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Wave propagation in a nonlocal prestressed piezoelectric polygonal plate with non-homogeneity and hygroscopic effect

  • Rajendran Selvamani (Department of Mathematics, Karunya Institute of Technology and Sciences) ;
  • Hepzibah Christinal (Department of Mathematics, Karunya Institute of Technology and Sciences) ;
  • Farzad Ebrahimi (Department of Mechanical Engineering, Imam Khomieni International University)
  • Received : 2022.04.13
  • Accepted : 2023.05.19
  • Published : 2023.12.25
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Abstract

The humid thermal vibration characteristics of a nonhomogeneous thermopiezoelectric nonlocal plate of polygonal shape are addressed in the purview of generalized nonlocal thermoelasticity. The plate is initially stressed, and the three-dimensional linear elasticity equations are taken to form motion equations. The problem is solved using the Fourier expansion collocation method along the irregular boundary conditions. The numerical results of physical variables have been discussed for the triangle, square, pentagon, and hexagon shapes of the plates and are given as dispersion curves. The amplitude of non-dimensional frequencies is tabulated for the longitudinal and flexural symmetric modes of the thermopiezoelectric plate via moisture and thermal constants. Also, a comparison of numerical results is made with existing literature, and good agreement is reached.

Keywords

References

  1. Abbas, I.A., Abdalla, A. and Sapoor, H. (2022), "Nonlocal heat conduction approach in biological tissue generated by laser irradiation", Adv. Mater. Res., 11(2), 111-120. https://doi.org/10.12989/amr.2022.11.2.111.
  2. Adams, D.F. and Keith Miller, A. (1977), "Hygrothermal microstress in a unidirectional composite exhibiting inelastic material behavior". J. Compos. Mater., 11, 285-299. https://doi.org/10.1177/002199837701100304.
  3. Al-Osta, M.A., Saidi, H., Tounsi, A., Al-Dulaijan, S.U., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2021), "Influence of porosity on the hygro-thermo-mechanical bending response of an AFG ceramic-metal plates using an integral plate model", Smart Struct. Syst., 28(4), 499-513. http://doi.org/10.12989/sss.2021.28.4.499.
  4. Amar, L.H.H., Bourada, F., Bousahla, A.A., Tounsi, A., Benrahou, K.H., Albalawi, H. and Tounsi, A. (2023), "Buckling analysis of FG plates via 2D and quasi-3D refined shear deformation theories", Struct. Eng. Mech., 85(6), 765-780. https://doi.org/10.12989/sem.2023.85.6.765.
  5. Bakoura, A., Djedid, I.K., Bourada, F., Bousahla, A.A., Mahmoud, S.R., Tounsi, A., ... & Alnujaie, A. (2022), "A mechanical behavior of composite plates using a simple three variable refined plate theory", Struct. Eng. Mech., 83(5), 617-625. https://doi.org/10.12989/sem.2022.83.5.617.
  6. Belbachir, N., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Osta, M.A., Ghazwani, M.H., ... & Tounsi, A. (2023), "A refined quasi-3D theory for stability and dynamic investigation of cross-ply laminated composite plates on Winkler-Pasternak foundation", Struct. Eng. Mech., 85(4), 433-443. https://doi.org/10.12989/sem.2023.85.4.433.
  7. Bennedjadi, M., Aldosari, S.M., Chikh, A., Kaci, A., Bousahla, A.A., Bourada, F., ... & Tounsi, A. (2023), "Visco-elastic foundation effect on buckling response of exponentially graded sandwich plates under various boundary conditions", Geomech. Eng., 32(2), 159-177. https://doi.org/10.12989/gae.2023.32.2.159.
  8. Bin, W., Jiangong, J. and Cunfu, H. (2008), "Wave propagation in non-homogeneous magneto-electroelastic plates", J. Sound Vib., 317, 250-264. http://doi.org/10.1016/j.jsv.2008.03.008.
  9. Bot, I.K., Bousahla, A.A., Zemri, A., Sekkal, M., Kaci, A., Bourada, F., ... & Mahmoud, S.R. (2022), "Effects of Pasternak foundation on the bending behavior of FG porous plates in hygrothermal environment", Steel Compos. Struct., 43(6), 821-837. https://doi.org/10.12989/scs.2022.43.6.821.
  10. Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., ... & Tounsi, A. (2021), "Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model", Steel Compos. Struct., 41(4), 487-503. https://doi.org/10.12989/scs.2021.41.4.487.
  11. Bounouara, F., Aldosari, S.M., Chikh, A., Kaci, A., Bousahla, A.A., Bourada, F., ... & Albalawi, H. (2023), "The effect of visco-Pasternak foundation on the free vibration behavior of exponentially graded sandwich plates with various boundary conditions", Steel Compos. Struct., 46(3), 367-383. https://doi.org/10.12989/scs.2023.46.3.367.
  12. Chakraverty, S., Jindal, R. and Agarwal, V.K. (2005), "Flexural vibrations of non-homogeneous elliptic plates", Int. J. Eng. Mat. Sci., 12, 521-528.
  13. Chen, W.Q., Lee, K.Y. and Ding, H.J. (2005), "On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plate", J. Sound Vib., 279, 237-251. https://doi.org/10.1016/j.jsv.2003.10.033.
  14. Dastjerdi, S., Malikan, M. and Dimitri, R. (2021), "Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment", Compos. Struct., 225, 112925. https://doi.org/10.1016/j.compstruct.2020.112925.
  15. Djilali, N., Bousahla, A.A., Kaci, A., Selim, M.M., Bourada, F., Tounsi, A., ... & Mahmoud, S.R. (2022), "Large cylindrical deflection analysis of FG carbon nanotube-reinforced plates in thermal environment using a simple integral HSDT", Steel Compos. Struct., 42(6), 779-789. https://doi.org/10.12989/scs.2022.42.6.779.
  16. Eringen, A.C. (1981), "Theory of nonlocal thermoelastcity", Int. J. Eng. Sci., 12(12), 1063-1077. https://doi.org/10.1016/0020-7225(74)90033-0.
  17. Fesharaki, J.J., Fesharaki, V.J., Yazdipoor, M. and Razavian, B. (2012), "Two dimensional solution of electro mechanical behavior of functionally graded piezoelectric hollow cylinder", Appl. Math. Model., 36, 5521-5533. https://doi.org/10.1016/j.apm.2012.01.01.
  18. Gawin, D., Majorana, C.E. and Scherfler, B.A. (1999), "Numerical analysis of hygro thermal behavior and damage of concrete at high temperature", Mech. Cohes.-frict. Mater.: J. Exper. Model. Comput. Mater. Struct., 4, 37-74. https://doi.org/10.1002/(SICI)1099-1484(199901)4:1<37::AID-CFM58>3.0.CO;2-S.
  19. Hadji, M., Bouhadra, A., Mamen, B., Menasria, A., Bousahla, A.A., Bourada, F., ... & Tounsi, A. (2023), "Combined influence of porosity and elastic foundation parameters on the bending behavior of advanced sandwich structures", Steel Compos. Struct., 46(1), 1-13. https://doi.org/10.12989/scs.2023.46.1.001.
  20. Hebali, H., Chikh, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., ... & Tounsi, A. (2022), "Effect of the variable visco-Pasternak foundations on the bending and dynamic behaviors of FG plates using integral HSDT model", Geomech. Eng., 28(1), 49-64. https://doi.org/10.12989/gae.2021.28.1.049.
  21. Hou, P.F., Andrew, Y.T. and Leung, H. (2008), "Point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material", Int. J. Eng. Sci., 46, 273-285. https://doi.org/10.1016/j.ijengsci.2007.11.006.
  22. Hutchinson, J.R. (1979), "Axisymmetric flexural vibrations of a thick free circular plate", J. Appl. Mech., 46, 139-144. https://doi.org/10.1115/1.3424485.
  23. Janson, K.M.B., Zhang, M.F. and Ernst, L.J. (2020), "Effect of temperature and humidity on moisture diffusion in an epoxy moulding compound material", Micro. Reliab., 107, 113596. https://doi.org/10.1016/j.microrel.2020.113596.
  24. Jiyangi, C., Hualing, C. and Ernian, P. (2006), "Free vibration of functionally graded, magneto-thermo-electro-elastic and multilayered plates", Acta Mechanica Solida Sinica, 19, 60-66. http://doi.org/10.1007/s10338-006-0619-3.
  25. Kakar, R. (2013), "Magneto elastic torsional surface waves in prestressed fiber reinforced medium", Int. J. Math. Mech., 9, 1-19. https://doi.org/10.1007/s10999-011-9168-0
  26. Kallavanar, V., Kattimani, S. and Elahi, M. (2021), "Neural network-based prediction model to investigate the influence of temperature and moisture on vibration characteristics of skew laminated composite sandwich plates", Mater., 14(12), 3170. https://doi.org/10.3390/ma14123170.
  27. Kouider, D., Kaci, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., ... & Hussain, M. (2021), "An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core", Steel Compos. Struct., 41(2), 167-191. http://doi.org/10.12989/scs.2021.41.2.167.
  28. Lata, P. and Singh, S. (2022), "Effect of rotation and inclined load in a nonlocal magnetothermoelastic solid with two temperature", Adv. Mater. Res., 11(1), 23-39. https://doi.org/10.12989/amr.2022.11.1.023.
  29. Loghman, A., Nasar, M. and Arefi, M. (2017), "Non symmetric thermo mechanical analysis of a functionally graded cylinder subjected to mechanical, thermal and magnetic loads", J. Therm. Stress., 40, 765-782. https://doi.org/10.1080/01495739.2017.1280380.
  30. Mehditabar, A., Rahimi, G.H. and Tarahhomi, M.H. (2018), "Thermo-elastic analysis of a functionally graded piezoelectric rotating hollow cylindrical shell subjected to dynamic loads", Mech. Adv. Mater. Struct., 25(12), 1068-1079. https://doi.org/10.1080/15376494.2017.1329466.
  31. Mesbah, A., Belabed, Z., Amara, K., Tounsi, A., Bousahla, A.A. and Bourada, F. (2023), "Formulation and evaluation a finite element model for free vibration and buckling behaviours of functionally graded porous (FGP) beams", Struct. Eng. Mech., 86(3), 291-309. https://doi.org/10.12989/sem.2023.86.3.291.
  32. Mudhaffar, I.M., Chikh, A., Tounsi, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2023), "Impact of viscoelastic foundation on bending behavior of FG plate subjected to hygro-thermomechanical loads", Struct. Eng. Mech., 86(2), 167-180. https://doi.org/10.12989/sem.2023.86.2.167.
  33. Mudhaffar, I.M., Tounsi, A., Chikh, A., Al-Osta, M.A., Al-Zahrani, M.M. and Al-Dulaijan, S.U. (2021), "Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation", Struct., 33, 2177-2189. https://doi.org/10.1016/j.istruc.2021.05.090.
  34. Nagaya, K. (1974), "Simplified method for solving problems of vibrating plates of doubly connected arbitrary shape", J. Sound Vib., 74, 553-564. https://doi.org/10.1016/0022-460X(81)90418-1.
  35. Nagaya, K. (1980), "Method for solving vibration problems of a plate with arbitrary shape", J. Acoust. Soc. Am., 67, 2029-2033. https://doi.org/10.1121/1.384444.
  36. Nagaya, K. (1981), "Dispersion of elastic waves in bars with polygonal cross section", J. Acoust. Soc. Am., 70, 763-770. https://doi.org/10.1121/1.386914.
  37. Pan, E. (2001), "Exact solution for simply supported and multilayered magneto-electro-elastic plates", J. Appl. Mech., 68, 608-618. https://doi.org/10.1115/1.1380385.
  38. Ramu, I., Narendra, M. and Venu, M. (2018). "Effect of hygrothermal environment on free vibration characteristics of FGM plates by finite element approach", IOP Conf. Ser.: Mater. Sci. Eng., 377(1), 012021. http://doi.org/10.1088/1757-899X/377/1/012021.
  39. Reddy, J.N. and Chin, C.D. (2007), "Thermo mechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21, 593-626. https://doi.org/10.1080/01495739808956165.
  40. Selvamani, R. (2015), "Wave propagation in a rotating disc of polygonal cross-section immersed in an inviscid fluid", Cogent Eng., 2(1), 1002162. https://doi.org/10.1080/23311916.2014.1002162.
  41. Selvamani, R. (2016), "Influence of thermo-piezoelctric field in a circular bar subjected to thermal loading due to laser pulse", Mater. Phys. Mech., 27, 1-8.
  42. Selvamani, R. (2017), "Stress waves in a generalized thermo elastic polygonal plate of inner and outer cross sections", J. Solid Mech., 9(2), 263-275.
  43. Selvamani, R. and Infant Sujitha, G. (2018a), "Effect of non homogeneity in a magneto electro elastic plate of polygonal cross sections", Mater. Phys. Mech., 40(1), 1-24. http://doi.org/10.18720/MPM.4012018_11.
  44. Selvamani, R. and Ponnusamy, P. (2013), "Elasto dynamic wave propagation in a transversely isotropic piezoelectric circular plate immersed in fluid", Mater. Phys. Mech., 17(2), 164-177.
  45. Selvamani, R. and Ponnusamy, P. (2013), "Generalized thermoelastic waves in a rotating ring shaped circular plate immersed in an inviscid fluid", Mater. Phys. Mech., 18(1), 77-92. https://doi.org/10.1115/1.1380385.
  46. Selvamani, R. and Ponnusamy, P. (2015), "Wave propagation in a generalized piezothermoelastic rotating bar of circular cross section", Multidisc. Model. Mater. Struct., 11(2), 216-237. https://doi.org/10.1108/MMMS-06-2014-0038.
  47. Selvamani, R. and Sujitha, G.I. (2018), "Wave propagation in a non-homogeneous magneto-thermo-electro-elastic disc of polygonal cross sections immersed in an in viscid fluid", J. Phys.: Conf. Ser., 1139(1), 012013. http://doi.org/10.1088/1742-6596/1139/1/012013.
  48. Singh, B. and Bijarnia, R. (2020), "Nonlocal effects on propagation of waves in a generalized thermoelastic solid half space", Struct. Eng. Mech., 7(4), 473-479. https://doi.org/10.12989/sem.2021.77.4.473.
  49. Singh, S. and Lata, P. (2020), "Effects of nonlocality and two temperature in a nonlocal thermo elastic solid due to ramp type heat source", Arab J. Basic Appl. Sci., 27(1), 358-364. https://doi.org/10.1080/25765299.2020.1825157.
  50. Tounsi, A., Mostefa, A.H., Attia, A., Bousahla, A.A., Bourada, F., Tounsi, A. and Al-Osta, M.A. (2023), "Free vibration investigation of functionally graded plates with temperature-dependent properties resting on a viscoelastic foundation", Struct. Eng. Mech., 86(1), 1-16. https://doi.org/10.12989/sem.2023.86.1.001.
  51. Vinyas, M. and Kattimani, S.C. (2017), "Hygrothermal analysis of magneto-electro-elastic plate using 3D finite element analysis", Compos. Struct., 180, 617-637. https://doi.org/10.1016/j.compstruct.2017.08.015.
  52. Vinyas, M. and Kattimani, S.C. (2018), "Finite element evaluation of free vibration characteristics of magneto-electro-elastic rectangular plates in hygrothermal environment using higher order shear deformation theory", Compos. Struct., 202, 1339-1352. https://doi.org/10.1016/j.compstruct.2018.06.069.
  53. Vinyas, M., Kattimani, S.C. and Joladarashi, S. (2018), "Hygrothermal coupling analysis of magneto-electroelastic beams using finite element methods", J. Therm. Stress., 40, 1063-1079. https://doi.org/10.1080/01495739.2018.1447856.
  54. Wang, W., Dong, X.K. and Wang, X.Y. (2004), "Hygro thermal effect on dynamic inter laminar stresses in laminated plates with piezoelectric actuators", Compos. Struct., 71(2), 220-228. https://doi.org/10.1016/j.compstruct.2004.10.004.
  55. Zaitoun, M.W., Chikh, A., Tounsi, A., Al-Osta, M.A., Sharif, A., Al-Dulaijan, S.U. and Al-Zahrani, M.M. (2022), "Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic-metal plate in a hygrothermal environment", Thin Wall. Struct., 170, 108549. https://doi.org/10.1016/j.tws.2021.108549.
  56. Zenkour, A.M. (2012), "Piezoelectric behavior of an inhomogeneous hollow cylinder with thermal gradient", Int. J. Thermophys., 33, 1288-1301. https://doi.org/10.1007/s10765-012-1248-3.
  57. Zhang, X.M. and Yu, J.G. (2013), "Effects of initial stresses on guided waves in unidirectional plates", Arch. Mech., 65(1), 3-26.