Dynamics of a cylindrical sandwich shell with a functionally graded auxetic honeycomb core
Subject Areas : Structural Mechanics
Hossein Amirabadi
1
(Fars province, Abadeh, Islamic Azad University)
Keywords: Free vibration, Cylindrical shell, Sandwich shell, Functionally graded material, Auxetic honeycomb structure,
Abstract :
In this paper, a study is conducted on the free vibrational analysis of a cylindrical sandwich shell with a re-entrant auxetic honeycomb (AH) core made of ceramic-metal functionally graded material (FGM). The volume fraction (mass fraction) of ceramic in the functionally graded auxetic honeycomb (FGAH) core varies from zero at the inner surface to one at the outer one based on a power-law function. It is supposed that the core is covered with a homogenous inner layer made of metal and a homogenous outer one made of ceramic. The first-order shear deformation theory (FSDT) is hired and the shell is modeled mathematically. The governing equations are attained via Hamilton’s principle, and an analytical solution is presented for a simply supported shell via the Navier method. The impacts of several parameters on the natural frequencies are inspected including the power-law index (material gradation in the core), the thickness of the core-to-thickness of the shell ratio, the thickness-to-radius ratio of the shell, and geometric factors of the re-entrant cells (inclined angle, aspect ratio, and thickness of the walls). It is discovered that the natural frequencies decrease by growing the inclined angle in the FGAH core. It is concluded that for each vibrational mode, there is an optimal ratio between the values of the thickness of the core and the thickness of the shell which leads to the highest natural frequency.
[1] A. Ghorbanpour Arani, M. Jamali, A.H. Ghorbanpour Arani, R. Kolahchi, M. Mosayyebi, Electro-magneto wave propagation analysis of viscoelastic sandwich nanoplates considering surface effects, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231(2) (2017) 387-403.
[2] E. Haghparast, A.A. Ghorbanpour Arani, A. Ghorbanpour Arani, Effect of fluid–structure interaction on vibration of moving sandwich plate with Balsa wood core and nanocomposite face sheets, International Journal of Applied Mechanics 12(07) (2020) 2050078.
[3] A.H. Ghorbanpour Arani, M. Abdollahian, A. Ghorbanpour Arani, Nonlinear dynamic analysis of temperature-dependent functionally graded magnetostrictive sandwich nanobeams using different beam theories, Journal of the Brazilian Society of Mechanical Sciences and Engineering 42 (2020) 1-20.
[4] A.A. Ghorbanpour Arani, Z. Khoddami Maraghi, A. Ghorbanpour Arani, The Frequency Response of Intelligent Composite Sandwich Plate Under Biaxial In-Plane Forces, Journal of Solid Mechanics 15(1) (2023).
[5] A.H. Ghorbanpour Arani, A. Rastgoo, M. Sharafi, R. Kolahchi, A. Ghorbanpour Arani, Nonlocal viscoelasticity based vibration of double viscoelastic piezoelectric nanobeam systems, Meccanica 51 (2016) 25-40.
[6] A.H. Ghorbanpour Arani, A. Rastgoo, A. Hafizi Bidgoli, R. Kolahchi, A. Ghorbanpour Arani, Wave propagation of coupled double-DWBNNTs conveying fluid-systems using different nonlocal surface piezoelasticity theories, Mechanics of Advanced Materials and Structures 24(14) (2017) 1159-1179.
[7] P. Sourani, A. Ghorbanpour Arani, M. Hashemian, S. Niknejad, Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 238(10) (2024) 4307-4342.
[8] A. Ghorbanpour Arani, N. Miralaei, A. Farazin, M. Mohammadimehr, An extensive review of the repair behavior of smart self-healing polymer matrix composites, Journal of Materials Research 38(3) (2023) 617-632.
[9] K. Torabi, H. Afshari, F. Hajiaboutalebi, Vibration and flutter analyses of cantilever trapezoidal honeycomb sandwich plates, Journal of Sandwich Structures & Materials 21(8) (2019) 2887-2920.
[10] S. Galehdari, H. Khodarahmi, A. Atrian, Design and analysis of graded honeycomb shock absorber for increasing the safety of passengers in armored vehicles exposed to mine explosion, Journal of Solid Mechanics 9(2) (2017) 370-383.
[11] H. Alikhani, S. Derakhshan, H. Khoramishad, Experimental and Numerical Investigations of the Effect of Impact Angle and Impactor Geometry on the High-Velocity Impact Response of Aluminum Honeycomb Structures, Journal of Solid Mechanics 14(4) (2022).
[12] T.D. Qing, C.Y. Zhi, Wave propagation in sandwich panel with auxetic core, Journal of Solid Mechanics 2(4) (2010) 393-402.
[13] N.D. Duc, K. Seung-Eock, P.H. Cong, N.T. Anh, N.D. Khoa, Dynamic response and vibration of composite double curved shallow shells with negative Poisson's ratio in auxetic honeycombs core layer on elastic foundations subjected to blast and damping loads, International Journal of Mechanical Sciences 133 (2017) 504-512.
[14] H. Eipakchi, F.M. Nasrekani, Vibrational behavior of composite cylindrical shells with auxetic honeycombs core layer subjected to a moving pressure, Composite Structures 254 (2020) 112847.
[15] N.V. Nguyen, H. Nguyen-Xuan, T.N. Nguyen, J. Kang, J. Lee, A comprehensive analysis of auxetic honeycomb sandwich plates with graphene nanoplatelets reinforcement, Composite Structures 259 (2021) 113213.
[16] P. Xiao, Z. Yifeng, S. Jie, S. Zheng, Global buckling analysis of composite honeycomb sandwich plate with negative Poisson’s ratio (CHSP-NPR) using variational asymptotic equivalent model, Composite Structures 264 (2021) 113721.
[17] F. Xu, K. Yu, L. Hua, In-plane dynamic response and multi-objective optimization of negative Poisson's ratio (NPR) honeycomb structures with sinusoidal curve, Composite Structures 269 (2021) 114018.
[18] Q.-H. Pham, P.-C. Nguyen, T.T. Tran, Free vibration response of auxetic honeycomb sandwich plates using an improved higher-order ES-MITC3 element and artificial neural network, Thin-Walled Structures 175 (2022) 109203.
[19] T.Q. Quan, V.M. Anh, V. Mahesh, N.D. Duc, Vibration and nonlinear dynamic response of imperfect sandwich piezoelectric auxetic plate, Mechanics of Advanced Materials and Structures 29(1) (2022) 127-137.
[20] N.D. Dat, T.Q. Quan, N.D. Duc, Vibration analysis of auxetic laminated plate with magneto-electro-elastic face sheets subjected to blast loading, Composite Structures 280 (2022) 114925.
[21] Y. Li, B. Liu, Thermal buckling and free vibration of viscoelastic functionally graded sandwich shells with tunable auxetic honeycomb core, Applied Mathematical Modelling 108 (2022) 685-700.
[22] A. Pakrooyan, P. Yousefi, K. Khorshidi, M.M. Najafizadeh, A. Nezamabadi, Free vibration analysis of an auxetic honeycomb sandwich plate placed at the wall of a fluid tank, Ocean Engineering 263 (2022) 112353.
[23] P.H. Cong, V.D. Trung, N.D. Khoa, N.D. Duc, Vibration and nonlinear dynamic response of temperature-dependent FG-CNTRC laminated double curved shallow shell with positive and negative Poisson’s ratio, Thin-Walled Structures 171 (2022) 108713.
[24] B. Liu, S. Li, Y. Li, Bending of FGM sandwich plates with tunable auxetic core using DQM, European Journal of Mechanics-A/Solids 97 (2023) 104838.
[25] S. Sadikbasha, V. Pandurangan, Crashworthiness of auxetic hexachiral core under in-plane loading, Materials Today: Proceedings (2023).
[26] B. Nečemer, Ž. Božić, S. Glodež, Fatigue resistance of the auxetic honeycombs, Procedia Structural Integrity 46 (2023) 68-73.
[27] M. Rai, A. Chawla, S. Mukherjee, Parametric study of re-entrant honeycomb cored auxetic sandwich panel exposed to blast loading, Materials Today: Proceedings (2023).
[28] M. Sarafraz, H. Seidi, F. Kakavand, N.S. Viliani, Free vibration and buckling analyses of a rectangular sandwich plate with an auxetic honeycomb core and laminated three-phase polymer/GNP/fiber face sheets, Thin-Walled Structures 183 (2023) 110331.
[29] M. Sarafraz, H. Seidi, F. Kakavand, N.S. Viliani, Flutter characteristics of a rectangular sandwich plate with laminated three-phase polymer/GNP/fiber face sheets and an auxetic honeycomb core in yawed supersonic fluid flow, Journal of the Brazilian Society of Mechanical Sciences and Engineering 45(4) (2023) 197.
[30] M. Koizumi, The concept of FGM, Ceramic transactions 34 (1993) 3-10.
[31] J.-h. Zhang, B.-j. Dong, B. He, Y. Sun, Free vibrations and impact resistance of a functionally graded honeycomb sandwich plate, Shock and Vibration 2021 (2021) 1-15.
[32] F. Li, W. Yuan, C. Zhang, Free vibration and sound insulation of functionally graded honeycomb sandwich plates, Journal of Sandwich Structures & Materials 24(1) (2022) 565-600.
[33] H. Amirabadi, A. Darakhsh, M. Sarafraz, H. Afshari, Vibration characteristics of a cylindrical sandwich shell with an FG auxetic honeycomb core and nanocomposite face layers subjected to supersonic fluid flow, Noise & Vibration Worldwide (2024) 09574565241252994.
[34] H. Amirabadi, A. Mottaghi, M. Sarafraz, H. Afshari, Free vibrational behavior of a conical sandwich shell with a functionally graded auxetic honeycomb core, Journal of Vibration and Control (2024) 10775463241240215.
[35] X. Zhu, J. Zhang, W. Zhang, J. Chen, Vibration frequencies and energies of an auxetic honeycomb sandwich plate, Mechanics of Advanced Materials and Structures 26(23) (2019) 1951-1957.
[36] H. Murakami, Laminated composite plate theory with improved in-plane responses, (1986).
[37] A. Ghorbanpour Arani, F. Kiani, H. Afshari, Free and forced vibration analysis of laminated functionally graded CNT-reinforced composite cylindrical panels, Journal of Sandwich Structures & Materials 23(1) (2021) 255-278.
[38] A. Ghorbanpour Arani, F. Kiani, H. Afshari, Aeroelastic analysis of laminated FG-CNTRC cylindrical panels under yawed supersonic flow, International Journal of Applied Mechanics 11(06) (2019) 1950052.
[39] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis, CRC press 2003.
[40] V. Mohammadlou, Z. Khoddami Maraghi, A. Ghorbanpour Arani, Thermoelastic analysis of axisymmetric conical shells: Investigating stress–strain response under uniform heat flow with semi-coupled approach, Numerical Heat Transfer, Part A: Applications (2024) 1-22.
[41] J.N. Reddy, Energy principles and variational methods in applied mechanics, John Wiley & Sons 2017.
[42] A. Ghorbanpour Arani, E. Haghparast, A.H. Ghorbanpour Arani, Size‐dependent vibration of double‐bonded carbon nanotube‐reinforced composite microtubes conveying fluid under longitudinal magnetic field, Polymer Composites 37(5) (2016) 1375-1383.
[43] H. Li, K.-Y. Lam, T.-Y. Ng, Rotating shell dynamics, Elsevier 2005.
[44] C. Loy, K. Lam, J. Reddy, Vibration of functionally graded cylindrical shells, International Journal of Mechanical Sciences 41(3) (1999) 309-324.