Electro-thermoelastic vibration of functionally graded porous sandwich plates with piezoelectric and stiffened layers
Email:
thamvv@huce.edu.vn
Từ khóa:
electro-thermoelastic vibration, sandwich plate, porous material, piezoelectric material, HSDT4, pb²-Ritz method
Tóm tắt
A semi-analytical model is developed for the electro-thermoelastic free vibration of functionally graded porous sandwich plates with orthogonal stiffeners. The plate comprises a PoFGPie top face sheet, a porous metal-foam core, and a fully dense stiffened FGM bottom face sheet. A four-variable shear deformation theory (HSDT4), the Lekhnitskii smeared-stiffener model, and the pb²-Ritz method are combined in a unified formulation. A cosine-linear electric potential and uniform (UTR), linear (LTR), and nonlinear (NLTR) temperature rises are considered. The model is validated against published 3D, finite-element, and coupled-field solutions. Parametric studies cover core porosity, material gradation, layer thickness, stiffeners, voltage, geometry, boundary conditions, and thermal loading. Within the investigated ranges, increasing core porosity raises the fundamental dimensionless frequency because mass reduction dominates stiffness loss. Greater stiffener height raises the frequency, but the best stiffener orientation depends on the boundary condition and two-directional stiffening is not always optimal. Negative voltage produces a stiffening effect, positive voltage a softening effect, and thermal loading reduces the frequency, with UTR causing the largest decrease.Tài liệu tham khảo
[1]. B. Behjat, M. Salehi, M. Sadighi, A. Armin, M. Abbasi, Static, dynamic, and free vibration analysis of functionally graded piezoelectric panels using finite element method, Journal of Intelligent Material Systems and Structures, 20 (2009) 1635-1646. https://doi.org/10.1177/1045389X09104113
[2]. X.-H. Wu, C. Chen, Y.-P. Shen, X.-G. Tian, A high order theory for functionally graded piezoelectric shells, International Journal of Solids and Structures, 39 (2002) 5325-5344. https://doi.org/10.1016/S0020-7683(02)00418-3
[3]. M.R. Sedighi, M. Shakeri, A three-dimensional elasticity solution of functionally graded piezoelectric cylindrical panels, Smart Materials and Structures, 18 (2009) 055015. https://doi.org/10.1088/0964-1726/18/5/055015
[4]. Y.Q. Wang, Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state, Acta Astronautica, 143 (2018) 263-271. https://doi.org/10.1016/j.actaastro.2017.12.004
[5]. Z. Zhong, T. Yu, Vibration of a simply supported functionally graded piezoelectric rectangular plate, Smart Materials and Structures, 15 (2006) 1404-1412. https://doi.org/10.1088/0964-1726/15/5/029
[6]. M.R. Barati, A.M. Zenkour, Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions, Journal of Vibration and Control, 24 (2018) 1910-1926. https://doi.org/10.1177/1077546316672788
[7]. I. Esen, K.G. Aktaş, F. Pehlivan, Investigation of the critical buckling temperatures and free vibration response of porous functionally graded magneto-electro-elastic sandwich higher-order nanoplates with temperature-dependent material properties, Journal of Vibration Engineering & Technologies, 13 (2025) 162. https://doi.org/10.1007/s42417-024-01542-6
[8]. F. Ebrahimi, A. Jafari, M.R. Barati, Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations, Thin-Walled Structures, 119 (2017) 33-46. https://doi.org/10.1016/j.tws.2017.04.002
[9]. M. Askari, A.R. Saidi, A.S. Rezaei, On natural frequencies of Levy-type thick porous-cellular plates surrounded by piezoelectric layers, Composite Structures, 179 (2017) 340-354. https://doi.org/10.1016/j.compstruct.2017.07.073
[10]. M. Askari, A.R. Saidi, A.S. Rezaei, An investigation over the effect of piezoelectricity and porosity distribution on natural frequencies of porous smart plates, Journal of Sandwich Structures & Materials, 22 (2020) 2091-2124. https://doi.org/10.1177/1099636218791092
[11]. H.-Q. Tran, V.-T. Vu, M.-T. Tran, Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method, Composite Structures, 305 (2023) 116535. https://doi.org/10.1016/j.compstruct.2022.116535
[12]. D.O. Brush, B.O. Almroth, Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, 1975.
[13]. M.M. Najafizadeh, A. Hasani, P. Khazaeinejad, Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling, 33 (2009) 1151-1157. https://doi.org/10.1016/j.apm.2008.01.009
[14]. D.D. Thuy, B.D. Huy, N.P. Nhu, H.P. Thanh, P.N. Thi, Nonlinear buckling and postbuckling analysis of FG-GRMMC cylindrical panels with oblique and orthogonal stiffeners in thermal environment, Transport and Communications Science Journal, 77 (2026) 70-84. https://doi.org/10.47869/tcsj.77.1.6
[15]. P.H. Cong, P.K. Quyet, N.D. Duc, Effects of lattice stiffeners and blast load on nonlinear dynamic response and vibration of auxetic honeycomb plates, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235 (2021) 7192-7211. https://doi.org/10.1177/0954406221992797
[16]. H.-A. Pham, H.-Q. Tran, M.-T. Tran, V.-L. Nguyen, Q.-T. Huong, Free vibration analysis and optimization of doubly-curved stiffened sandwich shells with functionally graded skins and auxetic honeycomb core layer, Thin-Walled Structures, 179 (2022) 109571. https://doi.org/10.1016/j.tws.2022.109571
[17]. D. Van Dung, N.T. Nga, Thermomechanical postbuckling analysis of eccentrically stiffened FGM sandwich plates with general Sigmoid and power laws based on TSDT, Journal of Sandwich Structures & Materials, 20 (2018) 907-945. https://doi.org/10.1177/1099636216682545
[18]. T.-T. Pham, H.-Q. Tran, V.-L. Nguyen, K.-H. Le, M.-T. Tran, Free and forced vibration of functionally graded porous sandwich plates reinforced by arbitrarily oblique stiffeners, Thin-Walled Structures, 210 (2025) 113039. https://doi.org/10.1016/j.tws.2025.113039
[19]. T.-T. Pham, H.-Q. Tran, M.-T. Tran, H.-N. Nguyen, V.-T. Vu, Vibration behavior of stiffened functionally graded porous sandwich plates with a magneto-electro-elastic face resting on an elastic foundation under hygrothermal, electrical, and magnetic fields, Mechanics Based Design of Structures and Machines, 54 (2026) 2574890. https://doi.org/10.1080/15397734.2025.2574890
[20]. V.-T. Vu, H.-Q. Tran, Free vibration characteristics of stiffened sandwich plates with auxetic core and functionally graded piezoelectric face sheet, Acta Mechanica, 235 (2024) 4029-4056. https://doi.org/10.1007/s00707-024-03932-z
[21]. N. Wattanasakulpong, V. Ungbhakorn, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology, 32 (2014) 111-120. https://doi.org/10.1016/j.ast.2013.12.002
[22]. C. Liang, Y.Q. Wang, A quasi-3D trigonometric shear deformation theory for wave propagation analysis of FGM sandwich plates with porosities resting on viscoelastic foundation, Composite Structures, 247 (2020) 112478. https://doi.org/10.1016/j.compstruct.2020.112478
[23]. M. Bodaghi, M. Shakeri, An analytical approach for free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to impulsive loads, Composite Structures, 94 (2012) 1721-1735. https://doi.org/10.1016/j.compstruct.2012.01.009
[24]. G. Shi, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
[25]. H.Q. Tran, V.-T. Vu, M.T. Tran, P. Nguyen-Tri, A new four-variable refined plate theory for static analysis of smart laminated functionally graded carbon nanotube reinforced composite plates, Mechanics of Materials, 142 (2020) 103294. https://doi.org/10.1016/j.mechmat.2019.103294
[26]. H.-Q. Tran, V.-C. Nguyen, T.-P. Hoang, Vibration and buckling of sandwich plates with honeycomb auxetic core and three-phase bi-directional functionally graded face sheets, Engineering Structures, 343 (2025) 121133. https://doi.org/10.1016/j.engstruct.2025.121133
[27]. Q. Wang, Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer, International Journal of Solids and Structures, 39 (2002) 3023-3037. https://doi.org/10.1016/S0020-7683(02)00233-0
[28]. L. Wu, Y. Lu, Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method, International Journal of Mechanical Sciences, 53 (2011) 494-504. https://doi.org/10.1016/j.ijmecsci.2011.04.006
[29]. Q. Li, V.P. Iu, K.P. Kou, Three-dimensional vibration analysis of functionally graded material sandwich plates, Journal of Sound and Vibration, 311 (2008) 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
[30]. I.E. Harik, M. Guo, Finite element analysis of eccentrically stiffened plates in free vibration, Computers & Structures, 49 (1993) 1007-1015. https://doi.org/10.1016/0045-7949(93)90012-3
[2]. X.-H. Wu, C. Chen, Y.-P. Shen, X.-G. Tian, A high order theory for functionally graded piezoelectric shells, International Journal of Solids and Structures, 39 (2002) 5325-5344. https://doi.org/10.1016/S0020-7683(02)00418-3
[3]. M.R. Sedighi, M. Shakeri, A three-dimensional elasticity solution of functionally graded piezoelectric cylindrical panels, Smart Materials and Structures, 18 (2009) 055015. https://doi.org/10.1088/0964-1726/18/5/055015
[4]. Y.Q. Wang, Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state, Acta Astronautica, 143 (2018) 263-271. https://doi.org/10.1016/j.actaastro.2017.12.004
[5]. Z. Zhong, T. Yu, Vibration of a simply supported functionally graded piezoelectric rectangular plate, Smart Materials and Structures, 15 (2006) 1404-1412. https://doi.org/10.1088/0964-1726/15/5/029
[6]. M.R. Barati, A.M. Zenkour, Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions, Journal of Vibration and Control, 24 (2018) 1910-1926. https://doi.org/10.1177/1077546316672788
[7]. I. Esen, K.G. Aktaş, F. Pehlivan, Investigation of the critical buckling temperatures and free vibration response of porous functionally graded magneto-electro-elastic sandwich higher-order nanoplates with temperature-dependent material properties, Journal of Vibration Engineering & Technologies, 13 (2025) 162. https://doi.org/10.1007/s42417-024-01542-6
[8]. F. Ebrahimi, A. Jafari, M.R. Barati, Vibration analysis of magneto-electro-elastic heterogeneous porous material plates resting on elastic foundations, Thin-Walled Structures, 119 (2017) 33-46. https://doi.org/10.1016/j.tws.2017.04.002
[9]. M. Askari, A.R. Saidi, A.S. Rezaei, On natural frequencies of Levy-type thick porous-cellular plates surrounded by piezoelectric layers, Composite Structures, 179 (2017) 340-354. https://doi.org/10.1016/j.compstruct.2017.07.073
[10]. M. Askari, A.R. Saidi, A.S. Rezaei, An investigation over the effect of piezoelectricity and porosity distribution on natural frequencies of porous smart plates, Journal of Sandwich Structures & Materials, 22 (2020) 2091-2124. https://doi.org/10.1177/1099636218791092
[11]. H.-Q. Tran, V.-T. Vu, M.-T. Tran, Free vibration analysis of piezoelectric functionally graded porous plates with graphene platelets reinforcement by pb-2 Ritz method, Composite Structures, 305 (2023) 116535. https://doi.org/10.1016/j.compstruct.2022.116535
[12]. D.O. Brush, B.O. Almroth, Buckling of Bars, Plates, and Shells, McGraw-Hill, New York, 1975.
[13]. M.M. Najafizadeh, A. Hasani, P. Khazaeinejad, Mechanical stability of functionally graded stiffened cylindrical shells, Applied Mathematical Modelling, 33 (2009) 1151-1157. https://doi.org/10.1016/j.apm.2008.01.009
[14]. D.D. Thuy, B.D. Huy, N.P. Nhu, H.P. Thanh, P.N. Thi, Nonlinear buckling and postbuckling analysis of FG-GRMMC cylindrical panels with oblique and orthogonal stiffeners in thermal environment, Transport and Communications Science Journal, 77 (2026) 70-84. https://doi.org/10.47869/tcsj.77.1.6
[15]. P.H. Cong, P.K. Quyet, N.D. Duc, Effects of lattice stiffeners and blast load on nonlinear dynamic response and vibration of auxetic honeycomb plates, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235 (2021) 7192-7211. https://doi.org/10.1177/0954406221992797
[16]. H.-A. Pham, H.-Q. Tran, M.-T. Tran, V.-L. Nguyen, Q.-T. Huong, Free vibration analysis and optimization of doubly-curved stiffened sandwich shells with functionally graded skins and auxetic honeycomb core layer, Thin-Walled Structures, 179 (2022) 109571. https://doi.org/10.1016/j.tws.2022.109571
[17]. D. Van Dung, N.T. Nga, Thermomechanical postbuckling analysis of eccentrically stiffened FGM sandwich plates with general Sigmoid and power laws based on TSDT, Journal of Sandwich Structures & Materials, 20 (2018) 907-945. https://doi.org/10.1177/1099636216682545
[18]. T.-T. Pham, H.-Q. Tran, V.-L. Nguyen, K.-H. Le, M.-T. Tran, Free and forced vibration of functionally graded porous sandwich plates reinforced by arbitrarily oblique stiffeners, Thin-Walled Structures, 210 (2025) 113039. https://doi.org/10.1016/j.tws.2025.113039
[19]. T.-T. Pham, H.-Q. Tran, M.-T. Tran, H.-N. Nguyen, V.-T. Vu, Vibration behavior of stiffened functionally graded porous sandwich plates with a magneto-electro-elastic face resting on an elastic foundation under hygrothermal, electrical, and magnetic fields, Mechanics Based Design of Structures and Machines, 54 (2026) 2574890. https://doi.org/10.1080/15397734.2025.2574890
[20]. V.-T. Vu, H.-Q. Tran, Free vibration characteristics of stiffened sandwich plates with auxetic core and functionally graded piezoelectric face sheet, Acta Mechanica, 235 (2024) 4029-4056. https://doi.org/10.1007/s00707-024-03932-z
[21]. N. Wattanasakulpong, V. Ungbhakorn, Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology, 32 (2014) 111-120. https://doi.org/10.1016/j.ast.2013.12.002
[22]. C. Liang, Y.Q. Wang, A quasi-3D trigonometric shear deformation theory for wave propagation analysis of FGM sandwich plates with porosities resting on viscoelastic foundation, Composite Structures, 247 (2020) 112478. https://doi.org/10.1016/j.compstruct.2020.112478
[23]. M. Bodaghi, M. Shakeri, An analytical approach for free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to impulsive loads, Composite Structures, 94 (2012) 1721-1735. https://doi.org/10.1016/j.compstruct.2012.01.009
[24]. G. Shi, A new simple third-order shear deformation theory of plates, International Journal of Solids and Structures, 44 (2007) 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031
[25]. H.Q. Tran, V.-T. Vu, M.T. Tran, P. Nguyen-Tri, A new four-variable refined plate theory for static analysis of smart laminated functionally graded carbon nanotube reinforced composite plates, Mechanics of Materials, 142 (2020) 103294. https://doi.org/10.1016/j.mechmat.2019.103294
[26]. H.-Q. Tran, V.-C. Nguyen, T.-P. Hoang, Vibration and buckling of sandwich plates with honeycomb auxetic core and three-phase bi-directional functionally graded face sheets, Engineering Structures, 343 (2025) 121133. https://doi.org/10.1016/j.engstruct.2025.121133
[27]. Q. Wang, Axi-symmetric wave propagation in a cylinder coated with a piezoelectric layer, International Journal of Solids and Structures, 39 (2002) 3023-3037. https://doi.org/10.1016/S0020-7683(02)00233-0
[28]. L. Wu, Y. Lu, Free vibration analysis of rectangular plates with internal columns and uniform elastic edge supports by pb-2 Ritz method, International Journal of Mechanical Sciences, 53 (2011) 494-504. https://doi.org/10.1016/j.ijmecsci.2011.04.006
[29]. Q. Li, V.P. Iu, K.P. Kou, Three-dimensional vibration analysis of functionally graded material sandwich plates, Journal of Sound and Vibration, 311 (2008) 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
[30]. I.E. Harik, M. Guo, Finite element analysis of eccentrically stiffened plates in free vibration, Computers & Structures, 49 (1993) 1007-1015. https://doi.org/10.1016/0045-7949(93)90012-3
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03/11/2026
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Kiểu trích dẫn
Van-Tham, V. (1794675600). Electro-thermoelastic vibration of functionally graded porous sandwich plates with piezoelectric and stiffened layers. Tạp Chí Khoa Học Giao Thông Vận Tải, 77(9), 1226-1242. https://doi.org/10.47869/tcsj.77.9.8
