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Nonlocal strain gradient-based vibration analysis of embedded curved porous piezoelectric nano-beams in thermal environment

  • Ebrahimi, Farzad (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Daman, Mohsen (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University) ;
  • Jafari, Ali (Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University)
  • 투고 : 2017.03.31
  • 심사 : 2017.09.15
  • 발행 : 2017.12.25

초록

This disquisition proposes a nonlocal strain gradient beam theory for thermo-mechanical dynamic characteristics of embedded smart shear deformable curved piezoelectric nanobeams made of porous electro-elastic functionally graded materials by using an analytical method. Electro-elastic properties of embedded curved porous FG nanobeam are assumed to be temperature-dependent and vary through the thickness direction of beam according to the power-law which is modified to approximate material properties for even distributions of porosities. It is perceived that during manufacturing of functionally graded materials (FGMs) porosities and micro-voids can be occurred inside the material. Since variation of pores along the thickness direction influences the mechanical and physical properties, so in this study thermo-mechanical vibration analysis of curve FG piezoelectric nanobeam by considering the effect of these imperfections is performed. Nonlocal strain gradient elasticity theory is utilized to consider the size effects in which the stress for not only the nonlocal stress field but also the strain gradients stress field. The governing equations and related boundary condition of embedded smart curved porous FG nanobeam subjected to thermal and electric field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is utilized to achieve the natural frequencies of porous FG curved piezoelectric nanobeam resting on Winkler and Pasternak foundation. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality parameter, electric voltage, coefficient of porosity, elastic foundation parameters, thermal effect, gradient index, strain gradient, elastic opening angle and slenderness ratio on the natural frequency of embedded curved FG porous piezoelectric nanobeam are successfully discussed. It is concluded that these parameters play important roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

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참고문헌

  1. Akgoz, B. and Civalek,O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403
  2. Ansari, R., Gholami, R. and Sahmani, S. (2013), "Size-dependent vibration of functionally graded curved microbeams based on the modified strain gradient elasticity theory", Archive Appl. Mech., 83(10), 1439-1449. https://doi.org/10.1007/s00419-013-0756-3
  3. Benveniste, Y. (1995), "Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases", Phys. Rev. B., 51(22), 16424. https://doi.org/10.1103/PhysRevB.51.16424
  4. Bounouara, F., et al., (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  5. Boutahar, L. and Benamar, R. (2016), "A homogenization procedure for geometrically non-linear free vibration analysis of functionally graded annular plates with porosities resting on elastic foundations",. Ain Shams Engineering Journal,.
  6. Doroushi, A., Eslami, M. and Komeili, A. (2011), "Vibration analysis and transient response of an FGPM beam under thermo-electro-mechanical loads using higher-order shear deformation theory", J. Intel. Mat.Syst. Str.,. 22(3), 231-243. https://doi.org/10.1177/1045389X11398162
  7. Ebrahimi, F. (2013), "Analytical investigation on vibrations and dynamic response of functionally graded plate integrated with piezoelectric layers in thermal environment", Mech. Adv. Mater. Struct., 20(10), 854-870. https://doi.org/10.1080/15376494.2012.677098
  8. Ebrahimi, F. and Barati, M.R. (2016a), "Magneto-electro-elastic buckling analysis of nonlocal curved nanobeams", European Phys. J. Plus, 131(9), 346. https://doi.org/10.1140/epjp/i2016-16346-5
  9. Ebrahimi, F. and Barati, M.R. (2016b), "Static stability analysis of smart magneto-electro-elastic heterogeneous nanoplates embedded in an elastic medium based on a four-variable refined plate theory", Smart Mater. Struct., 25(10), 105014. https://doi.org/10.1088/0964-1726/25/10/105014
  10. Ebrahimi, F. and Barati, M.R. (2016c), "Temperature distribution effects on buckling behavior of smart heterogeneous nanosize plates based on nonlocal four-variable refined plate theory", Int. J. Smart Nano Mater., 1-25.
  11. Ebrahimi, F. and Barati, M.R. (2016d), "An exact solution for buckling analysis of embedded piezoelectro-magnetically actuated nanoscale beams", Adv. Nano Res., 4(2), 65-84. https://doi.org/10.12989/anr.2016.4.2.065
  12. Ebrahimi, F. and Barati, M.R. (2016e), "Buckling analysis of smart size-dependent higher order magneto-electro-thermo- elastic functionally graded nanosize beams", J. Mech., 1-11.
  13. Ebrahimi, F. and Barati, M.R. (2016f), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size- dependent functionally graded nanobeams", Arabian J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  14. Ebrahimi, F. and Barati, M.R. (2016g), "Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment", J. Vib. Control, 1077546316646239. https://doi.org/10.1177/1077546316646239
  15. Ebrahimi, F. and Barati, M.R. (2016h), "Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium", J. Brazilian Soc. Mech. Sci. Eng., 1-16.
  16. Ebrahimi, F. and Barati, M.R. (2016i), "Small scale effects on hygro-thermo-mechanical vibration of temperature dependent nonhomogeneous nanoscale beams", Mech. Adv. Mater. Struct. , (just-accepted).
  17. Ebrahimi, F. and Barati, M.R. (2016j), "Dynamic modeling of a thermo-piezo-electrically actuated nanosize beam subjected to a magnetic field", Appl. Phys, A, 122(4), 1-18.
  18. Ebrahimi, F. and Barati, M.R. (2016k), "Magnetic field effects on buckling behavior of smart size-dependent graded nanoscale beams", European Phys. J. Plus, 131(7), 1-14. https://doi.org/10.1140/epjp/i2016-16001-3
  19. Ebrahimi, F. and Barati, M.R. (2016l), "Vibration analysis of nonlocal beams made of functionally graded material in thermal environment", European Phys. J. Plus, 131(8), 279. https://doi.org/10.1140/epjp/i2016-16279-y
  20. Ebrahimi, F. and Barati, M.R. (2017a), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092
  21. Ebrahimi, F. and Barati, M.R. (2017b), "A nonlocal strain gradient refined beam model for buckling analysis of size-dependent shear-deformable curved FG nanobeams", Compos. Struct., 159, 174-182. https://doi.org/10.1016/j.compstruct.2016.09.058
  22. Ebrahimi, F. and Daman, M. (2016a), "An investigation of radial vibration modes of embedded double-curved-nanobeam-systems", Cankaya Univ J Sci Eng,. 13, 058-079.
  23. Ebrahimi, F. and Daman, M. (2016b), "Dynamic modeling of embedded curved nanobeams incorporating surface effects", Coupled Syst. Mech.,. 5(3), 255-267. https://doi.org/10.12989/csm.2016.5.3.255
  24. Ebrahimi, F. and Daman, M. (2016c), "Investigating surface effects on thermomechanical behavior of embedded circular curved nanosize beams", J. Engineering, 2016.
  25. Ebrahimi, F. and Daman, M. (2017), "Analytical investigation of the surface effects on nonlocal vibration behavior of nanosize curved beams", Adv. Nano Res,. 5(1), 35-47. https://doi.org/10.12989/anr.2017.5.1.035
  26. Ebrahimi, F. and Hosseini, S.H.S. (2016a), "Double nanoplate- based NEMS under hydrostatic and electrostatic actuations", European Phys. J. Plus, 131(5), 1-19. https://doi.org/10.1140/epjp/i2016-16001-3
  27. Ebrahimi, F. and Hosseini, S.H.S. (2016b), "Nonlinear electroelastic vibration analysis of NEMS consisting of double- viscoelastic nanoplates", Appl. Phys. A, 122(10), 922. https://doi.org/10.1007/s00339-016-0452-6
  28. Ebrahimi, F. and Hosseini, S.H.S. (2016c), "Thermal effects on nonlinear vibration behavior of viscoelastic nanosize plates", J. Therm. Stresses, 39(5), 606-625. https://doi.org/10.1080/01495739.2016.1160684
  29. Ebrahimi, F. and Jafari, A. (2016a), "Thermo-mechanicalvibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory", Struct. Eng. Mech., 59(2), 343-371. https://doi.org/10.12989/sem.2016.59.2.343
  30. Ebrahimi, F. and Jafari, A. (2016b), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Engineering.
  31. Ebrahimi, F. and Jafari, A. (2016c), "Buckling behavior of smart MEE-FG porous plate with various boundary conditions based on refined theory", Adv. Mater. Res., 5(4), 279-298. https://doi.org/10.12989/amr.2016.5.4.279
  32. Ebrahimi, F. and Jafari, A. (2017), "A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities", Mech. Adv. Mater. Struct., 1-13.
  33. Ebrahimi, F. and Mokhtari, M. (2015), "Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method", J. Brazilian Soc. Mech. Sci. Eng., 37(4), 1435-1444. https://doi.org/10.1007/s40430-014-0255-7
  34. Ebrahimi, F. and Nasirzadeh, P. (2015), "A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method",. J. Theor. Appl. Mech., 53(4), 1041-1052.
  35. Ebrahimi, F. and Salari, E. (2015), "Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions", Compos B, 78, 272-290. https://doi.org/10.1016/j.compositesb.2015.03.068
  36. Ebrahimi, F. and Salari, E. (2015a), "Size-dependent thermo- electrical buckling analysis of functionally graded piezoelectric nanobeams", Smart Mater. Struct., 24(12), 125007, 2015 https://doi.org/10.1088/0964-1726/24/12/125007
  37. Ebrahimi, F. and Salari, E. (2015b), "Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment", Acta Astronautica, 113, 29-50. https://doi.org/10.1016/j.actaastro.2015.03.031
  38. Ebrahimi, F. and Salari, E. (2015c), "Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method", Composites Part B: Eng.,. 79, 156-169. https://doi.org/10.1016/j.compositesb.2015.04.010
  39. Ebrahimi, F. and Salari, E. (2015d), "A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position", CMES: Comput. Model. Eng. Sci., 105, 151-181.
  40. Ebrahimi, F. and Salari, E. (2015e), "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
  41. Ebrahimi, F. and Salari, E. (2015f), "Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions", Compos. B, 78, 272-290. https://doi.org/10.1016/j.compositesb.2015.03.068
  42. Ebrahimi, F. and Salari, E. (2016), "Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams", Mech. Adv. Mater. Struct., 23(12), 1379-1397. https://doi.org/10.1080/15376494.2015.1091524
  43. Ebrahimi, F. and Zia, M. (2015), "Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities", Acta Astronautica, 116, 117-125. https://doi.org/10.1016/j.actaastro.2015.06.014
  44. Ebrahimi, F., Barati, M.R. and Haghi, P. (2017), "Thermal effects on wave propagation characteristics of rotating strain gradient temperature-dependent functionally graded nanoscale beams", J. Therm. Stresses, 40(5), 535-547. https://doi.org/10.1080/01495739.2016.1230483
  45. Ebrahimi, F., Ehyaei, J. and Babaei, R. (2016), "Thermal buckling of FGM nanoplates subjected to linear and nonlinear varying loads on Pasternak foundation", Adv. Mater. Res., 5(4), 245-261. https://doi.org/10.12989/amr.2016.5.4.245
  46. Ebrahimi , F. , Ghadiri, M., Salari, E., Hoseini, S.A.H. and Shaghaghi, G.R. (2015b), "Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams", J. Mech. Sci. Tech., 29, 1207-1215. https://doi.org/10.1007/s12206-015-0234-7
  47. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016a), "Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  48. Ebrahimi, F., Jafari, A. and Barati, M.R. (2016), "Free vibration analysis of smart porous plates subjected to various physical fields considering neutral surface position", Arabian J. Sci. Eng., 5(42), 1865-1881.
  49. Ebrahimi, F., Jafari, A. and Barati, M.R. (2017), "Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations", Thin. Wall. Struct., 119, 33-46. https://doi.org/10.1016/j.tws.2017.04.002
  50. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2015), "Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions", J. Therm. Stresses, 38(12), 1360-1386. https://doi.org/10.1080/01495739.2015.1073980
  51. Ebrahimi, F., Salari, E. and Hosseini, S.A.H. (2016c), "In-plane thermal loading effects on vibrational characteristics of functionally graded nanobeams", Meccanica, 51(4), 951-977. https://doi.org/10.1007/s11012-015-0248-3
  52. Eltaher, M., Emam, S.A. and Mahmoud, F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Comput.,. 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090
  53. Eringen, A.C. (1972a), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5
  54. Eringen, A.C. (1972b), "Linear theory of nonlocal elasticity and dispersion of plane waves", Int. J. Eng. Sci., 10(5), 425-435. https://doi.org/10.1016/0020-7225(72)90050-X
  55. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-4710. https://doi.org/10.1063/1.332803
  56. Eringen, A.C. (2002), Nonlocal continuum field theories,: Springer Science &Business Media.
  57. Fallah, A. and Aghdam, M.M. (2011), "Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation", European J. Mech. -A /Solids, 30(4), 571-583. https://doi.org/10.1016/j.euromechsol.2011.01.005
  58. Fleck, N.A. and Hutchinson, J.W. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solids,. 41(12), 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-N
  59. Harshe, G., Dougherty, J. and Newnham, R. (1993), "Theoretical modelling of multilayer magnetoelectric composites", Int. J. Appl. Electromagnetics Mater.. 4(2), 145-145.
  60. Hashemi, S.H., Taher, H.R.D. and Omidi, M. (2008), "3-D free vibration analysis of annular plates on Pasternak elastic foundation via p-Ritz method", J. Sound Vib., 311(3), 1114-1140. https://doi.org/10.1016/j.jsv.2007.10.020
  61. Hosseini, S. and Rahmani, O. (2016), "Free vibration of shallow and deep curved FG nanobeam via nonlocal Timoshenko curved beam model", Appl. Phys. A,. 122(3), 1-11.
  62. Huang, Z., Lu, C. and Chen, W. (2008), "Benchmark solutions for functionally graded thick plates resting on Winkler-Pasternak elastic foundations", Compos. Struct., 85(2), 95-104. https://doi.org/10.1016/j.compstruct.2007.10.010
  63. Kananipour, H., Ahmadi, M. and Chavoshi, H. (2014), "Application of nonlocal elasticity and DQM to dynamic analysis of curved nanobeams", Latin Am. J. Solids Struct.,. 11(5), 848-853. https://doi.org/10.1590/S1679-78252014000500007
  64. Koizumi, M. and Niino, M. (1995), "Overview of FGM Research in Japan", Mrs Bulletin, 20(1), 19-21.
  65. Komijani, M., Reddy, J. and Eslami, M. (2014), "Nonlinear analysis of microstructure-dependent functionally graded piezoelectric material actuators", J. Mech. Phys. Solids,. 63, 214-227. https://doi.org/10.1016/j.jmps.2013.09.008
  66. Lam, D.C.C., et al. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids,. 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X
  67. Li, L. and Hu, Y. (2015), "Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory", Int. J. Eng. Sci.,. 97, 84-94. https://doi.org/10.1016/j.ijengsci.2015.08.013
  68. Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct., 133, 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014
  69. Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  70. Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids,. 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  71. Malekzadeh, P. (2009), "Three-dimensional free vibration analysis of thick functionally graded plates on elastic foundations", Compos. Struct., 89(3), 367-373. https://doi.org/10.1016/j.compstruct.2008.08.007
  72. Malekzadeh, P., Haghighi, M.G. and Atashi, M. (2010), "Out-of-plane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct., 92(2), 541-552. https://doi.org/10.1016/j.compstruct.2009.08.040
  73. Mechab, I., et al., (2016), "Free vibration analysis of FGM nanoplate with porosities resting on Winkler Pasternak elastic foundations based on two-variable refined plate theories", J. Brazilian Soc. Mech. Sci. Eng.,1-19.
  74. Mortensen, A. and Suresh, S. (2013), "Functionally graded metals and metal-ceramic composites: Part 1 Processing", International Materials Reviews.
  75. Nan, C.W. (1994), "Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases", Phys. Rev. B,. 50(9), 6082. https://doi.org/10.1103/PhysRevB.50.6082
  76. Pradhan, S. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vib., 321(1), 342-362. https://doi.org/10.1016/j.jsv.2008.09.018
  77. Wang, C.M. and Duan, W.H. (2008), "Free vibration of nanorings/arches based on nonlocal elasticity", J. Appl. Phys., 104(1), 014303. https://doi.org/10.1063/1.2951642
  78. Wattanasakulpong, N., Prusty, B.G. and Kelly, D.W. (2011), "Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams", Int. J. Mech. Sci., 53(9), 734-743. https://doi.org/10.1016/j.ijmecsci.2011.06.005
  79. Yahia, S.A., et al. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  80. Yan, Z. and Jiang, L. (2011), "Electromechanical response of a curved piezoelectric nanobeam with the consideration of surface effects", J. Phys. D: Appl. Phys.,. 44(36), 365301. https://doi.org/10.1088/0022-3727/44/36/365301
  81. Ying, J., Lu, C. and Chen, W. (2008), "Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations", Compos. Struct., 84(3), 209-219. https://doi.org/10.1016/j.compstruct.2007.07.004
  82. Zhou, D., et al. (2006), "Three-dimensional free vibration of thick circular plates on Pasternak foundation", J. Sound Vib., 292(3), 726-741. https://doi.org/10.1016/j.jsv.2005.08.028