Abstract
This article performs an analytical study on the damping vibration behavior of metal foam nanocomposite plate reinforced with graphene oxide powders (GOPs) in thermal environment. The GOPs are dispersed through the thickness of the structure according to three functionally graded (FG) and one uniform distribution patterns. The Halpin–Tsai micromechanical model is chosen for estimating the effective material properties of the structure having GOPs as reinforcement phase. Also, different porosity types are taken into account for the metal foam matrix. The plate is resting on a three-parameter viscoelastic medium containing Winkler and Pasternak layers in combination with viscous dampers which can dissipate the oscillation of the structure in some special cases. The Governing differential equations are derived via Hamilton’s principle on the basis of refined higher order shear deformation theory and then solved with employing Galerkin solution method to obtain the natural frequencies of the proposed structure. Moreover, various boundary conditions (B.Cs) including simply supported, fully clamped and different combinations of these B.Cs are considered in this study. The influences and confrontation of different significant parameters such as GOPs’ weight fraction, foundation parameters, aspect and side-to-thickness ratios, porosity coefficients, thermal environment, and FG patterns are investigated through various graphical and numerical results. Our findings declare that the dynamic behavior of the graphene oxide powder reinforced metal foam (GOPRMF) plate remarkably depends on these parameters.
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References
Magnucki K, Stasiewicz P. Elastic buckling of a porous beam. J Theor Appl Mech. 2004;42:859–68.
Smith B, Szyniszewski S, Hajjar J, Schafer B, Arwade S. Steel foam for structures: a review of applications, manufacturing and material properties. J Constr Steel Res. 2012;71:1–10.
Chen D, Yang J, Kitipornchai S. Free and forced vibrations of shear deformable functionally graded porous beams. Int J Mech Sci. 2016;108:14–22.
Jabbari M, Mojahedin A, Khorshidvand A, Eslami M. Buckling analysis of a functionally graded thin circular plate made of saturated porous materials. J Eng Mech. 2014;140:287–95.
Rezaei A, Saidi A. Application of Carrera Unified Formulation to study the effect of porosity on natural frequencies of thick porouS-Cellular plates. Compos B Eng. 2016;91:361–70.
Wang YQ, Liang C, Zu JW. Examining wave propagation characteristics in metal foam beams: Euler–Bernoulli and Timoshenko models. J Braz Soc Mech Sci Eng. 2018;40:565.
Jasion P, Magnucka-Blandzi E, Szyc W, Magnucki K. Global and local buckling of sandwich circular and beam-rectangular plates with metal foam core. Thin-Walled Struct. 2012;61:154–61.
Liu J, He S, Zhao H, Li G, Wang M. Experimental investigation on the dynamic behaviour of metal foam: from yield to densification. Int J Impact Eng. 2018;114:69–77.
T. Belica, M. Malinowski, K. Magnucki, Dynamic stability of an isotropic metal foam cylindrical shell subjected to external pressure and axial compression, J Appl Mech, 78 (2011).
E. Arshid, S. Amir, A. Loghman, Static and dynamic analyses of FG-GNPs reinforced porous nanocomposite annular micro-plates based on MSGT, Int J Mech Sci, (2020) 105656.
Cong PH, Chien TM, Khoa ND, Duc ND. Nonlinear thermomechanical buckling and post-buckling response of porous FGM plates using Reddy’s HSDT. Aerosp Sci Technol. 2018;77:419–28.
Arshid E, Khorshidvand AR, Khorsandijou SM. The effect of porosity on free vibration of SPFG circular plates resting on visco-Pasternak elastic foundation based on CPT FSDT and TSDT. Struct Eng Mech. 2019;70:97–112.
Nguyen LB, Thai CH, Zenkour A, Nguyen-Xuan H. An isogeometric Bézier finite element method for vibration analysis of functionally graded piezoelectric material porous plates. Int J Mech Sci. 2019;157:165–83.
Chandrasekaran S, Sato N, Tölle F, Mülhaupt R, Fiedler B, Schulte K. Fracture toughness and failure mechanism of graphene based epoxy composites. Compos Sci Technol. 2014;97:90–9.
Formica G, Lacarbonara W, Alessi R. Vibrations of carbon nanotube-reinforced composites. J Sound Vib. 2010;329:1875–89.
Alibeigloo A, Emtehani A. Static and free vibration analyses of carbon nanotube-reinforced composite plate using differential quadrature method. Meccanica. 2015;50:61–76.
Zhu P, Lei Z, Liew KM. Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Compos Struct. 2012;94:1450–60.
Wattanasakulpong N, Ungbhakorn V. Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation. Comput Mater Sci. 2013;71:201–8.
Shen H-S, Xiang Y. Postbuckling of axially compressed nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments. Compos B Eng. 2014;67:50–61.
Heshmati M, Yas M, Daneshmand F. A comprehensive study on the vibrational behavior of CNT-reinforced composite beams. Compos Struct. 2015;125:434–48.
Lei Z, Zhang L, Liew K. Free vibration analysis of laminated FG-CNT reinforced composite rectangular plates using the kp-Ritz method. Compos Struct. 2015;127:245–59.
Zhang L, Liew K, Reddy J. Postbuckling analysis of bi-axially compressed laminated nanocomposite plates using the first-order shear deformation theory. Compos Struct. 2016;152:418–31.
H. Chen, H. Song, Y. Li, M. Safarpour, Hygro-thermal buckling analysis of polymer–CNT–fiber-laminated nanocomposite disk under uniform lateral pressure with the aid of GDQM, Eng Comput, (2020) 1–25.
N.D. Dat, T.Q. Quan, N.D. Duc, Nonlinear thermal vibration of carbon nanotube polymer composite elliptical cylindrical shells, International J Mech Mater Des, (2019) 1–20.
Song Z, Zhang L, Liew K. Dynamic responses of CNT reinforced composite plates subjected to impact loading. Compos B Eng. 2016;99:154–61.
Ansari R, Torabi J, Shojaei MF. Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading. Compos B Eng. 2017;109:197–213.
Garcia-Macias E, Rodriguez-Tembleque L, Saez A. Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates. Compos Struct. 2018;186:123–38.
Pourasghar A, Chen Z. Hyperbolic heat conduction and thermoelastic solution of functionally graded CNT reinforced cylindrical panel subjected to heat pulse. Int J Solids Struct. 2019;163:117–29.
Ke L-L, Yang J, Kitipornchai S. Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams. Compos Struct. 2010;92:676–83.
Chatterjee S, Nafezarefi F, Tai N, Schlagenhauf L, Nüesch F, Chu B. Size and synergy effects of nanofiller hybrids including graphene nanoplatelets and carbon nanotubes in mechanical properties of epoxy composites. Carbon. 2012;50:5380–6.
Yadav SK, Cho JW. Functionalized graphene nanoplatelets for enhanced mechanical and thermal properties of polyurethane nanocomposites. Appl Surf Sci. 2013;266:360–7.
Yang J, Wu H, Kitipornchai S. Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams. Compos Struct. 2017;161:111–8.
Duc ND, Seung-Eock K, Chan DQ. Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT. J Therm Stress. 2018;41:331–65.
Sobhy M. An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment. Int J Mech Sci. 2016;110:62–77.
Song M, Kitipornchai S, Yang J. Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Compos Struct. 2017;159:579–88.
Feng C, Kitipornchai S, Yang J. Nonlinear bending of polymer nanocomposite beams reinforced with non-uniformly distributed graphene platelets (GPLs). Compos B Eng. 2017;110:132–40.
Barati MR, Zenkour AM. Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection. Compos Struct. 2017;181:194–202.
Liu D, Kitipornchai S, Chen W, Yang J. Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell. Compos Struct. 2018;189:560–9.
Shen H-S, Xiang Y, Fan Y, Hui D. Nonlinear bending analysis of FG-GRC laminated cylindrical panels on elastic foundations in thermal environments. Compos B Eng. 2018;141:148–57.
Potts JR, Dreyer DR, Bielawski CW, Ruoff RS. Graphene-based polymer nanocomposites. Polymer. 2011;52:5–25.
Mahkam M, Rafi AA, Faraji L, Zakerzadeh E. Preparation of poly (methacrylic acid)–graphene oxide nanocomposite as a pH-sensitive drug carrier through in-situ copolymerization of methacrylic acid with polymerizable graphene. Polym-Plast Technol Eng. 2015;54:916–22.
Gómez-Navarro C, Burghard M, Kern K. Elastic properties of chemically derived single graphene sheets. Nano Lett. 2008;8:2045–9.
Tang L-C, Wan Y-J, Yan D, Pei Y-B, Zhao L, Li Y-B, Wu L-B, Jiang J-X, Lai G-Q. The effect of graphene dispersion on the mechanical properties of graphene/epoxy composites. Carbon. 2013;60:16–27.
Zhang Z, Li Y, Wu H, Zhang H, Wu H, Jiang S, Chai G. Mechanical analysis of functionally graded graphene oxide-reinforced composite beams based on the first-order shear deformation theory. Mech Adv Mater Struct. 2020;27:3–11.
Ebrahimi F, Nouraei M, Dabbagh A. Modeling vibration behavior of embedded graphene-oxide powder-reinforced nanocomposite plates in thermal environment. Mech Based Des Struct Mach. 2020;48:217–40.
Ebrahimi F, Nouraei M, Dabbagh A. Thermal vibration analysis of embedded graphene oxide powder-reinforced nanocomposite plates. Eng Comput. 2020;36:879–95.
Bakshi SR, Lahiri D, Agarwal A. Carbon nanotube reinforced metal matrix composites-a review. Int Mater Rev. 2010;55:41–64.
M. Van Es, Polymer-clay nanocomposites, Delft: PhD Thesis, (2001).
Wang YQ, Zu JW. Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment. Aerosp Sci Technol. 2017;69:550–62.
Yang J, Chen D, Kitipornchai S. Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method. Compos Struct. 2018;193:281–94.
Sobhy M. Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions. Compos Struct. 2013;99:76–87.
Xue Y, Jin G, Ma X, Chen H, Ye T, Chen M, Zhang Y. Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach. Int J Mech Sci. 2019;152:346–62.
Mahi A, Tounsi A. A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates. Appl Math Model. 2015;39:2489–508.
Acknowledgement
This research is financially supported by the Ministry of Science and Technology of China (Grant No. 2019YFE0112400), the Taishan Scholar Priority Discipline Talent Group program funded by the Shan Dong Province, and the first-class discipline project funded by the Education Department of Shandong Province.
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Appendix
Appendix
The components of the stiffness matrix are as follows:
\(\begin{gathered} m_{11} = I_{0} r_{11} , \, m_{12} = 0, \, m_{13} = - I_{1} r_{11} , \, m_{14} = - J_{1} r_{11} \hfill \\ m_{21} = 0, \, m_{22} = I_{0} r_{12} , \, m_{23} = - I_{1} r_{12} , \, m_{24} = - J_{1} r_{12} \hfill \\ m_{31} = - I_{1} r_{10} , \, m_{32} = I_{1} r_{9} , \, m_{33} = I_{0} r_{8} - I_{2} (r_{10} + r_{9} ) \hfill \\ m_{34} = I_{0} r_{8} + J_{2} (r_{10} + r_{9} ), \, m_{41} = - J_{1} r_{10} , \, m_{42} = J_{1} r_{9} \hfill \\ m_{43} = I_{0} r_{8} - J_{2} (r_{10} + r_{9} ), \, m_{44} = I_{0} r_{8} - K_{2} (r_{10} + r_{9} ) \hfill \\ \end{gathered}\)The components of the mass matrix are defined as
Also the nonzero components of the damping matrix are stated as
where
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Zhang, C., Wang, L., Eyvazian, A. et al. Analytical study of the damping vibration behavior of the metal foam nanocomposite plates reinforced with graphene oxide powders in thermal environments. Archiv.Civ.Mech.Eng 21, 142 (2021). https://doi.org/10.1007/s43452-021-00269-5
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DOI: https://doi.org/10.1007/s43452-021-00269-5