391
Views
36
CrossRef citations to date
0
Altmetric
Articles

Structural dynamics and stability analysis of 2D-FG microbeams with two-directional porosity distribution and variable material length scale parameter

ORCID Icon & ORCID Icon
Pages 164-191 | Received 22 Oct 2018, Accepted 31 May 2019, Published online: 18 Jun 2019

References

  • Aghazadeh, R., E. Cigeroglu, and S. Dag. 2014. Static and free vibration analyses of small-scale functionally graded beams possessing a variable length scale parameter using different beam theories. European Journal of Mechanics - A/Solids 46:1–11. doi: 10.1016/j.euromechsol.2014.01.002.
  • Akbarzadeh Khorshidi, M., M. Shariati, and S. Emam. 2016. Postbuckling of functionally graded nanobeams based on modified couple stress theory under general beam theory. International Journal of Mechanical Sciences 110:160–9. doi: 10.1016/j.ijmecsci.2016.03.006.
  • Akbarzadeh Khorshidi, M. 2018. The material length scale parameter used in couple stress theories is not a material constant. International Journal of Engineering Science 133:15–25. doi: 10.1016/j.ijengsci.2018.08.005.
  • Akgöz, B., and Ö. Civalek. 2013. Free vibration analysis of axially functionally graded tapered bernoulli–euler microbeams based on the modified couple stress theory. Composite Structures 98:314–22. doi: 10.1016/j.compstruct.2012.11.020.
  • Akgöz, B., and Ö. Civalek. 2014. Thermo-mechanical buckling behavior of functionally graded microbeams embedded in elastic medium. International Journal of Engineering Science 85:90–104. doi: 10.1016/j.ijengsci.2014.08.011.
  • Al-Basyouni, K., A. Tounsi, and S. Mahmoud. 2015. Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position. Composite Structures 125:621–30. doi: 10.1016/j.compstruct.2014.12.070.
  • Arefi, M., and A. 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 46(6):669–92. doi: 10.1080/15397734.2018.1434002.
  • Asghari, M., M. Ahmadian, M. Kahrobaiyan, and M. Rahaeifard. 2010. On the size-dependent behavior of functionally graded micro-beams. Materials & Design (1980-2015) 31(5):2324–9. doi: 10.1016/j.matdes.2009.12.006.
  • Asghari, M., M. Rahaeifard, M. Kahrobaiyan, and M. Ahmadian. 2011. The modified couple stress functionally graded Timoshenko beam formulation. Materials & Design 32(3):1435–43. doi: 10.1016/j.matdes.2010.08.046.
  • Barati, M., and A. Zenkour. 2017. Investigating post-buckling of geometrically imperfect metal foam nanobeams with symmetric and asymmetric porosity distributions. Composite Structures 182 :91–8. doi: 10.1016/j.compstruct.2017.09.008.
  • Biswas, S. 2019. Fundamental solution of steady oscillations for porous materials with dual-phase-lag model in micropolar thermoelasticity. Mechanics Based Design of Structures and Machines 1–23. doi: 10.1080/15397734.2018.1557528.
  • Chen, D., J. Yang, and S. Kitipornchai. 2016a. Corrigendum to “Elastic Buckling and Static Bending of Shear Deformable Functionally Graded Porous Beam” [Compos. Struct. 133 (2015) 54–61]. Composite Structures 139:221. doi: 10.1016/j.compstruct.2015.12.063.
  • Chen, D., J. Yang, and S. Kitipornchai. 2016b. Free and forced vibrations of shear deformable functionally graded porous beams. International Journal of Mechanical Sciences 108-109:14–22. doi: 10.1016/j.ijmecsci.2016.01.025.
  • Chen, X., X. Zhang, Y. Lu, and Y. Li. 2019a. Static and dynamic analysis of the postbuckling of bi-directional functionally graded material microbeams. International Journal of Mechanical Sciences 151:424–43. doi: 10.1016/j.ijmecsci.2018.12.001.
  • Chen, X., Y. Lu, and Y. Li. 2019b. Free vibration, buckling and dynamic stability of bi-directional FG microbeam with a variable length scale parameter embedded in elastic medium. Applied Mathematical Modelling 67:430–48. doi: 10.1016/j.apm.2018.11.004.
  • Dastjerdi, S., and Y. Tadi Beni. 2019. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment. Mechanics Based Design of Structures and Machines 1–26. doi: 10.1080/15397734.2018.1557529.
  • Dehrouyeh-Semnani, A., H. Mostafaei, and M. Nikkhah-Bahrami. 2016. Free flexural vibration of geometrically imperfect functionally graded microbeams. International Journal of Engineering Science 105:56–79. doi: 10.1016/j.ijengsci.2016.05.002.
  • Faleh, N., R. Ahmed, and R. Fenjan. 2018. On vibrations of porous FG nanoshells. International Journal of Engineering Science 133:1–14. doi: 10.1016/j.ijengsci.2018.08.007.
  • Goupee, A., and S. Vel. 2006. Optimization of natural frequencies of bidirectional functionally graded beams. Structural and Multidisciplinary Optimization 32(6):473–84. doi: 10.1007/s00158-006-0022-1.
  • 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 45(1):1–11. doi: 10.1080/15397734.2015.1125298.
  • Heshmati, M., Y. Amini, and F. Daneshmand. 2019. Vibration and instability analysis of closed-cell poroelastic pipes conveying fluid. European Journal of Mechanics - A/Solids 73:356–65. doi: 10.1016/j.euromechsol.2018.09.012.
  • Jamshidi, M., and J. Arghavani. 2017. Optimal design of two-dimensional porosity distribution in shear deformable functionally graded porous beams for stability analysis. Thin-Walled Structures 120:81–90. doi: 10.1016/j.tws.2017.08.027.
  • Kahrobaiyan, M., M. Rahaeifard, S. Tajalli, and M. Ahmadian. 2012. A strain gradient functionally graded Euler–Bernoulli beam formulation. International Journal of Engineering Science 52:65–76. doi: 10.1016/j.ijengsci.2011.11.010.
  • Karamanlı, A., and T. Vo. 2018. Size dependent bending analysis of two directional functionally graded microbeams via a quasi-3D theory and finite element method. Composites Part B: Engineering 144:171–83. doi: 10.1016/j.compositesb.2018.02.030.
  • Karamanlı, A. 2018. Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory. Composite Structures 189:127–36. doi: 10.1016/j.compstruct.2018.01.060.
  • Karamanlı, A. 2017a. Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3D shear deformation theory. Composite Structures 174:70–86. doi: 10.1016/j.compstruct.2017.04.046.
  • Karamanlı, A. 2017b. Elastostatic analysis of two-directional functionally graded beams using various beam theories and symmetric smoothed particle hydrodynamics method. Composite Structures 160:653–69. doi: 10.1016/j.compstruct.2016.10.065.
  • Ke, L., Y. Wang, J. Yang, and S. Kitipornchai. 2012. Nonlinear free vibration of size-dependent functionally graded microbeams. International Journal of Engineering Science 50(1):256–67. doi: 10.1016/j.ijengsci.2010.12.008.
  • Ke, L., and Y. Wang. 2011. Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory. Composite Structures 93(2):342–50. doi: 10.1016/j.compstruct.2010.09.008.
  • Kim, J., K. Żur, and J. 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.
  • Kitipornchai, S., D. Chen, and J. Yang. 2017. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Materials & Design 116 :656–65. doi: 10.1016/j.matdes.2016.12.061.
  • Lezgy-Nazargah, M. 2015. Fully coupled thermo-mechanical analysis of bi-directional FGM Beams using NURBS isogeometric finite element approach. Aerospace Science and Technology 45:154–64. doi: 10.1016/j.ast.2015.05.006.
  • Li, L., X. Li, and Y. Hu. 2018. Nonlinear bending of a two-dimensionally functionally graded beam. Composite Structures 184:1049–61. doi: 10.1016/j.compstruct.2017.10.087.
  • Li, L., and Y. Hu. 2017. Torsional statics of two-dimensionally functionally graded microtubes. Mechanics of Advanced Materials and Structures 26:430–442. doi: 10.1080/15376494.2017.1400617.
  • Lü, C., W. Chen, R. Xu, and C. Lim. 2008. Semi-analytical elasticity solutions for bi-directional functionally graded beams. International Journal of Solids and Structures 45(1):258–75. doi: 10.1016/j.ijsolstr.2007.07.018.
  • Mindlin, R. 1963. Influence of couple-stresses on stress concentrations. Experimental Mechanics 3(1):1–7. doi: 10.1007/BF02327219.
  • Mojahedin, A., M. Jabbari, A. Khorshidvand, and M. Eslami. 2016. Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory. Thin-Walled Structures 99:83–90. doi: 10.1016/j.tws.2015.11.008.
  • Nateghi, A., and M. Salamat-Talab. 2013. Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory. Composite Structures 96:97–110. doi: 10.1016/j.compstruct.2012.08.048.
  • Nateghi, A., M. Salamat-Talab, J. Rezapour, and B. Daneshian. 2012. Size dependent buckling analysis of functionally graded micro beams based on modified couple stress theory. Applied Mathematical Modelling 36(10):4971–87. doi: 10.1016/j.apm.2011.12.035.
  • Nemat-Alla, M. 2003. Reduction of thermal stresses by developing two-dimensional functionally graded materials. International Journal of Solids and Structures 40(26):7339–56. doi: 10.1016/j.ijsolstr.2003.08.017.
  • Nguyen, N.,. T. Nguyen, H. Thai, and T. Vo. 2018. A ritz type solution with exponential trial functions for laminated composite beams based on the modified couple stress theory. Composite Structures 191:154–67. doi: 10.1016/j.compstruct.2018.02.025.
  • Pydah, A., and R. Batra. 2017. Shear deformation theory using logarithmic function for thick circular beams and analytical solution for bi-directional functionally graded circular beams. Composite Structures 172:45–60. doi: 10.1016/j.compstruct.2017.03.072.
  • Rashidi, S., J. Esfahani, and N. Karimi. 2018. Porous materials in building energy technologies—a review of the applications, modelling and experiments. Renewable and Sustainable Energy Reviews 91:229–47. doi: 10.1016/j.rser.2018.03.092.
  • Reddy, J. 2011. Microstructure-dependent couple stress theories of functionally graded beams. Journal of the Mechanics and Physics of Solids 59(11):2382–99. doi: 10.1016/j.jmps.2011.06.008.
  • Repka, M., V. Sladek, and J. Sladek. 2018. Gradient elasticity theory enrichment of plate bending theories. Composite Structures 202:447–57. doi: 10.1016/j.compstruct.2018.02.065.
  • Rezaiee-Pajand, M., M. Mokhtari, and S. Hozhabrossadati. 2019. Application of Hencky bar-chain model to buckling analysis of elastically restrained timoshenko axially functionally graded carbon nanotube reinforced composite beams. Mechanics Based Design of Structures and Machines 1–22. doi: 10.1080/15397734.2019.1596129.
  • Roberts, A., and E. Garboczi. 2001. Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia 49(2):189–97. doi: 10.1016/S1359-6454(00)00314-1.
  • Salamat-Talab, M., A. Nateghi, and J. Torabi. 2012. Static and dynamic analysis of third-order shear deformation FG micro beam based on modified couple stress theory. International Journal of Mechanical Sciences 57(1):63–73. no. doi: 10.1016/j.ijmecsci.2012.02.004.
  • Shafiei, N., and M. Kazemi. 2017. Buckling analysis on the bi-dimensional functionally graded porous tapered nano-/micro-scale beams. Aerospace Science and Technology 66:1–11. doi: 10.1016/j.ast.2017.02.019.
  • Shafiei, N., S. Mirjavadi, B. MohaselAfshari, S. Rabby, and M. Kazemi. 2017. Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams. Computer Methods in Applied Mechanics and Engineering 322:615–32. doi: 10.1016/j.cma.2017.05.007.
  • Shafiei, N., M. Kazemi, and M. Ghadiri. 2016. Nonlinear vibration of axially functionally graded tapered microbeams. International Journal of Engineering Science 102:12–26. doi: 10.1016/j.ijengsci.2016.02.007.
  • Shahverdi, H., and M. Barati. 2017. Vibration analysis of porous functionally graded nanoplates. International Journal of Engineering Science 120:82–99. doi: 10.1016/j.ijengsci.2017.06.008.
  • She, G., F. Yuan, Y. Ren, H. Liu, and W. 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.
  • Shojaeefard, M., H. Saeidi Googarchin, M. Ghadiri, and M. Mahinzare. 2017. Micro temperature-dependent FG porous plate: free vibration and thermal buckling analysis using modified couple stress theory with CPT And FSDT. Applied Mathematical Modelling 50:633–55. doi: 10.1016/j.apm.2017.06.022.
  • Şimşek, M. 2015a. Size dependent nonlinear free vibration of an axially functionally graded (AFG) microbeam using He’s variational method. Composite Structures 131:207–14. doi: 10.1016/j.compstruct.2015.05.004.
  • Şimşek, M., T. Kocatürk, and Ş. Akbaş. 2013. Static bending of a functionally graded microscale Timoshenko beam based on the modified couple stress theory. Composite Structures 95:740–7. doi: 10.1016/j.compstruct.2012.08.036.
  • Şimşek, M., and J. Reddy. 2013a. Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory. International Journal of Engineering Science 64:37–53. doi: 10.1016/j.ijengsci.2012.12.002.
  • Şimşek, M., and J. Reddy. 2013b. A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory. Composite Structures 101 :47–58. doi: 10.1016/j.compstruct.2013.01.017.
  • Şimşek, M. 2015b. Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions. Composite Structures 133:968–78. doi: 10.1016/j.compstruct.2015.08.021.
  • Şimşek, M. 2016. Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions. Composite Structures 149:304–14. doi: 10.1016/j.compstruct.2016.04.034.
  • Tang, H., L. Li, and Y. Hu. 2018. Buckling analysis of two-directionally porous beam. Aerospace Science and Technology 78:471–9. doi: 10.1016/j.ast.2018.04.045.
  • Thai, H., T. Vo, T. Nguyen, and J. Lee. 2015. Size-dependent behavior of functionally graded sandwich microbeams based on the modified couple stress theory. Composite Structures 123:337–49. doi: 10.1016/j.compstruct.2014.11.065.
  • Thai, H., T. Vo, T. Nguyen, and S. Kim. 2017. A review of continuum mechanics models for size-dependent analysis of beams and plates. Composite Structures 177:196–219. doi: 10.1016/j.compstruct.2017.06.040.
  • Thai, C., A. Ferreira, and H. Nguyen-Xuan. 2018. Isogeometric analysis of size-dependent isotropic and sandwich functionally graded microplates based on modified strain gradient elasticity theory. Composite Structures 192:274–88. doi: 10.1016/j.compstruct.2018.02.060.
  • Toone, N., W. Fazio, J. Lund, G. Teichert, B. Jensen, S. Burnett, and L. Howell. 2014. Investigation of unique carbon nanotube cell restraint compliant mechanisms. Mechanics Based Design of Structures and Machines 42(3):343–54. doi: 10.1080/15397734.2014.908298.
  • Trinh, L., H. Nguyen, T. Vo, and T. Nguyen. 2016. Size-dependent behaviour of functionally graded microbeams using various shear deformation theories based on the modified couple stress theory. Composite Structures 154:556–72. doi: 10.1016/j.compstruct.2016.07.033.
  • Trinh, L., T. Vo, H. Thai, and T. Nguyen. 2018. Size-dependent vibration of bi-directional functionally graded microbeams with arbitrary boundary conditions. Composites Part B: Engineering 134:225–45. doi: 10.1016/j.compositesb.2017.09.054.
  • Vo, T., H. Thai, T. Nguyen, D. Lanc, and A. Karamanli. 2017. Flexural analysis of laminated composite and sandwich beams using a four-unknown shear and normal deformation theory. Composite Structures 176:388–97. doi: 10.1016/j.compstruct.2017.05.041.
  • Wattanasakulpong, N., A. Chaikittiratana, and S. Pornpeerakeat. 2018. Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory. Acta Mechanica Sinica 34(6):1124–35. doi: 10.1007/s10409-018-0770-3.
  • Wattanasakulpong, N., and V. Ungbhakorn. 2014. Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology 32(1):111–20. doi: 10.1016/j.ast.2013.12.002.
  • Xu, L., and Q. Yang. 2015. Multi-field coupled dynamics for a micro beam. Mechanics Based Design of Structures and Machines 43(1):57–73. doi: 10.1080/15397734.2014.928221.
  • Xue, Y., G. Jin, X. Ma, H. Chen, T. Ye, M. Chen, and Y. Zhang. 2019. Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach. International Journal of Mechanical Sciences 152:346–62. doi: 10.1016/j.ijmecsci.2019.01.004.
  • Yang, F., A. Chong, D. Lam, and P. Tong. 2002. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures 39(10):2731–43. doi: 10.1016/S0020-7683(02)00152-X.
  • Yu, T., J. Zhang, H. Hu, and T. Bui. 2019. A novel size-dependent quasi-3D isogeometric beam model for two-directional FG microbeams analysis. Composite Structures 211:76–88. doi: 10.1016/j.compstruct.2018.12.014.
  • Hajilak, Z. E., J. Pourghader, D. Hashemabadi, F. S. Bagh, M. Habibi, and H. Safarpour. 2019. Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory. Mechanics Based Design of Structures and Machines doi: 10.1080/15397734.2019.1566743.
  • Zhao, L., W. Chen, and C. Lü. 2012. Symplectic elasticity for bi-directional functionally graded materials. Mechanics of Materials 54:32–42. doi: 10.1016/j.mechmat.2012.06.001.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.