Free vibration analysis of rotating FGP sandwich cylindrical shells with metal-foam core layer

References

• R.N. Arnold, and G.B. Warburton, Flexural vibrations of the walls of thin cylindrical shells having freely supported ends, Proc. R. Soc. London Ser. A Math. Phys. Sci., vol. 197, no. 1049, pp. 238–256, 1949.
   Google Scholar
• C.W. Bert, and V. Birman, Parametric instability of thick, orthotropic, circular cylindrical shells, Acta Mech., vol. 71, no. 1–4, pp. 61–76, 1988. DOI: 10.1007/BF01173938.
   Web of Science ®Google Scholar
• A. Bhimaraddi, A higher order theory for free vibration analysis of circular cylindrical shells, Int. J. Solids Struct., vol. 20, no. 7, pp. 623–630, 1984. DOI: 10.1016/0020-7683(84)90019-2.
   Web of Science ®Google Scholar
• F.A. Fazzolari, and E. Carrera, Advances in the Ritz formulation for free vibration response of doubly-curved anisotropic laminated composite shallow and deep shells, Compos. Struct., vol. 101, pp. 111–128, 2013. DOI: 10.1016/j.compstruct.2013.01.018.
   Web of Science ®Google Scholar
• F. Fraternali, and J.N. Reddy, A penalty model for the analysis of laminated composite shells, Int. J. Solids Struct., vol. 30, no. 24, pp. 3337–3355, 1993. DOI: 10.1016/0020-7683(93)90088-O.
   Web of Science ®Google Scholar
• Y. Huang, B. Karami, D. Shahsavari, and A. Tounsi, Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels, Archiv. Civ. Mech. Eng., vol. 21, no. 4, pp. 139, 2021. DOI: 10.1007/s43452-021-00291-7.
   Web of Science ®Google Scholar
• A.A. Khdeir, and L. Librescu, Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory: Part II—Buckling and free vibration, Compos. Struct., vol. 9, no. 4, pp. 259–277, 1988. DOI: 10.1016/0263-8223(88)90048-7.
   Web of Science ®Google Scholar
• I. Kreja, R. Schmidt, and J.N. Reddy, Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures, International J. Non-Linear Mech., vol. 32, no. 6, pp. 1123–1142, 1997. DOI: 10.1016/S0020-7462(96)00124-2.
   Web of Science ®Google Scholar
• A.M .A. Neves, et al., Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations, Eur. J. Mech. - A/Solids, vol. 37, pp. 24–34, 2013. DOI: 10.1016/j.euromechsol.2012.05.005.
   Google Scholar
• A. Nosier, and J.N. Reddy, Vibration and stability analyses of cross-ply laminated circular cylindrical shells, J. Sound Vibr., vol. 157, no. 1, pp. 139–159, 1992. DOI: 10.1016/0022-460X(92)90571-E.
   Web of Science ®Google Scholar
• A. Pagani, E. Carrera, R. Augello, and D. Scano, Use of Lagrange polynomials to build refined theories for laminated beams, plates and shells, Compo. Struct., vol. 276, pp. 114505, 2021. DOI: 10.1016/j.compstruct.2021.114505.
   Web of Science ®Google Scholar
• J.N. Reddy, Exact solutions of moderately thick laminated shells, J. Eng. Mech., vol. 110, no. 5, pp. 794–809, 1984. DOI: 10.1061/(ASCE)0733-9399(1984)110:5(794).
   Web of Science ®Google Scholar
• K.P. Soldatos, and V.P. Hadjigeorgiou, Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels, J. Sound Vibr., vol. 137, no. 3, pp. 369–384, 1990. DOI: 10.1016/0022-460X(90)90805-A.
   Web of Science ®Google Scholar
• K.Y. Lam, and C.T. Loy, Analysis of rotating laminated cylindrical shells by different thin shell theories, J. Sound Vibr., vol. 186, no. 1, pp. 23–35, 1995. DOI: 10.1006/jsvi.1995.0431.
   Web of Science ®Google Scholar
• K.Y. Lam, and C.T. Loy, Influence of boundary conditions for a thin laminated rotating cylindrical shell, Compos. Struct., vol. 41, no. 3–4, pp. 215–228, 1998. DOI: 10.1016/S0263-8223(98)00012-9.
   Web of Science ®Google Scholar
• K.Y. Lam, and C.T. Loy, On vibrations of thin rotating laminated composite cylindrical shells, Compos. Eng., vol. 4, no. 11, pp. 1153–1167, 1994. DOI: 10.1016/0961-9526(95)91289-S.
   Google Scholar
• K.Y. Lam, and W. Qian, Free vibration of symmetric angle-ply thick laminated composite cylindrical shells, Compos. Part B: Eng., vol. 31, no. 4, pp. 345–354, 2000. DOI: 10.1016/S1359-8368(99)00075-X.
   Web of Science ®Google Scholar
• K.Y. Lam, and W. Qian, Vibrations of thick rotating laminated composite cylindrical shells, J. Sound Vibr., vol. 225, no. 3, pp. 483–501, 1999. DOI: 10.1006/jsvi.1999.2205.
   Web of Science ®Google Scholar
• H.T. Hu, and K.L. Wang, Vibration analysis of rotating laminated cylindrical shells, AIAA J., vol. 45, no. 8, pp. 2051–2061, 2007. DOI: 10.2514/1.28674.
   Google Scholar
• K. Bouafia, et al., Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model, Steel Compos. Struct., vol. 41, no. 4, pp. 487–503, 2021.
   Web of Science ®Google Scholar
• S. Brischetto, F. Tornabene, N. Fantuzzi, and E. Viola, 3D exact and 2D generalized differential quadrature models for free vibration analysis of functionally graded plates and cylinders, Meccanica, vol. 51, no. 9, pp. 2059–2098, 2016. DOI: 10.1007/s11012-016-0361-y.
   Web of Science ®Google Scholar
• Y. Han, X. Zhu, T. Li, Y. Yu, and X. Hu, Free Vibration and Elastic Critical Load of Functionally Graded Material Thin Cylindrical Shells Under Internal Pressure, Int. J. Str. Stab. Dyn., vol. 18, no. 11, pp. 1850138, 2018. DOI: 10.1142/S0219455418501389.
   Web of Science ®Google Scholar
• V.T. Long, and H.V. Tung, Mechanical buckling analysis of thick FGM toroidal shell segments with porosities using Reddy’s higher order shear deformation theory, Mech. Adv. Mater. Struct., pp. 1–10, 2021. DOI: 10.1080/15376494.2021.1969606.
   Web of Science ®Google Scholar
• C.T. Loy, K.Y. Lam, and J.N. Reddy, Vibration of functionally graded cylindrical shells, Int. J. Mech. Sci., vol. 41, no. 3, pp. 309–324, 1999. DOI: 10.1016/S0020-7403(98)00054-X.
   Web of Science ®Google Scholar
• I.M. Mudhaffar, A. Tounsi, A. Chikh, M.A. Al-Osta, M.M. Al-Zahrani, and S.U. Al-Dulaijan, Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation, Structures, vol. 33, pp. 2177–2189, 2021. DOI: 10.1016/j.istruc.2021.05.090.
   Web of Science ®Google Scholar
• N.T. Phuong, V.H. Nam, N.T. Trung, V.M. Duc, and P.V. Phong, Nonlinear stability of sandwich functionally graded cylindrical shells with stiffeners under axial compression in thermal environment, Int. J. Str. Stab. Dyn., vol. 19, no. 07, pp. 1950073, 2019. DOI: 10.1142/S0219455419500731.
   Google Scholar
• S.C. Pradhan, C.T. Loy, K.Y. Lam, and J.N. Reddy, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Appl. Acoust., vol. 61, no. 1, pp. 111–129, 2000. DOI: 10.1016/S0003-682X(99)00063-8.
   Web of Science ®Google Scholar
• S. Pradyumna, and J.N. Bandyopadhyay, Free vibration and buckling of functionally graded shell panels in thermal environments, Int. J. Str. Stab. Dyn., vol. 10, no. 05, pp. 1031–1053, 2010. DOI: 10.1142/S0219455410003889.
   Google Scholar
• A. Rachid, et al., Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs, Thin-Walled Struct., vol. 172, pp. 108783, 2022. DOI: 10.1016/j.tws.2021.108783.
   Web of Science ®Google Scholar
• J.N. Reddy, Analysis of functionally graded plates, Int. J. Numer. Methods Eng., vol. 47, no. 1–3, pp. 663–684, 2000. DOI: 10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8.
   Web of Science ®Google Scholar
• H. Safarpour, Z.E. Hajilak, and M. Habibi, A size-dependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation, Int. J. Mech. Mater. Des., vol. 15, no. 3, pp. 569–583, 2019. DOI: 10.1007/s10999-018-9431-8.
   Web of Science ®Google Scholar
• P. Toan Thang, T. Nguyen-Thoi, and J. Lee, Mechanical stability of metal foam cylindrical shells with various porosity distributions, Mech. Adv. Mater. Struct., vol. 27, no. 4, pp. 295–303, 2020. DOI: 10.1080/15376494.2018.1472338.
   Web of Science ®Google Scholar
• P.M. Vuong, and N.D. Duc, Nonlinear vibration of FGM moderately thick toroidal shell segment within the framework of Reddy’s third order-shear deformation shell theory, Int. J. Mech. Mater. Des., vol. 16, no. 2, pp. 245–220, 2020. DOI: 10.1007/s10999-019-09473-x.
   Web of Science ®Google Scholar
• E. Zarouni, M.J. Rad, and H. Tohidi, Free vibration analysis of fiber reinforced composite conical shells resting on Pasternak-type elastic foundation using Ritz and Galerkin methods, Int. J. Mech. Mater. Des., vol. 10, no. 4, pp. 421–438, 2014. DOI: 10.1007/s10999-014-9254-1.
   Web of Science ®Google Scholar
• J.-H. Zhang, and S.-R. Li, Free vibration of functionally graded truncated conical shells using the GDQ method, Mech. Adv. Mater. Struct., vol. 20, no. 1, pp. 61–73, 2013. DOI: 10.1080/15376494.2011.581415.
   Web of Science ®Google Scholar
• S. Hosseini-Hashemi, M.R. Ilkhani, and M. Fadaee, Accurate natural frequencies and critical speeds of a rotating functionally graded moderately thick cylindrical shell, Int. J. Mech. Sci., vol. 76, pp. 9–20, 2013. DOI: 10.1016/j.ijmecsci.2013.08.005.
   Web of Science ®Google Scholar
• P. Malekzadeh, and Y. Heydarpour, Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment, Compos. Struct., vol. 94, no. 9, pp. 2971–2981, 2012. DOI: 10.1016/j.compstruct.2012.04.011.
   Web of Science ®Google Scholar
• S. Sun, D. Cao, and Q. Han, Vibration studies of rotating cylindrical shells with arbitrary edges using characteristic orthogonal polynomials in the Rayleigh–Ritz method, Int. J. Mech Sci., vol. 68, pp. 180–189, 2013. DOI: 10.1016/j.ijmecsci.2013.01.013.
   Web of Science ®Google Scholar
• M. Talebitooti, Thermal effect on free vibration of ring-stiffened rotating functionally graded conical shell with clamped ends, Mech. Adv. Mater. Struct., vol. 25, no. 2, pp. 155–165, 2018. DOI: 10.1080/15376494.2016.1255809.
   Web of Science ®Google Scholar
• M. Talebitooti, K. Daneshjou, and R. Talebitooti, Vibration and critical speed of orthogonally stiffened rotating fg cylindrical shell under thermo-mechanical loads using differential quadrature method, J. Therm. Stress., vol. 36, no. 2, pp. 160–188, 2013. DOI: 10.1080/01495739.2013.764807.
   Web of Science ®Google Scholar
• M.-T. Tran, and V.-L. Nguyen, Free vibration of rotating functionally graded material cylindrical shells with orthogonal stiffeners. In: S.V. Hoa, H. Hamada and N.D. Duc (eds.), Proceedings of the Eleventh Joint Canada-Japan Workshop on Composites and the First Joint Canada-Japan-Vietnam Workshop on Composites. Ho Chi Minh City, Vietnam: DEStech Publications, Inc, 2017.
   Google Scholar
• M.-T. Tran, and V.-L. Nguyen, Vibration analysis of rotating functionally graded cylindrical shells with orthogonal stiffeners, Latin Am. J. Solids Struct., vol. 13, no. 15, pp. 2652–2669, 2016.
   Web of Science ®Google Scholar
• S. Xiang, G.C. Li, W. Zhang, and M.S. Yang, Natural frequencies of rotating functionally graded cylindrical shells, Appl. Math. Mech-Engl. Ed., vol. 33, no. 3, pp. 345–356, 2012. DOI: 10.1007/s10483-012-1554-6.
   Google Scholar
• V.L. Nguyen, and T.P. Hoang, Analytical solution for free vibration of stiffened functionally graded cylindrical shell structure resting on elastic foundation, SN Appl. Sci., vol. 1, no. 10, pp. 1150, 2019. DOI: 10.1007/s42452-019-1168-y.
   Web of Science ®Google Scholar
• Z. Qin, F. Chu, and J. Zu, Free vibrations of cylindrical shells with arbitrary boundary conditions: A comparison study, Int. J. Mech. Sci., vol. 133, pp. 91–99, 2017. DOI: 10.1016/j.ijmecsci.2017.08.012.
   Web of Science ®Google Scholar
• Z. Qin, X. Pang, B. Safaei, and F. Chu, Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions, Compos. Struct., vol. 220, pp. 847–860, 2019. DOI: 10.1016/j.compstruct.2019.04.046.
   Web of Science ®Google Scholar
• S. Sun, L. Liu, and D. Cao, Nonlinear travelling wave vibrations of a rotating thin cylindrical shell, J. Sound Vibr., vol. 431, pp. 122–136, 2018. DOI: 10.1016/j.jsv.2018.05.042.
   Web of Science ®Google Scholar
• M.-T. Tran, V.-L. Nguyen, S.-D. Pham, and J. Rungamornrat, Free vibration of stiffened functionally graded circular cylindrical shell resting on Winkler–Pasternak foundation with different boundary conditions under thermal environment, Acta Mech., vol. 231, no. 6, pp. 2545–2564, 2020. DOI: 10.1007/s00707-020-02658-y.
   Web of Science ®Google Scholar
• Y. Wang, and D. Wu, Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory, Aerosp. Sci. Technol., vol. 66, pp. 83–91, 2017. DOI: 10.1016/j.ast.2017.03.003.
   Web of Science ®Google Scholar
• M. Jabbari, A. Mojahedin, A.R. Khorshidvand, and M.R. Eslami, Buckling analysis of a functionally graded thin circular plate made of saturated porous materials, J. Eng. Mech., vol. 140, no. 2, pp. 287–295, 2014. DOI: 10.1061/(ASCE)EM.1943-7889.0000663.
   Web of Science ®Google Scholar
• D. Chen, J. Yang, and S. Kitipornchai, Free and forced vibrations of shear deformable functionally graded porous beams, Int. J. Mech. Sci., vol. 108–109, pp. 14–22, 2016. DOI: 10.1016/j.ijmecsci.2016.01.025.
   Web of Science ®Google Scholar
• T.M. Tu, L.K. Hoa, D.X. Hung, and L.T. Hai, Nonlinear buckling and post-buckling analysis of imperfect porous plates under mechanical loads, J. Sandwich Struct. Mater., vol. 22, no. 6, pp. 1910–1930, 2020. DOI: 10.1177/1099636218789612.
   Web of Science ®Google Scholar
• Y.Q. Wang, C. Ye, and J.W. Zu, Vibration analysis of circular cylindrical shells made of metal foams under various boundary conditions, Int. J. Mech. Mater. Des., vol. 15, no. 2, pp. 333–344, 2019. DOI: 10.1007/s10999-018-9415-8.
   Web of Science ®Google Scholar
• H. Li, F. Pang, H. Chen, and Y. Du, Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method, Compos. Part B: Eng., vol. 164, pp. 249–264, 2019. DOI: 10.1016/j.compositesb.2018.11.046.
   Web of Science ®Google Scholar
• H. Li, F. Pang, Y. Ren, X. Miao, and K. Ye, Free vibration characteristics of functionally graded porous spherical shell with general boundary conditions by using first-order shear deformation theory, Thin-Walled Struct., vol. 144, pp. 106331, 2019. DOI: 10.1016/j.tws.2019.106331.
   Web of Science ®Google Scholar
• A.R. Ghasemi, and M. Meskini, Free vibration analysis of porous laminated rotating circular cylindrical shells, J. Vibr. Control., vol. 25, no. 18, pp. 2494–2508, 2019.
   Web of Science ®Google Scholar
• N.D. Duc, V.D. Quang, P.D. Nguyen, and T.M. Chien, Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads, J. Appl. Comput. Mech., vol. 4, no. 4, pp. 245–259, 2018.
   Web of Science ®Google Scholar
• A.V. Lopatin, and E.V. Morozov, Fundamental frequency of a sandwich cylindrical panel with clamped edges, J. Sandwich Struct. Mater., vol. 23, no. 1, pp. 345–364, 2021.
   Web of Science ®Google Scholar
• M. Abouhamzeh, and M. Sadighi, Buckling optimisation of sandwich cylindrical panels, Curved Layered Struct., vol. 3, no. 1, pp. 137–145, 2016. DOI: 10.1515/cls-2016-0011.
   Google Scholar
• A. Alibeigloo, and A. Rajaee Piteh Noee, Static and free vibration analysis of sandwich cylindrical shell based on theory of elasticity and using DQM, Acta Mech., vol. 228, no. 12, pp. 4123–4140, 2017. DOI: 10.1007/s00707-017-1914-4.
   Web of Science ®Google Scholar
• N.D. Duc, N.D. Tuan, P. Tran, T.Q. Quan, and N.V. Thanh, Nonlinear dynamic response and vibration of imperfect eccentrically stiffened sandwich third-order shear deformable FGM cylindrical panels in thermal environments, J. Sandwich Struct. Mater., vol. 21, no. 8, pp. 2816–2845, 2019. DOI: 10.1177/1099636217725251.
   Web of Science ®Google Scholar
• M.C. Trinh, N.D. Duc, and S.E. Kim, Effects of porosity and thermomechanical loading on free vibration and nonlinear dynamic response of functionally graded sandwich shells with double curvature, Aerosp. Sci. Technol., vol. 87, pp. 119–132, 2019. DOI: 10.1016/j.ast.2019.02.010.
   Web of Science ®Google Scholar
• S.I. Tahir, A. Tounsi, A. Chikh, M.A. Al-Osta, S.U. Al-Dulaijan, and M.M. Al-Zahrani, The effect of three-variable viscoelastic foundation on the wave propagation in functionally graded sandwich plates via a simple quasi-3D HSDT, Steel Compos. Struct., vol. 42, no. 4, pp. 501, 2022.
   Web of Science ®Google Scholar
• M.W. Zaitoun, et al., Influence of the visco-Pasternak foundation parameters on the buckling behavior of a sandwich functional graded ceramic–metal plate in a hygrothermal environment, Thin-Walled Struct., vol. 170, pp. 108549, 2022. DOI: 10.1016/j.tws.2021.108549.
   Web of Science ®Google Scholar
• S.I. Tahir, A. Chikh, A. Tounsi, M.A. Al-Osta, S.U. Al-Dulaijan, and M.M. Al-Zahrani, Wave propagation analysis of a ceramic-metal functionally graded sandwich plate with different porosity distributions in a hygro-thermal environment, Compos. Struct., vol. 269, pp. 114030, 2021. DOI: 10.1016/j.compstruct.2021.114030.
   Web of Science ®Google Scholar
• D. Kouider, et al., 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., vol. 41, no. 2, pp. 167–191, 2021.
   Web of Science ®Google Scholar
• Y. Conde, A. Pollien, and A. Mortensen, Functional grading of metal foam cores for yield-limited lightweight sandwich beams, Scr. Mater., vol. 54, no. 4, pp. 539–543, 2006. DOI: 10.1016/j.scriptamat.2005.10.050.
   Web of Science ®Google Scholar
• D.K. Thai, T.M. Tu, L.K. Hoa, D.X. Hung, and N.N. Linh, Nonlinear stability analysis of eccentrically stiffened functionally graded truncated conical sandwich shells with porosity, Materials, vol. 11, no. 11, pp. 2200, 2018. DOI: 10.3390/ma11112200.
   PubMed Web of Science ®Google Scholar
• A.M. Zenkour, and N.A. Alghamdi, Thermoelastic bending analysis of functionally graded sandwich plates, J. Mater. Sci., vol. 43, no. 8, pp. 2574–2589, 2008. DOI: 10.1007/s10853-008-2476-6.
   Web of Science ®Google Scholar
• D. Chen, S. Kitipornchai, and J. Yang, Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core, Thin-Walled Struct., vol. 107, pp. 39–48, 2016. DOI: 10.1016/j.tws.2016.05.025.
   Web of Science ®Google Scholar
• J. Zhao, Q. Wang, X. Deng, K. Choe, F. Xie, and C. Shuai, A modified series solution for free vibration analyses of moderately thick functionally graded porous (FGP) deep curved and straight beams, Compos. Part B: Eng., vol. 165, pp. 155–166, 2019. DOI: 10.1016/j.compositesb.2018.11.080.
   Web of Science ®Google Scholar
• J.N. Reddy, Theory and Analysis of Elastic Plates and Shells, CRC Press, Boca Raton, 2006.
   Google Scholar
• P. Van Vinh, and A. Tounsi, Free vibration analysis of functionally graded doubly curved nanoshells using nonlocal first-order shear deformation theory with variable nonlocal parameters, Thin-Walled Struct., vol. 174, pp. 109084, 2022. DOI: 10.1016/j.tws.2022.109084.
   Web of Science ®Google Scholar
• H. Li, K.Y. Lam, and T.Y. Ng, Rotating Shell Dynamics, 1st ed. Elsevier, Amsterdam, 2005.
   Google Scholar
• Z. Qin, B. Safaei, X. Pang, and F. Chu, Traveling wave analysis of rotating functionally graded graphene platelet reinforced nanocomposite cylindrical shells with general boundary conditions, Results Phys., vol. 15, pp. 102752, 2019. DOI: 10.1016/j.rinp.2019.102752.
   Web of Science ®Google Scholar