Steel and Composite Structures

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Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams

  • Mirjavadi, Seyed Sajad (Department of Mechanical and Industrial Engineering, Qatar University) ;
  • Afshari, Behzad Mohasel (School of Mechanical Engineering, College of Engineering, University of Tehran) ;
  • Shafiei, Navvab (Department of Mechanical Engineering, Payame Noor University (PNU)) ;
  • Hamouda, A.M.S. (Department of Mechanical and Industrial Engineering, Qatar University) ;
  • Kazemi, Mohammad (Hoonam Sanat Farnak Engineering and Technology Company)
  • Received : 2017.03.14
  • Accepted : 2017.08.01
  • Published : 2017.11.20
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Abstract

The thermo-mechanical vibration behavior of two dimensional functionally graded (2D-FG) porous nanobeam is reported in this paper. The material properties of the nanobeam are variable along thickness and length of the nanobeam according to the power law function. The nanobeam is modeled within the framework of Timoshenko beam theory. Eringen's nonlocal elasticity theory is used to develop the governing equations. Using the generalized differential quadrature method (GDQM) the governing equations are solved. The effect of porosity, temperature distribution, nonlocal value, L/h, FG power indexes along thickness and length and are investigated using parametric studies.

Keywords

References

  1. Ahouel, M., Houari, M.S.A., Bedia, E. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
  2. Amirian, B., Hosseini-ara, R. and Moosavi, H. (2014), "Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model", Appl. Math. Mech., 35(7), 875-886. https://doi.org/10.1007/s10483-014-1835-9
  3. Anne, G., Vanmeensel, K., Vleugels, J. and Van der biest, O. (2005), "Electrophoretic deposition as a novel near net shaping technique for functionally graded biomaterials", Mater. Sci. Forum, 492-493,213-218. https://doi.org/10.4028/www.scientific.net/MSF.492-493.213
  4. Ansari, R., Pourashraf, T. and Gholami, R. (2015), "An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory", Thin Wall. Struct., 93, 169-176. https://doi.org/10.1016/j.tws.2015.03.013
  5. Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E. and Mahmoud, S. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  6. Berrabah, H., Tounsu, A., Semmah, A. and Adda, B. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
  7. De pietro, G., Hui, Y., Giunta, G., Belouettar, S., Carrera, E. and Hu, H. (2016), "Hierarchical one-dimensional finite elements for the thermal stress analysis of three-dimensional functionally graded beams", Compos. Struct., 153, 514-528. https://doi.org/10.1016/j.compstruct.2016.06.012
  8. Della, C. and Shu, D.W. (2015), "Vibration of porous beams with embedded piezoelectric sensors and actuators.
  9. Ebrahimi, F. and SALARI, E. (2015), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
  10. Elsibai K.A. and Youssef, H.M. (2011), "State-space approach to vibration of gold nano-beam induced by ramp type heating without energy dissipation in femtoseconds scale", J. Therm. Stresses, 34(3), 244-263. https://doi.org/10.1080/01495739.2010.545737
  11. Eltaher, M., Alshorbagy, A.E. and Mahmoud, F. (2013a), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
  12. Eltaher, M., Mahmoud, F., Assie, A. and Meletis, E. (2013b), "Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams", Appl. Math. Comput., 224, 760-774.
  13. Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  14. Hassanin, H. and Jiang, K. (2010), "Infiltration-processed, functionally graded materials for microceramic componenets", Proceedings of the Micro Electro Mechanical Systems (MEMS), 2010 IEEE 23rd International Conference on, 2010. IEEE.
  15. Hayati, H., Hosseini, S.A. and Rahmani, O. (2017), "Coupled twist-bending static and dynamic behavior of a curved singlewalled carbon nanotube based on nonlocal theory", Microsyst. Technol., 23(7), 2393-2401. https://doi.org/10.1007/s00542-016-2933-0
  16. Hosseini-hashemi, S., Nahas, I., Fakher, M. and Nazemnezhad, R. (2014), "Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity", Acta Mechanica, 225(6), 1555-1564. https://doi.org/10.1007/s00707-013-1014-z
  17. Hosseini, S. and Rahmani, O. (2017), "Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory", Meccanica, 52(6), 1441-1457. https://doi.org/10.1007/s11012-016-0491-2
  18. Juntarasaid, C., Pulngern, T. and Chucheepsakul, S. (2012), "Bending and buckling of nanowires including the effects of surface stress and nonlocal elasticity", Physica E: Lowdimensional Syst. Nanostruct., 46, 68-76. https://doi.org/10.1016/j.physe.2012.08.005
  19. Kato, K., Kurimoto, M., Shumiya, H., Adachi, H., Sakuma, S. and Okubo, H. (2006), "Application of functionally graded material for solid insulator in gaseous insulation system", IEEE T. Dielect. El. In., 13(2), 362-372. https://doi.org/10.1109/TDEI.2006.1624281
  20. Ke, L.L. and Wang, Y.S. (2012), "Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory", Smart Mater. Struct., 21(2), 025018. https://doi.org/10.1088/0964-1726/21/2/025018
  21. Leclaire, P., Horoshenkov, K., Swift, M. and Hothersall, D. (2001), "The vibrational response of a clamped rectangular porous plate", J. Sound Vib., 247(1), 19-31. https://doi.org/10.1006/jsvi.2000.3657
  22. Lee, H.L. and Chang, W.J. (2011), "Surface effects on axial buckling of nonuniform nanowires using non-local elasticity theory", IET Micro & Nano Lett., 6(1), 19-21. https://doi.org/10.1049/mnl.2010.0191
  23. Lee, W.Y., Stinton, D.P., Berndt, C.C., Erdogan, F., Lee, Y.D. and Mutasim, Z. (1996), "Concept of functionally graded materials for advanced thermal barrier coating applications", J. Am. Ceram. Soc., 79(12), 3003-3012. https://doi.org/10.1111/j.1151-2916.1996.tb08070.x
  24. Lei, Y., Adhikari, S. and Friswell, M. (2013), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams", Int. J. Eng. Sci., 66-67, 1-13. https://doi.org/10.1016/j.ijengsci.2013.02.004
  25. Li, C. (2013), "Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory", Struct. Eng. Mech., 48, 415-434. https://doi.org/10.12989/sem.2013.48.3.415
  26. Li, C., Lim, C.W., Yu, J. and Zeng, Q. (2011), "Analytical solutions for vibration of simply supported nonlocal nanobeams with an axial force", Int. J. Struct. Stab. Dynam., 11(2), 257-271. https://doi.org/10.1142/S0219455411004087
  27. Malekzadeh, P. and Shojaee, M. (2013), "Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams", Composites Part B: Eng., 52, 84-92. https://doi.org/10.1016/j.compositesb.2013.03.046
  28. Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S. and Mohasel afshari, B. (2017), "Thermal buckling behavior of twodimensional imperfect functionally graded microscale-tapered porous beam", J. Therm. Stresses, 40(10), 1201-1214. Doi: 10.1080/01495739.2017.1332962.
  29. Muller, E., DraSar, C., Schilz, J. and Kaysser, W. (2003), "Functionally graded materials for sensor and energy applications", Mater. Sci. Eng., 362(1-2), 17-39. https://doi.org/10.1016/S0921-5093(03)00581-1
  30. Murmu, T. and Adhikari, S. (2010), "Nonlocal transverse vibration of double-nanobeam-systems", J. Appl. Phys., 108(8), 083514. https://doi.org/10.1063/1.3496627
  31. Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031
  32. Nazemnezhad, R. and Hosseini-hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. https://doi.org/10.1016/j.compstruct.2013.12.006
  33. Nemat-alla, M. (2003), "Reduction of thermal stresses by developing two-dimensional functionally graded materials", Int. J. Solids Struct., 40(26), 7339-7356. https://doi.org/10.1016/j.ijsolstr.2003.08.017
  34. Nemat-alla, M., Ahmed, K.I. and Hassab-allah, I. (2009), "Elastic-plastic analysis of two-dimensional functionally graded materials under thermal loading", Int. J. Solids Struct., 46(14-15), 2774-2786. https://doi.org/10.1016/j.ijsolstr.2009.03.008
  35. Olevsky, E., Wang, X., Maximenko, A. and Meyers, M. (2007), "Fabrication of net-shape functionally graded composites by electrophoretic deposition and sintering: modeling and experimentation", J. Am.Ceram. Soc., 90(10), 3047-3056. https://doi.org/10.1111/j.1551-2916.2007.01838.x
  36. Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D. and Schulte, K. (2003), "Functionally graded materials for biomedical applications", Mater. Sci. Eng., 362(1-2), 40-60. https://doi.org/10.1016/S0921-5093(03)00580-X
  37. Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers", Compos. Struct., 96, 716-725. https://doi.org/10.1016/j.compstruct.2012.10.005
  38. Rahmani, O., Hosseini, S., Ghoytasi, I. and Golmohammadi, H. (2017a), "Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties", Appl. Phys. A, 123, 4.
  39. Rahmani, O., Niaei, A.M., Hosseini, S. and Shojaei, M. (2017b), "In-plane vibration of FG micro/nano-mass sensor based on nonlocal theory under various thermal loading via differential transformation method", Superlattices Microstruct., 101, 23-39. https://doi.org/10.1016/j.spmi.2016.11.018
  40. Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
  41. Renault, A., Jaouen, L. and Sgard, F. (2011), "Characterization of elastic parameters of acoustical porous materials from beam bending vibrations", J. Sound Vib., 330(9), 1950-1963. https://doi.org/10.1016/j.jsv.2010.11.013
  42. Shafiei, N., Kazemi, M. and Ghadiri, M. (2016a), "Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler-Bernoulli microbeams", Physica E: Low-dimensional Syst. Nanost., 83, 74-87. https://doi.org/10.1016/j.physe.2016.04.011
  43. Shafiei, N., Kazemi, M. Safi, M. and Ghadiri, M. (2016b), "Nonlinear vibration of axially functionally graded non-uniform nanobeams", Int. J. Eng. Sci., 106, 77-94. https://doi.org/10.1016/j.ijengsci.2016.05.009
  44. Simsek, M. (2014), "Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory", Composites Part B: Eng., 56, 621-628. https://doi.org/10.1016/j.compositesb.2013.08.082
  45. Simsek, M. (2016), "Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions", Compos. Struct., 149, 304-314. https://doi.org/10.1016/j.compstruct.2016.04.034
  46. Simsek, M. and Yurtcu, H. (2013a), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  47. Simsek, M. and Yurtcu, H.H. (2013b), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
  48. Thau, H.T. and VO, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009
  49. Touloukian, Y.S. and Ho, C. (1970), "Thermal expansion. Nonmetallic solids", Thermophysical properties of matter-The TPRC Data Series, New York: IFI/Plenum, 1970-, (Eds., Touloukian, Y.S.), (series ed.); Ho, CY${\mid}e$ (series tech. ed.), 1.
  50. Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanotechnology, 18(10), 105401. https://doi.org/10.1088/0957-4484/18/10/105401
  51. Watari, F., Yokoyama, A., Omori, M., Hirai, T., Kondo, H., Uo, M. and Kawasaki, T. (2004), "Biocompatibility of materials and development to functionally graded implant for bio-medical application", Compos. Sci. Technol., 64(6), 893-908. https://doi.org/10.1016/j.compscitech.2003.09.005
  52. Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method", Meccanica, 50(5), 1331-1342. https://doi.org/10.1007/s11012-014-0094-8
  53. Wosko, M., Paszkiewicz, B., Piasecki, T., Szyszka, A., Paszkiewicz, R. and Tlaczala, M. (2005), "Applications of functionally graded materials in optoelectronic devices", Optica Applicata, 35(3), 663-667.
  54. Yang, J. and Shen, H.S. (2002), "Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments", J. Sound Vib., 255(3), 579-602. https://doi.org/10.1006/jsvi.2001.4161
  55. Youssef, H.M. and Elsibai, K.A. (2011), "Vibration of gold nanobeam induced by different types of thermal loading-a state-space approach", Nanosc. Microsc. Therm., 15(1), 48-69. https://doi.org/10.1080/15567265.2010.549929
  56. Zhang, Y., Wang, C. and Challamel, N. (2009), "Bending, buckling, and vibration of micro/nanobeams by hybrid nonlocal beam model", J. Eng. Mech., 136(5),, 562-574.
  57. Zhou, F.X. and Ma, Q. (2014), "Dynamic response of twodimensional fluid-saturated porous beam", Appl. Mech. Mater., 580-583, 169-174. https://doi.org/10.4028/www.scientific.net/AMM.580-583.169

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