Hygro-thermal vibration behavior of porous functionally graded nanobeams based on doublet mechanics

Downloads

Authors

  • U. Gul Department of Mechanical Engineering, Trakya University, Turkey
  • M. Aydogdu Department of Mechanical Engineering, Trakya University, Turkey

Abstract

This study deals with the vibration response of porous functionally graded (FG) nanobeams under hygro-thermal loadings. The FG nanobeam model is developed based on the Euler–Bernoulli beam theory, in which the doublet mechanics is implemented to account for the size effect. The material properties of the FG nanobeam are assumed to vary along the thickness direction of the beam according to the power-law form with the temperature dependent and porosity phases. The approximate Ritz method is employed to obtain the natural frequencies of porous FG nanobeam models for various boundary conditions. The influences of several parameters such as temperature rise, moisture concentration, porosity volume fraction, material gradient index, material length scale parameter and mode number on the free vibration response of the porous FG nanobeams under hygro-thermal environments are examined in detail. It is explicitly shown that the proposed approach can provide accurate frequency results of FG nanobeams as compared to existing studies in open literature. These study’s results may be useful for the optimal and safety design of nano-electro-mechanical systems.

Keywords:

porous functionally graded nanobeams, hygro-thermal loadings, vibration, doublet mechanics, Ritz method

References


  1. Hui, J.S. Gomez-Diaz, Z. Qian, A. Alu, M. Rinaldi, Plasmonic piezoelectric nanomechanical resonator for spectrally selective infrared sensing, Nature Communications, 7, 1, 11249, 2016.

  2. Soltan Rezaee, M. Afrashi, Modeling the nonlinear pull-in behavior of tunable nano-switches, International Journal of Engineering Science, 109, 73–87, 2016.

  3. Rahmanian, S. Hosseini-Hashemi, Size-dependent resonant response of a double-layered viscoelastic nanoresonator under electrostatic and piezoelectric actuations incorporating surface effects and Casimir regime, International Journal of Non-Linear Mechanics, 109, 118–131, 2019.

  4. Basutkar, Analytical modelling of a nanoscale series-connected bimorph piezoelectric energy harvester incorporating the flexoelectric effect, International Journal of Engineering Science, 139, 42–61, 2019.

  5. Rahaeifard, M.H. Kahrobaiyan, M.T. Ahmadian, Sensitivity analysis of atomic force microscope cantilever made of functionally graded materials, International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 49033, 539–544, 2009.

  6. Moser, M.A. Gijs, Miniaturized flexible temperature sensor, Journal of Microelectromechanical Systems, 16, 6, 1349–1354, 2007.

  7. Wang, Wave propagation in carbon nanotubes via nonlocal continuum mechanics, Journal of Applied Physics, 98, 12, 124301, 2005.

  8. Wang, V.K. Varadan, Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Materials and Structures, 15, 2, 659, 2006.

  9. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, 11, 1, 385–414, 1962.

  10. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics, 54, 9, 4703–4710, 1983.

  11. D. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, 16, 51–78, 1964.

  12. W. Lim, G. Zhang, J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 78, 298–313, 2015.

  13. A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the Mechanics and Physics of Solids, 48, 1, 175–209, 2000.

  14. A.C.M. Yang, A.C.M. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 10, 2731–2743, 2002.

  15. Romano, R. Barretta, Nonlocal elasticity in nanobeams: the stress-driven integral model, International Journal of Engineering Science, 115, 14–27, 2017.

  16. T. Granik, Microstructural mechanics of granular media, Technique Report IM/MGU, Institute of Mechanics of Moscow State University, pp. 78–241, 1978.

  17. L. Ke, Y.S. Wang, Size effect on dynamic stability of functionally graded microbeams based on a modified couple stress theory, Composite Structures, 93, 2, 342–350, 2011.

  18. N. Reddy, Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids, 59, 11, 2382–2399, 2011.

  19. Şimşek, J.N. Reddy, 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, 2013.

  20. Akgöz, Ö. Civalek, Buckling analysis of functionally graded microbeams based on the strain gradient theory, Acta Mechanica, 224, 9, 2185–2201, 2013.

  21. Akgöz, Ö. Civalek, Shear deformation beam models for functionally graded microbeams with new shear correction factors, Composite Structures, 112, 214–225, 2014.

  22. Rahmani, O. Pedram, Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, International Journal of Engineering Science, 77, 55–70, 2014.

  23. Gul, M. Aydogdu, Dynamic analysis of functionally graded beams with periodic nanostructures, Composite Structures, 257, 113169, 2021.

  24. Gul, M. Aydogdu, Buckling analysis of functionally graded beams with periodic nanostructures using doublet mechanics theory, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 1–8, 2021.

  25. Li, Y. Hu, Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material, International Journal of Engineering Science, 107, 77–97, 2016.

  26. E. Ghandourah, H.M. Ahmed, M.A. Eltaher, M.A. Attia, A.M. Abdraboh, Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model, Advances in Nano Research, 11, 4, 405–422, 2021.

  27. Messai, L. Fortas, T. Merzouki, M.S.A. Houari, Vibration analysis of FG reinforced porous nanobeams using two variables trigonometric shear deformation theory, Structural Engineering and Mechanics, 81, 4, 461–479, 2022.

  28. Uzun, M.Ö. Yayli, Rotary inertia effect on dynamic analysis of embedded FG porous nanobeams under deformable boundary conditions with the effect of neutral axis, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 46, 111, 2024.

  29. Ellali, M. Bouazza, A.M. Zenkour, N. Benseddiq, Polynomial-exponential integral shear deformable theory for static stability and dynamic behaviors of FG-CNT nanobeams, Archive of Applied Mechanics, 94, 1455–1474, 2024.

  30. Ebrahimi, E. Salari, Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment, Acta Astronautica, 113, 29–50, 2015.

  31. Ebrahimi, E. Salari, Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments, Composite Structures, 128, 363–380, 2015.

  32. Ebrahimi, E. Salari, Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions, Composites Part B: Engineering, 78, 272–290, 2015.

  33. Ebrahimi, F. Ghasemi, E. Salari, Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities, Meccanica, 51, 223–249, 2016.

  34. Z. Jouneghani, R. Dimitri, F. Tornabene, Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings, Composites Part B: Engineering, 152, 71–78, 2018.

  35. H. Jalaei, A.G. Arani, H. Nguyen-Xuan, Investigation of thermal and magnetic field effects on the dynamic instability of FG Timoshenko nanobeam employing nonlocal strain gradient theory, International Journal of Mechanical Sciences, 161, 105043, 2019.

  36. Ebrahimi, M.R. Barati, A unified formulation for dynamic analysis of nonlocal heterogeneous nanobeams in hygro-thermal environment, Applied Physics A, 122, 1–14, 2016.

  37. Wang, H. Ren, T. Fu, C. Shi, Hygrothermal mechanical behaviors of axially functionally graded microbeams using a refined first order shear deformation theory, Acta Astronautica, 166, 306–316, 2020.

  38. Penna, L. Feo, G. Lovisi, F. Fabbrocino, Hygro-thermal vibrations of porous FG nano-beams based on local/nonlocal stress gradient theory of elasticity, Nanomaterials, 11, 4, 910, 2021.

  39. Penna, L. Feo, G. Lovisi, Hygro-thermal bending behavior of porous FG nano-beams via local/nonlocal strain and stress gradient theories of elasticity, Composite Structures, 263, 113627, 2021.

  40. S. Li, B.L. Liu, J.J. Zhang, Hygro-thermal buckling of porous FG nanobeams considering surface effects, Structural Engineering and Mechanics, 79, 3, 359–371, 2021.

  41. Özmen, R. Kiliç, I. Esen, Thermomechanical vibration and buckling response of nonlocal strain gradient porous FG nanobeams subjected to magnetic and thermal fields, Mechanics of Advanced Materials and Structures, 31, 4, 834–853, 2024.

  42. Ebrahimi, M. Karimiasl, V. Mahesh, Vibration analysis of magneto-flexo-electrically actuated porous rotary nanobeams considering thermal effects via nonlocal strain gradient elasticity theory, Advances in Nano Research, 7, 4, 223–231, 2019.

  43. Bendaida, A.A. Bousahla, A. Mouffoki, H. Heireche, F. Bourada, Tounsi, M. Hussain, Dynamic properties of nonlocal temperature-dependent FG nanobeams under various thermal environments, Transport in Porous Media, 142, 1, 187–208, 2022.

  44. Ebrahimi, M.R. Barati, Vibration analysis of smart piezoelectrically actuated nanobeams subjected to magneto-electrical field in thermal environment, Journal of Vibration and Control, 24, 3, 549–564, 2018.

  45. Arefi, A.H. Soltan-Arani, 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, 669–692, 2018.

  46. Ebrahimi, M.R. Barati, Thermal environment effects on wave dispersion behavior of inhomogeneous strain gradient nanobeams based on higher order refined beam theory, Journal of Thermal Stresses, 39, 12, 1560–1571, 2016.

  47. Ghadiri, A. Jafari, Thermo-mechanical analysis of FG nanobeam with attached tip mass: an exact solution, Applied Physics A, 122, 1–13, 2016.

  48. Ebrahimi, M.R. Barati, Vibration analysis of viscoelastic inhomogeneous nanobeams resting on a viscoelastic foundation based on nonlocal strain gradient theory incorporating surface and thermal effects, Acta Mechanica, 228, 1197–1210, 2017.

  49. Ebrahimi, M.R. Barati, Small-scale effects on hygro-thermo-mechanical vibration of temperature-dependent nonhomogeneous nanoscale beams, Mechanics of Advanced Materials and Structures, 24, 11, 924–936, 2017.

  50. A. Hosseini, O. Rahmani, S. Bayat, Thermal effect on forced vibration analysis of FG nanobeam subjected to moving load by Laplace transform method, Mechanics Based Design of Structures and Machines, 51, 7, 3803–3822, 2023.

  51. Ebrahimi, E. Salari, S.A.H. Hosseini, Thermomechanical vibration behavior of FG nanobeams subjected to linear and non-linear temperature distributions, Journal of Thermal Stresses, 38, 12, 1360–1386, 2015.

  52. Lv, H. Liu, Uncertainty modeling for vibration and buckling behaviors of functionally graded nanobeams in thermal environment, Composite Structures, 184, 1165–1176, 2018.

  53. A. Alazwari, I. Esen, A.A. Abdelrahman, A.M. Abdraboh, M.A. Eltaher, Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermo-magnetic fields and moving load, Advances in Nano Research, 12, 3, 231–251, 2022.

  54. V. Tuyen, N.D. Du, Analytic solutions for static bending and free vibration analysis of FG nanobeams in thermal environment, Journal of Thermal Stresses, 46, 9, 871–894, 2023.

  55. M. Shajan, K. Sivadas, R. Piska, C. Parimi, Hygrothermal effects on vibration response of porous FG nanobeams using nonlocal strain gradient theory considering thickness effect, International Journal of Structural Stability and Dynamics, 23, 2440016, 2023.

  56. Fan, B. Lei, S. Sahmani, B. Safaei, On the surface elastic-based shear buckling characteristics of functionally graded composite skew nanoplates, Thin-Walled Structures, 154, 106841, 2020.

  57. Sahmani, A.M. Fattahi, N.A. Ahmed, Surface elastic shell model for nonlinear primary resonant dynamics of FG porous nanoshells incorporating modal interactions, International Journal of Mechanical Sciences, 165, 105203, 2020.

  58. K. Żur, S.A. Faghidian, Analytical and meshless numerical approaches to unified gradient elasticity theory, Engineering Analysis with Boundary Elements, 130, 238–248, 2021.

  59. S. Touloukian, Thermophysical Properties of High Temperature Solid Materials, Vol. 3: Ferrous Alloys, Macmillan, New York, 1967.

  60. K. Nguyen, B.D. Nguyen, T. Vo, H.T. Thai, Hygro-thermal effects on vibration and thermal buckling behaviours of functionally graded beams, Composite Structures, 176, 1050–1060, 2017.

  61. T. Granik, M. Ferrari, Microstructural mechanics of granular media, Mechanics of Materials, 15, 4, 301–322, 1993.

  62. Gul, M. Aydogdu, G. Gaygusuzoglu, Axial dynamics of a nanorod embedded in an elastic medium using doublet mechanics, Composite Structures, 160, 1268–1278, 2017.

  63. Gul, M. Aydogdu, Structural modelling of nanorods and nanobeams using doublet mechanics theory, International Journal of Mechanics and Materials in Design, 14, 195–212, 2018.

  64. Gul, M. Aydogdu, G. Gaygusuzoglu, Vibration and buckling analysis of nanotubes (nanofibers) embedded in an elastic medium using Doublet Mechanics, Journal of Engineering Mathematics, 109, 85–111, 2018.