Radial postbuckling of nanoscaled shells embedded in elastic foundations based on Ru's surface stress elasticity theory

References

• Ansari, M. I., and A. Kumar. 2019. Bending analysis of functionally graded CNT reinforced doubly curved singly ruled truncated rhombic cone. Mechanics Based Design of Structures and Machines, an International Journal 47 (1):67–86. doi:10.1080/15397734.2018.1519635.
   Web of Science ®Google Scholar
• Ansari, R., and S. Sahmani. 2011a. Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories. International Journal of Engineering Science 49 (11):1244–55. doi:10.1016/j.ijengsci.2011.01.007.
   Web of Science ®Google Scholar
• Ansari, R., and S. Sahmani. 2011b. Surface stress effects on the free vibration behavior of nanoplates. International Journal of Engineering Science 49 (11):1204–15. doi:10.1016/j.ijengsci.2011.06.005.
   Web of Science ®Google Scholar
• Ansari, R., and S. Sahmani. 2013. Prediction of biaxial buckling behavior of single-layered graphene sheets based on nonlocal plate models and molecular dynamics simulations. Applied Mathematical Modelling 37 (12-13):7338–51. doi:10.1016/j.apm.2013.03.004.
   Web of Science ®Google Scholar
• Ansari, M. I., A. Kumar, S. Fic, and D. Barnat-Hunek. 2018. Flexural and free vibration analysis of CNT-reinforced functionally graded plate. Materials 11 (12):2387. doi:10.3390/ma11122387.
   PubMed Web of Science ®Google Scholar
• Arefi, M., and A. H. Soltan Arani. 2018. Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments. Mechanics Based Design of Structures and Machines, an International Journal 46 (6):669–92. doi:10.1080/15397734.2018.1434002.
   Web of Science ®Google Scholar
• Cui, Y., Z. Zhong, D. Wang, W. U. Wang, and C. M. Lieber. 2003. High performance silicon nanowire field effect transistors. Nano Letters 3 (2):149–52. doi:10.1021/nl025875l.
   Web of Science ®Google Scholar
• Challamel, N., F. Hache, I. Elishakoff, and C. M. Wang. 2016. Buckling and vibrations of microstructured rectangular plates considering phenomenological and lattice-based nonlocal continuum models. Composite Structures 149:145–56. doi:10.1016/j.compstruct.2016.04.007.
   Web of Science ®Google Scholar
• Chaubey, A. K., C. Prakash, and A. Kumar. 2018. Biaxial and shear buckling of laminated composite elliptic paraboloids with cutouts and concentrated mass. Mechanics Research Communications 94:80–7. doi:10.1016/j.mechrescom.2018.09.008.
   Web of Science ®Google Scholar
• Chaubey, A. K., I. Jha, A. Kumar, M. D. Demirbas, and S. Dey. 2018b. Dual axis buckling of laminated composite skew hyperbolic paraboloids with openings. Journal of the Brazilian Society of Mechanical Sciences and Engineering 40:490.
   Web of Science ®Google Scholar
• Chiu, M. S., and T. Chen. 2013. Bending and resonance behavior of nanowires based on Timoshenko beam theory with high-order surface stress effects. Physica E 54:149–56. doi:10.1016/j.physe.2013.06.013.
   Google Scholar
• Dong, S., C. Zhu, Y. Chen, and J. Zhao. 2019. Buckling behaviors of metal nanowires encapsulating carbon nanotubes by considering surface/interface effects from a refined beam model. Carbon 141:348–62. doi:10.1016/j.carbon.2018.09.059.
   Web of Science ®Google Scholar
• Donnell, L. H. 1976. Beam, plates and shells. New York, NY: McGraw-Hill.
   Google Scholar
• Eptaimeros, K. G., C. Koutsoumaris, and G. J. Tsamasphyros. 2016. Nonlocal integral approach to the dynamical response of nanobeams. International Journal of Mechanical Sciences 115:68–80. doi:10.1016/j.ijmecsci.2016.06.013.
   Web of Science ®Google Scholar
• Fattahi, A. M., and S. Sahmani. 2017a. Nonlocal temperature-dependent postbuckling behavior of FG-CNT reinforced nanoshells under hydrostatic pressure combined with heat conduction. Microsystem Technologies 23 (10):5121–37. doi:10.1007/s00542-017-3377-x.
   Web of Science ®Google Scholar
• Fattahi, A. M., and S. Sahmani. 2017b. Size dependency in the axial postbuckling behavior of nanopanels made of functionally graded material considering surface elasticity. Arabian Journal for Science and Engineering 42 (11):4617–33. doi:10.1007/s13369-017-2600-5.
   Web of Science ®Google Scholar
• Feng, X., R. He, P. Yang, and M. Roukes. 2007. Very high frequency silicon nanowire electromechanical resonators. Nano Letters 7 (7):1953–9. doi:10.1021/nl0706695.
   Web of Science ®Google Scholar
• Gao, F., Q. Cheng, and J. Luo. 2014. Mechanics of nanowire buckling on elastomeric substrates with consideration of surface stress effects. Physica E 64:72–7. doi:10.1016/j.physe.2014.07.006.
   Google Scholar
• Ghorbani, K., K. Mohammadi, A. Rajabpour, and M. Ghadiri. 2019. Surface and size-dependent effects on the free vibration analysis of cylindrical shell based on Gurtin-Murdoch and nonlocal strain gradient theories. Journal of Physics and Chemistry of Solids 129:140–50. doi:10.1016/j.jpcs.2018.12.038.
   Web of Science ®Google Scholar
• Gurtin, M. E., and A. I. Murdoch. 1975. A continuum theory of elastic material surface. Archive for Rational Mechanics and Analysis 57 (4):291–323. doi:10.1007/BF00261375.
   Web of Science ®Google Scholar
• Gurtin, M. E., and A. I. Murdoch. 1978. Surface stress in solids. International Journal of Solids and Structures 14 (6):431–40. doi:10.1016/0020-7683(78)90008-2.
   Web of Science ®Google Scholar
• Hashemi, M., and M. Asghari. 2017. On the size-dependent flexural vibration characteristics of unbalanced couple stress-based micro-spinning beams. Mechanics Based Design of Structures and Machines, an International Journal 45 (1):1–11. doi:10.1080/15397734.2015.1125298.
   Web of Science ®Google Scholar
• Hu, Y. G., K. M. Liew, Q. Wang, X. Q. He, and B. I. Yakobson. 2008. Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes. Journal of the Mechanics and Physics of Solids 56 (12):3475–85. doi:10.1016/j.jmps.2008.08.010.
   Web of Science ®Google Scholar
• Jain, R. K., S. Datta, and S. Majumder. 2014. Biomimetic behavior of IPMC using EMG signal for microrobot. Mechanics Based Design of Structures and Machines, an International Journal 42 (3):398–417. doi:10.1080/15397734.2014.908729.
   Web of Science ®Google Scholar
• Kamali, M., M. Shamsi, and A. R. Saidi. 2018. Surface effect on buckling of microtubules in living cells using first-order shear deformation shell theory and standard linear solid model. Mechanics Research Communications 92:111–7. doi:10.1016/j.mechrescom.2018.08.011.
   Web of Science ®Google Scholar
• Kamenar, E., and S. Zelenika. 2017. Nanometric positioning accuracy in the presence of presliding and sliding friction: Modelling, identification and compensation. Mechanics Based Design of Structures and Machines, an International Journal 45 (1):111–26. doi:10.1080/15397734.2016.1149487.
   Web of Science ®Google Scholar
• Kasagi, A., and S. Sridharan. 1993. Buckling and postbuckling analysis of thick composite cylindrical shells under hydrostatic pressure. Composites Engineering 3 (5):467–87. doi:10.1016/0961-9526(93)90082-U.
   Google Scholar
• Kim, J., K. K. Żur, and J. N. Reddy. 2019. Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Composite Structures 209:879–88. doi:10.1016/j.compstruct.2018.11.023.
   Web of Science ®Google Scholar
• Li, Y., C. Chen, B. Fang, J. Zhang, and J. Song. 2012. Postbuckling of piezoelectric nanobeams with surface effects. International Journal of Applied Mechanics 04 (02):1250018. doi:10.1142/S1758825112500184.
   Google Scholar
• Li, C. 2017. Nonlocal thermo-electro-mechanical coupling vibrations of axially moving piezoelectric nanobeams. Mechanics Based Design of Structures and Machines, an International Journal 45 (4):463–78. doi:10.1080/15397734.2016.1242079.
   Web of Science ®Google Scholar
• Li, L. and Y. Hu. 2015. Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. International Journal of Engineering Science 97:84–94.
   Web of Science ®Google Scholar
• Liang, X., S. Hu, and S. Shen. 2015. Surface effects on the post-buckling of piezoelectric nanowires. Physica E 69:61–4. doi:10.1016/j.physe.2015.01.019.
   Google Scholar
• Liu, C., L.-L. Ke, Y. S. Wang, J. Yang, and S. Kitipornchai. 2014. Buckling and postbuckling of size-dependent piezoelectric Timoshenko nanobeams subject to thermo-electro-mechanical loadings. International Journal of Applied Mechanics 14:1350067.
   Google Scholar
• Luo, J., and Z. M. Xiao. 2009. Analysis of a screw dislocation interacting with an elliptical nano inhomogeneity. International Journal of Engineering Science 47 (9):883–93. doi:10.1016/j.ijengsci.2009.05.007.
   Web of Science ®Google Scholar
• Lou, J., K. He, J. Du, and H. Wu. 2016. Buckling and post-buckling analyses of piezoelectric hybrid microplates subject to thermo–electro-mechanical loads based on the modified couple stress theory. Composite Structures 153:332–44. doi:10.1016/j.compstruct.2016.05.107.
   Web of Science ®Google Scholar
• Miller, R. E., and V. B. Shenoy. 2000. Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11 (3):139–47. doi:10.1088/0957-4484/11/3/301.
   Web of Science ®Google Scholar
• Nielson, A. J., and L. L. Howell. 2001. An investigation of complaint micro-half-pantographs using the pseudorigid body model. Mechanics Based Design of Structures and Machines, an International Journal 29 (3):317–30. doi:10.1081/SME-100105653.
   Google Scholar
• Ru, C. Q. 2016. A strain-consistent elastic plate model with surface elasticity. Continuum Mechanics and Thermodynamics 28 (1-2):263–73. doi:10.1007/s00161-015-0422-9.
   Web of Science ®Google Scholar
• Sahmani, S., and R. Ansari. 2013a. Size-dependent buckling analysis of functionally graded third-order shear deformable microbeams including thermal environment effect. Applied Mathematical Modelling 37 (23):9499–515. doi:10.1016/j.apm.2013.04.051.
   Web of Science ®Google Scholar
• Sahmani, S., and R. Ansari. 2013b. On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory. Composite Structures 95:430–42.
   Web of Science ®Google Scholar
• Sahmani, S., M. Bahrami, and R. Ansari. 2014a. Nonlinear free vibration analysis of functionally graded third-order shear deformable microbeams based on the modified strain gradient elasticity theory. Composite Structures 110:219–30.
   Web of Science ®Google Scholar
• Sahmani, S., M. Bahrami, and R. Ansari. 2014b. Surface energy effects on the free vibration characteristics of postbuckled third-order shear deformable nanobeams. Composite Structures 116:552–61. doi:10.1016/j.compstruct.2014.05.035.
   Web of Science ®Google Scholar
• Sahmani, S., M. Bahrami, M. M. Aghdam, and R. Ansari. 2014. Surface effects on the nonlinear forced vibration response of third-order shear deformable nanobeams. Composite Structures 118:149–58. doi:10.1016/j.compstruct.2014.07.026.
   Web of Science ®Google Scholar
• Sahmani, S., M. Bahrami, M. M. Aghdam, and R. Ansari. 2015. Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects. Applied Mathematical Modelling 39 (13):3678–89. doi:10.1016/j.apm.2014.12.002.
   Web of Science ®Google Scholar
• Sahmani, S., M. M. Aghdam, and M. Bahrami. 2015. On the free vibration characteristics of postbuckled third-order shear deformable FGM nanobeams including surface effects. Composite Structures 121:377–85. doi:10.1016/j.compstruct.2014.11.033.
   Web of Science ®Google Scholar
• Sahmani, S., and M. M. Aghdam. 2017a. Temperature-dependent nonlocal instability of hybrid FGM exponential shear deformable nanoshells including imperfection sensitivity. International Journal of Mechanical Sciences 122:129–42. doi:10.1016/j.ijmecsci.2017.01.009.
   Web of Science ®Google Scholar
• Sahmani, S., and M. M. Aghdam. 2017b. Nonlinear instability of hydrostatic pressurized hybrid FGM exponential shear deformable nanoshells based on nonlocal continuum elasticity. Composites Part B: Engineering 114:404–17. doi:10.1016/j.compositesb.2017.01.038.
   Web of Science ®Google Scholar
• Sahmani, S., and M. M. Aghdam. 2017c. Imperfection sensitivity of the size-dependent postbuckling response of pressurized FGM nanoshells in thermal environments. Archives of Civil and Mechanical Engineering 17 (3):623–38. doi:10.1016/j.acme.2017.01.004.
   Web of Science ®Google Scholar
• Sahmani, S., and M. M. Aghdam. 2018a. Small scale effects on the large amplitude nonlinear vibrations of multilayer functionally graded composite nanobeams reinforced with graphene-nanoplatelets. International Journal of Nanoscience and Nanotechnology 14:207–27.
   Google Scholar
• Sahmani, S., and M. M. Aghdam. 2018b. Nonlinear instability of hydrostatic pressurized microtubules surrounded by cytoplasm of a living cell including nonlocality and strain gradient microsize dependency. Acta Mechanica 229 (1):403–20. doi:10.1007/s00707-017-1978-1.
   Web of Science ®Google Scholar
• Sahmani, S., and M. M. Aghdam. 2018c. Boundary layer modeling of nonlinear axial buckling behavior of functionally graded cylindrical nanoshells based on the surface elasticity theory. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 42 (3):229–45. doi:10.1007/s40997-017-0092-2.
   Web of Science ®Google Scholar
• Sahmani, S., and A. Khandan. 2018. Size dependency in nonlinear instability of smart magneto-electro-elastic cylindrical composite nanopanels based upon nonlocal strain gradient elasticity. Microsystem Technologies. doi:10.1007/s00542-018-4072-2.
   Web of Science ®Google Scholar
• Sahmani, S., A. M. Fattahi, and N. A. Ahmed. 2018. Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams. Engineering with Computers. doi:10.1007/s00366-018-0657-8.
   Web of Science ®Google Scholar
• Sahmani, S., M. M. Aghdam, and T. Rabczuk. 2018a. Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory. Composite Structures 186:68–78. doi:10.1016/j.compstruct.2017.11.082.
   Web of Science ®Google Scholar
• Sahmani, S., M. M. Aghdam, and T. Rabczuk. 2018b. A unified nonlocal strain gradient plate model for nonlinear axial instability of functionally graded porous micro/nano-plates reinforced with graphene platelets. Materials Research Express 5 (4):045048. doi:10.1088/2053-1591/aabdbb.
   Web of Science ®Google Scholar
• Sahmani, S., M. M. Aghdam, and T. Rabczuk. 2018c. Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs. Composite Structures 198:51–62. doi:10.1016/j.compstruct.2018.05.031.
   Web of Science ®Google Scholar
• Sahmani, S., M. M. Aghdam, and A. Akbarzadeh. 2018. Surface stress effect on nonlinear instability of imperfect piezoelectric nanoshells under combination of hydrostatic pressure and lateral electric field. AUT Journal of Mechanical Engineering 2:177–90.
   Google Scholar
• Sahmani, S., M. Shahali, A. Khandan, S. Saber-Samandari, and M. M. Aghdam. 2018a. Analytical and experimental analyses for mechanical and biological characteristics of novel nanoclay bio-nanocomposite scaffolds fabricated via space holder technique. Applied Clay Science 165:112–23. doi:10.1016/j.clay.2018.08.013.
   Web of Science ®Google Scholar
• Sahmani, S., S. Saber-Samandari, M. M. Aghdam, and A. Khandan. 2018b. Nonlinear resonance response of porous beam-type implants corresponding to various morphology shapes for bone tissue engineering applications. Journal of Materials Engineering and Performance 27 (10):5370–83. doi:10.1007/s11665-018-3619-9.
   Web of Science ®Google Scholar
• Sahmani, S., S. Saber-Samandari, M. Shahali, H. Joneidi Yekta, F. Aghadavoudi, A. H. Montazeran, M. M. Aghdam, and A. Khandan. 2018c. Mechanical and biological performance of axially loaded novel bio-nanocomposite sandwich plate-type implant coated by biological polymer thin film. Journal of the Mechanical Behavior of Biomedical Materials 88:238–50. doi:10.1016/j.jmbbm.2018.08.030.
   PubMed Web of Science ®Google Scholar
• Sahmani, S., and M. M. Aghdam. 2019. Size-Dependent nonlinear mechanics of biological nanoporous microbeams. In Nanomaterials for advanced biological applications, 181–207. Switzerland: Springer.
   Google Scholar
• Sahmani, S., and B. Safaei. 2019. Nonlinear free vibrations of bi-directional functionally graded micro/nano-beams including nonlocal stress and microstructural strain gradient size effects. Thin-Walled Structures 140:342–56. doi:10.1016/j.tws.2019.03.045.
   Web of Science ®Google Scholar
• Sahmani, S., A. M. Fattahi, and N. A. Ahmed. 2019. Develop a refined truncated cubic lattice structure for nonlinear large-amplitude vibrations of micro/nano-beams made of nanoporous materials. Engineering with Computers. doi:10.1007/s00366-019-00703-6.
   Web of Science ®Google Scholar
• Sahmani, S., M. Fotouhi, and M. M. Aghdam. 2019. Size-dependent nonlinear secondary resonance of micro-/nano-beams made of nano-porous biomaterials including truncated cube cells. Acta Mechanica 230 (3):1077–103. doi:10.1007/s00707-018-2334-9.
   Web of Science ®Google Scholar
• Sahmani, S., S. Saber-Samandari, A. Khandan, and M. M. Aghdam. 2019a. Nonlinear resonance investigation of nanoclay based bio-nanocomposite scaffolds with enhanced properties for bone substitute applications. Journal of Alloys and Compounds 773:636–53. doi:10.1016/j.jallcom.2018.09.211.
   Web of Science ®Google Scholar
• Sahmani, S., M. Shahali, M. Ghadiri Nejad, A. Khandan, M. M. Aghdam, and S. Saber-Samandari. 2019b. Effect of copper oxide nanoparticles on electrical conductivity and cell viability of calcium phosphate scaffolds with improved mechanical strength for bone tissue engineering. The European Physical Journal Plus 134:7.
   Web of Science ®Google Scholar
• Sahmani, S., S. Saber-Samandari, A. Khandan, and M. M. Aghdam. 2019c. Influence of MgO nanoparticles on the mechanical properties of coated hydroxyapatite nanocomposite scaffolds produced via space holder technique: Fabrication, characterization and simulation. Journal of the Mechanical Behavior of Biomedical Materials 95:76–88. doi:10.1016/j.jmbbm.2019.03.014.
   PubMed Web of Science ®Google Scholar
• Sarafraz, A., S. Sahmani, and M. M. Aghdam. 2019. Nonlinear secondary resonance of nanobeams under subharmonic and superharmonic excitations including surface free energy effects. Applied Mathematical Modelling 66:195–226. doi:10.1016/j.apm.2018.09.013.
   Web of Science ®Google Scholar
• Sekar, M., and Y. S. Han. 2014. Design and implementation of high-performance real-time free-form NURBS interpolator in micro CNC machine tool. Mechanics Based Design of Structures and Machines, an International Journal 42 (3):296–311. doi:10.1080/15397734.2014.899153.
   Web of Science ®Google Scholar
• Setoodeh, A. R., and M. Rezae. 2017. Large amplitude free vibration analysis of functionally graded nano/micro beams on nonlinear elastic foundation. Structural Engineering and Mechanics, an International Journal 61:711–20.
   Web of Science ®Google Scholar
• Shaat, M., F. F. Mahmoud, X. L. Gao, and A. F. Faheem. 2014. Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects. International Journal of Mechanical Sciences 79:31–7. doi:10.1016/j.ijmecsci.2013.11.022.
   Web of Science ®Google Scholar
• She, G.-L., F.-G. Yuan, Y.-R. Ren, H.-B. Liu, and W.-S. Xiao. 2018. Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory. Composite Structures 203:614–23. doi:10.1016/j.compstruct.2018.07.063.
   Web of Science ®Google Scholar
• Shen, H.-S. 2009. Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium. International Journal of Mechanical Sciences 51 (5):372–83. doi:10.1016/j.ijmecsci.2009.03.006.
   Web of Science ®Google Scholar
• Shen, H.-S., and C. L. Zhang. 2010. Torsional buckling and postbuckling of double-walled carbon nanotubes by nonlocal shear deformable shell model. Composite Structures 92 (5):1073–84. doi:10.1016/j.compstruct.2009.10.002.
   Web of Science ®Google Scholar
• Shen, H.-S. 2011. Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressure-loaded shells. Composite Structures 93 (10):2496–503. doi:10.1016/j.compstruct.2011.04.005.
   Web of Science ®Google Scholar
• Shen, H.-S. 2012. Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part I: Theory and solutions. Composite Structures 94 (4):1305–21. doi:10.1016/j.compstruct.2011.11.034.
   Web of Science ®Google Scholar
• Shen, H.-S. 2013. Nonlocal shear deformable shell model for torsional buckling and postbuckling of microtubules in thermal environment. Mechanics Research Communications 54:83–95.
   Web of Science ®Google Scholar
• Shen, H.-S., and Y. Xiang. 2014. Postbuckling of axially compressed nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Composites Part B: Engineering 67:50–61. doi:10.1016/j.compositesb.2014.06.020.
   Web of Science ®Google Scholar
• Sun, J., Z. Wang, Z. Zhou, X. Xu, and C. W. Lim. 2018. Surface effects on the buckling behaviors of piezoelectric cylindrical nanoshells using nonlocal continuum model. Applied Mathematical Modelling 59:341–56. doi:10.1016/j.apm.2018.01.032.
   Web of Science ®Google Scholar
• Tufekci, E., and S. A. Aya. 2016. A nonlocal beam model for out-of-plane static analysis of circular nanobeams. Mechanics Research Communications 76:11–23. doi:10.1016/j.mechrescom.2016.06.002.
   Web of Science ®Google Scholar
• Wang, Z. L., and J. Song. 2006. Piezoelectric nanogenerators based on zinc oxide nanowire arrays. Science 312 (5771):242–6. doi:10.1126/science.1124005.
   PubMed Web of Science ®Google Scholar
• Wang, G. F., and X. Q. Feng. 2007. Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Applied Physics Letters 90 (23):231904. doi:10.1063/1.2746950.
   Web of Science ®Google Scholar
• Wang, B., J. Zhao, and S. Zhou. 2010. A micro scale Timoshenko beam model based on strain gradient elasticity theory. European Journal of Mechanics – A/Solids 29 (4):591–9. doi:10.1016/j.euromechsol.2009.12.005.
   Web of Science ®Google Scholar
• Wang, Z. Q., Y. P. Zhao, and Z. P. Huang. 2010. The effects of surface tension on the elastic properties of nano structures. International Journal of Engineering Science 48 (2):140–50. doi:10.1016/j.ijengsci.2009.07.007.
   Web of Science ®Google Scholar
• Wang, L. 2012. Surface effect on buckling configuration of nanobeams containing internal flowing fluid: A nonlinear analysis. Physica E 44 (4):808–12. doi:10.1016/j.physe.2011.12.006.
   Google Scholar
• Wang, Y.-G., W.-H. Lin, and N. Liu. 2015. Nonlinear bending and post-buckling of extensible microscale beams based on modified couple stress theory. Applied Mathematical Modelling 39 (1):117–27. doi:10.1016/j.apm.2014.05.007.
   Web of Science ®Google Scholar
• Wang, Y. Q., X. B. Huang, and J. Li. 2016. Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process. International Journal of Mechanical Sciences 110:201–16. doi:10.1016/j.ijmecsci.2016.03.010.
   Web of Science ®Google Scholar
• Wang, Y. Q., and J. W. Zu. 2017a. Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerospace Science and Technology 69:550–62. doi:10.1016/j.ast.2017.07.023.
   Web of Science ®Google Scholar
• Wang, Y. Q., and J. W. Zu. 2017b. Nonlinear steady-state responses of longitudinally traveling functionally graded material plates in contact with liquid. Composite Structures 164:130–44. doi:10.1016/j.compstruct.2016.12.053.
   Web of Science ®Google Scholar
• Wang, Y. Q. 2018. Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state. Acta Astronautica 143:263–71. doi:10.1016/j.actaastro.2017.12.004.
   Web of Science ®Google Scholar
• Wang, Y. Q., and Z. Y. Zhang. 2018. Non-local buckling analysis of functionally graded nanoporous metal foam nanoplates. Coatings 8 (11):389. doi:10.3390/coatings8110389.
   Web of Science ®Google Scholar
• Wang, Y. Q., H. H. Li, Y. F. Zhang, and J. W. Zu. 2018. A nonlinear surface-stress-dependent model for vibration analysis of cylindrical nanoscale shells conveying fluid. Applied Mathematical Modelling 64:55–70. doi:10.1016/j.apm.2018.07.016.
   Web of Science ®Google Scholar
• Wang, Y. Q., and C. Liang. 2019. Wave propagation characteristics in nanoporous metal foam nanobeams. Results in Physics 12:287–97. doi:10.1016/j.rinp.2018.11.080.
   Web of Science ®Google Scholar
• Wang, Y. Q., Y. H. Wan, and J. W. Zu. 2019. Nonlinear dynamic characteristics of functionally graded sandwich thin nanoshells conveying fluid incorporating surface stress influence. Thin-Walled Structures 135:537–47. doi:10.1016/j.tws.2018.11.023.
   Web of Science ®Google Scholar
• Wang, Y. Q., Y. F. Liu, and J. W. Zu. 2019. Analytical treatment of nonlocal vibration of multilayer functionally graded piezoelectric nanoscale shells incorporating thermal and electrical effect. The European Physical Journal Plus 134:54.
   Web of Science ®Google Scholar
• Wang, Y. Q., C. Ye, and J. W. Zu. 2019. Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets. Aerospace Science and Technology 85:359–70. doi:10.1016/j.ast.2018.12.022.
   Web of Science ®Google Scholar
• Xia, W., L. Wang, and L. Yin. 2010. Nonlinear non-classical microscale beams: Static bending, postbuckling and free vibration. International Journal of Engineering Science 48 (12):2044–53. doi:10.1016/j.ijengsci.2010.04.010.
   Web of Science ®Google Scholar
• Xu, L., and Q. Yang. 2015. Multi-field coupled dynamics for a micro beam. Mechanics Based Design of Structures and Machines, an International Journal 43 (1):57–73. doi:10.1080/15397734.2014.928221.
   Web of Science ®Google Scholar
• Yang, Z., and D. He. 2017. Vibration and buckling of orthotropic functionally graded micro-plates on the basis of a re-modified couple stress theory. Results in Physics 7:3778–87.
   Web of Science ®Google Scholar
• Yokota, S. 2008. Micro actuators by making use of jet flows due to electro-conjugate fluid. Mechanics Based Design of Structures and Machines, an International Journal 36 (4):330–45. doi:10.1080/15397730802405879.
   Web of Science ®Google Scholar
• Zhang, Y. Q., M. Pang, and W. Q. Chen. 2015. Transverse vibrations of embedded nanowires under axial compression with high-order surface stress effects. Physica E 66:238–44. doi:10.1016/j.physe.2014.10.027.
   Google Scholar
• Zhao, X. J., and R. K. N. D. Rajapakse. 2009. Analytical solutions for a surface loaded isotropic elastic layer with surface energy effects. International Journal of Engineering Science 47 (11-12):1433–44. doi:10.1016/j.ijengsci.2008.12.013.
   Web of Science ®Google Scholar
• Zhen, Y.-X., S.-L. Wen, and Y. Tang. 2019. Free vibration analysis of viscoelastic nanotubes under longitudinal magnetic field based on nonlocal strain gradient Timoshenko beam model. Physica E 105:116–24. doi:10.1016/j.physe.2018.09.005.
   Google Scholar