Vibration of a Nanocomposite Annular Sandwich Microplate Based on HSDT Using DQM
Tóm tắt
In this article, a numerical solution for free vibration of double-bonded composite annular sandwich microplate using modified couple stress and higher order shear deformation theories are presented. The structure is composed of carbon nanotube reinforced composite and a honeycomb aluminum core. Both of these two annular sandwich plates reinforced with carbon nanotubes are completely the same and there is no delamination between each other of layers. They are placed on each other by a Pasternak foundation. Constitutive equations in the elastic region and the kinematic equations are linear. Due to the complexity of the equations and the existence of non-linear equations, the numerical solution method is used. In addition, among partial equations, low-order methods need to increase the numbers of nodes (finite difference method) or elements (finite element method) and thus leads to enhance more computing volume and solution time to have higher accuracy. In this research, differential quadrature method (DQM) is used, in which, in this study, by a lower number of nodes on the structure domain, are more accurate than the previous methods and convert higher order complex equations into lower order simple equations. In this research, the scale of the investigated structures is micro, thus, the classical theories cannot be used. As a result, for predictions depending on the size of the analysed structure, non-classical higher order continuum theory, including modified couple stress theory (MCST) is employed. The Hamiltonian principle is used to derive the equations of motion and DQM is considered to solve them. The convergence of the solution method for examining the accuracy of the present work is shown and several comparison studies are investigated. In this research, the effects of inclined angle, geometric features of the core layer, aspect ratio of unit cell, volume fractions of carbon nanotubes, material length scale parameters and aspect ratio, side ratio, two elastic foundation parameters on dimensionless natural frequency for a micro annular sandwich plate is investigated. It is also concluded that changing the geometric parameters of the honeycomb core layer affects on the dimensionless frequency. The results of this research can be served for the design of materials science, as a benchmark data to validate other researcher method in micro-electro-mechanical systems, and nano-electro-mechanical systems.
Từ khóa
Tài liệu tham khảo
H. An, B.D. Youn, H.S. Kim, A methodology for sensor number and placement optimization for vibration-based damage detection of composite structures under model uncertainty. Compos. Struct. 279, 114863 (2022). https://doi.org/10.1016/j.compstruct.2021.114863
H. Arvin, Free vibration analysis of micro rotating beams based on the strain gradient theory using the differential transform method: Timoshenko versus Euler-Bernoulli beam models. Euro. J Mech. A Solids 65, 336–348 (2017). https://doi.org/10.1016/j.euromechsol.2017.05.006
K. Alambeigi, M. Mohammadimehr, M. Bamdad, T. Rabczuk, Free and forced vibration analysis of sandwich beam considering porous core and SMA hybrid composite face layers on Vlaosv’s foundation. Acta Mech. 231, 3199–3218 (2020)
M.S.H. Al-Furjan, E.S. Sohrforozani, M. Habibi, D. Jung, H. Safarpour, Vibrational characteristics of a higher-order laminated composite viscoelastic annular microplate via modified couple stress theory. Compos. Struct. (2020). https://doi.org/10.1016/j.compstruct.2020.113
E. Arshid, S. Amir, A. Loghman, Bending and buckling behaviors of heterogeneous temperature-dependent micro annular/circular porous sandwich plates integrated by FGPEM nano-composite layers. J. Sandw. Struct. Mater.Sandw. Struct. Mater. (2020). https://doi.org/10.1177/1099636220955027
B. Bouderba, M.S.A. Houari, A. Tounsi, S.R. Mahmoud, Thermal stability of functionally graded sandwich plates using a simple shear deformation theory. Struct. Eng. Mech. 58(3), 397–422 (2016). https://doi.org/10.12989/sem.2016.58.3.397
F. Bounouara, K.H. Benrahou, I. Belkorissat, A. Tounsi, 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 (2016). https://doi.org/10.12989/scs.2016.20.2.227
J. Bang, B. Yang, Application of machine learning to predict the engineering characteristics of construction material. Multiscale Sci. Eng. 5, 1–9 (2023)
M. Charekhli-Inanllo, M. Mohammadimehr, The effect of various shape core materials by FDM on low velocity impact behavior of a sandwich composite plate. Eng. Struct. 294, 116721 (2023). https://doi.org/10.1016/j.engstruct.2023.116721
H.S. Chang, J.L. Tsai, Predict elastic properties of fiber composites by an artificial neural network. Multiscale Sci. Eng. 5, 53–61 (2023). https://doi.org/10.1007/s42493-023-00094-3
H.S. Chang, J.H. Huang, J.L. Tsai, Predicting mechanical properties of unidirectional composites using machine learning. Multiscale Sci. Eng. 4, 202–210 (2022). https://doi.org/10.1007/s42493-022-00087-8
T.H. Daouadji, B. Adim, Mechanical behaviour of FGM sandwich plates using a quasi-3D higher order shear and normal deformation theory. Struct. Eng. Mech. 61(1), 49–63 (2017). https://doi.org/10.12989/sem.2017.61.1.049
M. Emdadi, M. Mohammadimehr, B. Rousta-Navi, Free vibration of an annular sandwich plate with CNTRC facesheets and FG porous cores using Ritz method. Adv. Nano Res. 7(2), 109–123 (2019). https://doi.org/10.12989/anr.2019.7.2.109
S. Gohari, N. Moslemi, M. Ahmed, S. Mouloodi, H. Rahmanpanah, M. Kajtaz, C. Burvill, On 3D exact free torsional-bending vibration and buckling of biaxially loaded isotropic and anisotropic Timoshenko beams with complex cross-section. Structures 49, 1044–1077 (2023). https://doi.org/10.1016/j.istruc.2023.01.138
M.H. Hajmohammad, R. Kolahchi, M.S. Zarei, A.H. Nouri, Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory. Int. J. Mech. Sci. 153, 391–401 (2019). https://doi.org/10.1016/j.ijmecsci.2019.02.008
H. Hedayati, B. Sobhani Aragh, Influence of graded agglomerated CNTs on vibration of CNT-reinforced annular sectorial plates resting on Pasternak foundation. Appl. Math. Comput.Comput. 218, 8715–8735 (2012). https://doi.org/10.1016/j.amc.2012.01.080
Z.L. Hu, Y. Yang, X.F. Li, Bending of a nanoplate with strain-dependent surface stress containing two collinear through cracks. Meccanica 57(8), 1937–1954 (2022). https://doi.org/10.1007/s11012-022-01553-1
X. Hoang, T.N. Nguyen, M. Nguyen, S.P.A. Abdel-Wahab, P.V. Thuc, A refined quasi-3D isogeometric analysis for functionally graded microplates based on the modified couple stress theory. Comput. Methods Appl. Mech. Eng. 313, 904–940 (2017). https://doi.org/10.1016/j.cma.2016.10.002
V.H. Ho, D.T. Ho, S.Y. Kim, The effect of single vacancy defects on graphene nanoresonators. Multiscale Sci. Eng. 2, 1–6 (2020). https://doi.org/10.1007/s42493-020-00030-9
S. Khalid, H.S. Kim, Recent studies on stress function-based approaches for the free edge stress analysis of smart composite laminates: a brief review. Multiscale Sci. Eng. 4, 73–78 (2022). https://doi.org/10.1007/s42493-022-00079-8
T. Kant, K. Swaminathan, Analytical solutions using a higher order refined theory for the stability analysis of laminated composite and sandwich plates. Struct. Eng. Mech. 10(4), 337–357 (2000). https://doi.org/10.12989/sem.2000.10.4.337
A. Khan, D.K. Ko, S.C. Lim, H.S. Kim, Structural vibration-based classification and prediction of delamination in smart composite laminates using deep learning neural network. Compos. B Eng. 161, 586–594 (2019). https://doi.org/10.1016/j.compositesb.2018.12.118
A. Khan, J.K. Shin, W.C. Lim, N.Y. Kim, H.S. Kim, A deep learning framework for vibration-based assessment of delamination in smart composite laminates. Sensors 20, 2335 (2020). https://doi.org/10.3390/s20082335
D.C.C. Lam, F. Yang, A.C.M. Chong, Experiments and theory in strain gradient elasticity. J. Mech. Phys. Solids 51, 1477–1508 (2003). https://doi.org/10.1016/S0022-5096(03)00053
M.J. Lashkari, O. Rahmani, Bending analysis of sandwich plates with composite face sheets and compliance functionally graded syntactic foam core. Proc. IMechE Part C J. Mech. Eng. Sci. 230(20), 3606–3630 (2018). https://doi.org/10.1177/0954406215616417
N. Liang, D. Wang, Y. Guo, R. Yang, Q. Liao, Z. Bai, Y. Fu, C.H. Chen Luo, H. Zhu, Analysis of energy dissipated by damping for paper honeycomb sandwich plate-block system. Proc. IMechE Part C J. Mech. Eng. Sci. 233(18), 6483–6490 (2019). https://doi.org/10.1177/0954406219862301
K.M. Liew, Z.X. Lei, L.W. Zhang, Mechanical analysis of functionally graded carbon nanotube reinforced composites. A review. Compos. Struct. 120, 90–97 (2015). https://doi.org/10.1016/j.compstruct.2014.09.041
L.R. Lukešević, M. Janev, B.N. Novaković, T.M. Atanacković, Moving point load on a beam with viscoelastic foundation containing fractional derivatives of complex order. Acta Mech. (2022). https://doi.org/10.1007/s00707-022-03429-7
Y. Maximov, Y. Legovich, D. Maximov, Frequency characteristics of viscoelastic damper models and evaluation of a damper influence on induced oscillations of mechanical system elements. Meccanica 56(12), 3107–3124 (2021). https://doi.org/10.1007/s11012-021-01446-9
P. Malekzadeh, Three-dimensional free vibration analysis of thick laminated annular sector plates using a hybrid method. Compos. Struct. 90, 428–437 (2009). https://doi.org/10.1016/j.compstruct.2009.04.015
M. Meunier, R.A. Shenoi, Free vibration analysis of composite sandwich plates. Proc. IMechE Part C J. Mech. Eng. Sci. 213(7), 715–727 (1999). https://doi.org/10.1177/095440629921300707
Y.J.F. Minghui, Equivalent elastic parameters of the honeycomb core. Acta Mech. Sinica 31, 113–118 (1999)
M. Mohammadimehr, S. Shahedi, B. Rousta Navi, Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using GDQM. Proc. IMechE Part C J. Mech. Eng. Sci. 231(20), 3866–3885 (2016). https://doi.org/10.1177/0954406216653622
M. Mohammadimehr, S.J. Atifeh, B. Rousta Navi, Stress and free vibration analysis of piezoelectric hollow circular FG-SWBNNTs reinforced nanocomposite plate based on modified couple stress theory subjected to thermo-mechanical loadings. J. Vib. Control 24(15), 3471–3486 (2018)
M. Mohammadimehr, M. Emdadi, H. Afshari, B. Rousta Nav, Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM. Int. J. Smart Nano Mater. 9(4), 233–260 (2018). https://doi.org/10.1080/19475411.2017.1377312
M. Mohammadimehr, M. Emdadi, B. Rousta-Navi, Dynamic stability analysis of microcomposite annular sandwich plate with CNT reinforced composite facesheets based on MSGT. J. Sandw. Struct. Mater.Sandw. Struct. Mater. 22(4), 1199–1234 (2018). https://doi.org/10.1177/1099636218782770
M. Mohammadimehr, H. BabaAkbar Zarei, A. Parakandeh, A. Ghorbanpour Arani, Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields. Struct. Eng. Mech. 64(3), 361–379 (2017). https://doi.org/10.12989/sem.2017.64.3.361
M. Mohammadimehr, Buckling and bending analyses of a sandwich beam based on nonlocal stress-strain elasticity theory with porous core and functionally graded facesheets. Adv. Mater. Res. 11(4), 279–298 (2022). https://doi.org/10.12989/amr.2022.11.4.279
M. Mohanty, R. Maity, M. Pradhan, P. Dash, Parametric stability of Timoshenko taper sandwich beam on Pasternak foundation. Mater. Today Proc. (2023). https://doi.org/10.1016/j.matpr.2023.03.735
A. Mojahedin, M. Jabbari, A.R. Khorshidvand, M.R. Eslami, Buckling analysis of functionally graded circular plates made of saturated porous materials based on higher order shear deformation theory. Thin Wall. Struct. 99, 83–90 (2016). https://doi.org/10.1016/j.tws.2015.11.008
S. Natarajana, M. Haboussib, M. Ganapathic, Application of higher-order structural theory to bending and free vibration analysis of sandwich plates with CNT reinforced composite facesheets. Comp. Struct. 113, 197–207 (2014). https://doi.org/10.1016/j.compstruct.2014.03.007
A. Necira, S.A. Belalia, A. Boukhalfa, Size-dependent free vibration analysis of Mindlin nano-plates with curvilinear plan-forms by a high order curved hierarchical finite element. Mech. Adv. Mater. Struct. 27, 55–73 (2018). https://doi.org/10.1080/15376494.2018.1472342
F.J. Plantema, Sandwich Construction: The Bending and Buckling of Sandwich Beams, Plates and Shells (Wiley, New York, 1966)
T. Rabczuk, H. Ren, X. Zhuang, A Nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. Comput. Mater. Continua 59(1), 31–55 (2019). https://doi.org/10.32604/cmc.2019.04567
E. Reissner, Finite deflections of sandwich plates. J. Aeronaut. Sci 15(7), 435–440 (1948). https://doi.org/10.2514/8.11610
J.D.B. Santos, G.R. Anjos, M.A. Savi, An investigation of fluid-structure interaction in pipe conveying flow using reduced-order models. Meccanica 57(10), 2473–2491 (2022). https://doi.org/10.1007/s11012-022-01586-6
M. Safari, M. Mohammadimehr, H. Ashrafi, Forced vibration of a sandwich Timoshenko beam made of GPLRC and porous core. Struct. Eng. Mech. 88(1), 1–12 (2023). https://doi.org/10.12989/sem.2023.88.1.001
M. Shirzadifar, J. Marzbanrad, Bending characteristics of CFRP hexagon honeycombs stiffened with corrugated cores under transverse quasi-static impact loading. Iran. J. Sci. Technol. Trans. Mech. Eng. (2022). https://doi.org/10.1007/s40997-022-00550-9
F.A. Shishevan, H. Akbulut, Low-velocity impact behavior of carbon/basalt fiber- reinforced intra-ply hybrid composites. Iran. J. Sci. Technol. Trans. Mech. Eng. 43, 225–234 (2019). https://doi.org/10.1007/s40997-018-0151-3
S. Shahedi, M. Mohammadimehr, Vibration analysis of rotating fully-bonded and delaminated sandwich beam with CNTRC face sheets and AL-foam flexible core in thermal and moisture environments. Mech. Based Des. Struct. Mach. 48(5), 584–614 (2020). https://doi.org/10.1080/15397734.2019.1646661
C.H. Sun, F. Li, H.M. Cheng, G.Q. Lu, Axial Young’s modulus prediction of single walled carbon nanotube arrays with diameters from nanometer to meter scales. Appl. Phys. Lett. 87, 193–201 (2005). https://doi.org/10.1063/1.2119409
A. Talimian, P. Béda, Dynamic stability of a size-dependent micro-beam. Eur. J. Mech. A. Solids 72, 245–251 (2018). https://doi.org/10.1016/j.euromechsol.2018.04.020
S.S. Tomar, M. Talha, On the flexural and vibration behavior of imperfection sensitive higher order functionally graded material skew sandwich plates in thermal environment. Proc. IMechE Part C J. Mech. Eng. Sci. (2018). https://doi.org/10.1177/0954406218766959
J.R. Vinson, Sandwich structures. Appl. Mech. Rev. 54(3), 201–214 (2001). https://doi.org/10.1115/1.3097295
M. Vinyas, D. Harursampath, S.C. Kattimani, Thermal response analysis of multi-layered magneto-electro-thermo-elastic plates using higher order shear deformation theory. Struct. Eng. Mech. 73(6), 667–684 (2020). https://doi.org/10.12989/sem.2020.73.6.667
A. Zemri, M.S.A. Houari, A.A. Bousahla, A. Tounsi, A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory. Struct. Eng. Mech. Int. J. 54(4), 693–710 (2015). https://doi.org/10.12989/sem.2015.54.4.693
D. Zhou, S.H. Lo, Y.K. Cheung, 3-D vibration analysis of annular sector plates using the Chebyshev-Ritz method. J. Sound Vib. 320, 421–437 (2009). https://doi.org/10.1016/j.jsv.2008.08.001
Y. Zhao, J. Du, Y. Chen, Y. Liu, Dynamic behavior and vibration suppression of a generally restrained pre-pressure beam structure attached with multiple nonlinear energy sinks. Acta Mech. Solida Sin. 35(5), 31 (2022). https://doi.org/10.1007/s10338-022-00350-3
R. Yazdani, M. Mohammadimehr, Double bonded Cooper-Naghdi micro sandwich cylindrical shells with porous core and CNTRC face sheets: wave propagation solution. Comput. Concrete 24(6), 499–511 (2019). https://doi.org/10.12989/cac.2019.24.6.499
Y. Yang, N. Zhang, H. Liu et al., Piezoelectric and flexoelectric effects of DNA adsorbed films on microcantilevers. Appl. Math. Mech. 44, 1547–1562 (2023). https://doi.org/10.1007/s10483-023-3026-5