R. Liu, Meshfree Methods: Moving beyond the Finite Element Method, CRC Press Boca Raton, 2009.
   Google Scholar