Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

References

[1] J.N. Reddy, Mechanics of laminated composite plates and shells: theory and analysis. (2^nd ed.) New York: CRC Press, 2003.Search in Google Scholar

[2] A.W. Leissa, Vibration of shells, Acoustical Society of America, 1993.Search in Google Scholar

[3] W. Soedel, Vibrations of shells and plates, Third Edition, CRC Press, 2004.10.4324/9780203026304Search in Google Scholar

[4] F. Tornabene, N. Fantuzzi, Mechanics of laminated composite doubly-curved shell structures, the generalized differential quadrature method and the strong formulation finite element method, Società Editrice Esculapio, 2014.Search in Google Scholar

[5] Ö. Civalek, Finite element analyses of plates and shells, Elazığ: Fırat University, (in Turkish) 1998.Search in Google Scholar

[6] A.J.M. Ferreira, R.M.N. Roque, Jorge, E.J. Kansa, Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and multiquadrics discretizations, Eng. Anal. Bound Elem., 29 (2005), 1104-1114.10.1016/j.enganabound.2005.07.004Search in Google Scholar

[7] A.J.M. Ferreira, G.E. Fasshauer, Analysis of natural frequencies of composite plates by an RBF-pseudospectral method, Comp. Struct., 79(2) (2007), 202-210.10.1016/j.compstruct.2005.12.004Search in Google Scholar

[8] A.J.M. Ferreira, Polyharmonic (thin-plate) splines in the analysis of composite plates, Int. J. Mech. Sci., 46 (2004), 1549-1569.10.1016/j.ijmecsci.2004.09.002Search in Google Scholar

[9] F. Tornabene, N. Fantuzzi, E. Viola, A.J.M. Ferreira, Radial basis function method applied to doubly-curved laminated composite shells and panels with a General Higher-order Equivalent Single Layer formulation, Compos. Part B: Eng., 55 (2013), 642-659.10.1016/j.compositesb.2013.07.026Search in Google Scholar

[10] F. Tornabene, N. Fantuzzi, E. Viola, R. C. Batra, Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory, Comp. Struct., 119 (2015), 67-89.10.1016/j.compstruct.2014.08.005Search in Google Scholar

[11] F. Tornabene, E. Viola, D.J. Inman, 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shells and annular plate structures, J. Sound Vib., 328 (2009), 259-290.10.1016/j.jsv.2009.07.031Search in Google Scholar

[12] S.R. Li, R.C. Batra, Buckling of axially compressed thin cylindrical shells with functionally graded middle layer. Thin-Walled Struct., 44 (2006), 1039-1047.Search in Google Scholar

[13] E. Viola, F. Tornabene, E. Ferretti, N. Fantuzzi, On static analysis of composite plane state structures via GDQFEM and Cell Method, CMES, 94(2013), 421-458.Search in Google Scholar

[14] F. Tornabene, N. Fantuzzi, M Bacciocchi, The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: the free vibration analysis, Comp. Struct., 116 (2014), 637-660.10.1016/j.compstruct.2014.05.008Search in Google Scholar

[15] F. Tornabene, N. Fantuzzi, F. Ubertini, E. Viola, Strong formulation finite element method based on differential quadrature: a survey, Appl. Mech. Rev., 67 (2015), 1 – 55.10.1115/1.4028859Search in Google Scholar

[16] Ö. Civalek, A parametric study of the free vibration analysis of rotating laminated cylindrical shells using the method of discrete singular convolution, Thin. Wall. Struct., 45 (2007), 692-698.10.1016/j.tws.2007.05.004Search in Google Scholar

[17] Ö. Civalek, M. Gürses, Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique, Int. J. Press. Vessel. Pip., 86(10) (2009), 677-683.10.1016/j.ijpvp.2009.03.011Search in Google Scholar

[18] Ö. Civalek, Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory, Compos. Part B: Eng., 45(1) (2013), 1001-1009.10.1016/j.compositesb.2012.05.018Search in Google Scholar

[19] Ö. Civalek, Free vibration analysis of composite conical shells using the discrete singular convolution algorithm, Steel Compos. Struct., 6(4) (2006), 353-366.10.12989/scs.2006.6.4.353Search in Google Scholar

[20] Ö. Civalek, The determination of frequencies of laminated conical shells via the discrete singular convolution method, J. Mech. Mater. Struct., 1(1) (2006), 163-182.10.2140/jomms.2006.1.163Search in Google Scholar

[21] Ö. Civalek, Vibration analysis of conical panels using the method of discrete singular convolution, Commun. Numer. Meth. Eng., 24 (2008), 169-181.10.1002/cnm.961Search in Google Scholar

[22] J.C. Zhang, T.Y. Ng, K.M. Liew, Three-dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modeling, Int. J. Numer. Meth. Eng., 57 (2003), 1819–1844.10.1002/nme.746Search in Google Scholar

[23] Ö. Civalek, M. Ülker, Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates, Struc. Eng. Mech., 17(1) (2004), 1-14.10.12989/sem.2004.17.1.001Search in Google Scholar

[24] Ö. Civalek, Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ), Ph. D. Thesis, Firat University, Elazig, 2004 (in Turkish).Search in Google Scholar

[25] Ö. Civalek, Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches, Compos. Part B: Eng., 50 (2013), 171-179.10.1016/j.compositesb.2013.01.027Search in Google Scholar

[26] K.M. Liew, X. Zhao, T.Y. Ng, The element-free kp-Ritz method for vibration of laminated rotating cylindrical panels, Int. J. Struct. Stab. Dyn., 2 (2002), 523–58.10.1142/S0219455402000701Search in Google Scholar

[27] M. Kouzumi, The concept of FGM. Ceramic Transactions, Functionally Gradient Materials, 34 (1993), 3-10.Search in Google Scholar

[28] A. Ghosh, Y. Miyamoto, I. Reimanis, J.J. Lannutti, Functionally graded materials: Manufacture, properties and applications, Am. Cer. So., Ceramic Place, Westerville, Ohio (1997).Search in Google Scholar

[29] V. Birman, L.W. Byrd, Modeling and analysis of functionally graded materials and structures, Appl. Mech. Rev., 160 (2007), 195.216.Search in Google Scholar

[30] X.D. Zhang, D.Q. Liu, C.C. Ge, Thermal stress analysis of axial symmetry functionally gradient materials under steady temperature field, Journal of Functional Material, 25(1994), 452-455.Search in Google Scholar

[31] C.T. Loy, K.Y. Lam, J.N. Reddy, Vibration of functionally graded cylindrical shells, Int. J. Mech. Sci., 41 (1999), 309-324.10.1016/S0020-7403(98)00054-XSearch in Google Scholar

[32] P. Malekzadeh, Y. Heydarpour, Free vibration of rotating functionally gradient cylindrical shells in thermal environment, Compos. Struct., 94 (2012), 2971-2981.10.1016/j.compstruct.2012.04.011Search in Google Scholar

[33] Z. Iqbal, M.N. Naeem, N. Sultana, Vibration characteristics of FGM circular cylindrical shells using wave propagation approach, Acta Mech., 208 (2009),237-248.10.1007/s00707-009-0141-zSearch in Google Scholar

[34] S.C. Pradhan, C.T. Loy, K.Y. Lam, J.N. Reddy, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Appl. Acoustics, 61 (2000), 111–124.10.1016/S0003-682X(99)00063-8Search in Google Scholar

[35] M.M. Najafizadeh, M.R. Isvandzibaei, Vibration of functionally graded cylindrical shells based on higher order shear deformation plate theory with ring support, Acta Mech., 191 (2007), 75-91.10.1007/s00707-006-0438-0Search in Google Scholar

[36] H. Haddadpour, S. Mahmoudkhani, H.M. Navazi, Free vibration analysis of functionally graded cylindrical shells including thermal effects, Thin-Walled Struct., 45 (2007), 591-599.10.1016/j.tws.2007.04.007Search in Google Scholar

[37] M. N. Naeem, S. H. Arshad, and C. B. Sharma, The Ritz formulation applied to the study of the vibration frequency characteristics of functionally graded circular cylindrical shells, Proc. Inst. Mech. Eng. Part C: J. Mech. Sci., 224 (2010), 43–54.10.1243/09544062JMES1548Search in Google Scholar

[38] S.H. Arshad, M.N. Naeem, N. Sultana, A.G. Shah, Z. Iqbal, Vibration analysis of bi-layered FGM cylindrical shells, Arch. Appl. Mech., 81(3) (2011), 319-343.10.1007/s00419-010-0409-8Search in Google Scholar

[39] X. Han, G.R. Liu, Z.C. Xi, K.Y. Lam, Characteristics of waves in a functionally graded cylinder, Int. J. Mech. Eng., 53 (2002), 653-676.Search in Google Scholar

[40] H. Thai, S. Kim, A review of theories for the modeling and analysis of functionally graded plates and shells, Comp. Struct., 128 (2015), 70-86.10.1016/j.compstruct.2015.03.010Search in Google Scholar

[41] M. Merazi, L. Hadji, T. Daouadji, A. Tounsi, E. Adda Bedia, A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position, Geomechanics and Engineering, 8(3) (2015), 305-321.10.12989/gae.2015.8.3.305Search in Google Scholar

[42] A. Hamidi, M. Houari, S. Mahmoud, A. Tounsi, A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates, Steel Comp. Struct., 18(1) (2015), 235-253.10.12989/scs.2015.18.1.235Search in Google Scholar

[43] A.G. Shah, T. Mahmood, M.N. Naeem, Z. Iqbal, S.H. Arshad, Vibrations of functionally graded cylindrical shells based on elastic foundations. Acta Mech., 211 (2010), 293–307.Search in Google Scholar

[44] Z. Iqbal, M.N. Naeem, N. Sultana, Vibration characteristics of FGM circular cylindrical shells using wave propagation approach, Acta Mech., 208 (3-4) (2009) 237-248.10.1007/s00707-009-0141-zSearch in Google Scholar

[45] A.G. Shah, T. Mahmmod, M.N. Naeem, Vibration of FGM thin cylindrical shells with exponential volume fraction law, Appl. Math. Mech. (English Edition), 30 (5) (2009), 607-615.10.1007/s10483-009-0507-xSearch in Google Scholar

[46] G.W. Wei, A new algorithm for solving some mechanical problems, Comput. Methods Appl. Mech. Eng., 190 (2001), 2017-2030.10.1016/S0045-7825(00)00219-XSearch in Google Scholar

[47] G.W. Wei, Vibration analysis by discrete singular convolution, J. Sound Vib., 244 (2001), 535-553.10.1006/jsvi.2000.3507Search in Google Scholar

[48] G.W. Wei, Y.C. Zhou, Y. Xiang, A novel approach for the analysis of high-frequency vibrations, J. Sound Vib., 257(2) (2002), 207-246.10.1006/jsvi.2002.5055Search in Google Scholar

[49] G.W. Wei, Y.C. Zhou, Y. Xiang, Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm, Int. J. Numer. Methods Eng., 55 (2002), 913-946.10.1002/nme.526Search in Google Scholar

[50] G.W. Wei, Y.C. Zhou, Y. Xiang, The determination of natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution, Int. J. Mech. Sci. 43 (2001), 1731-1746.10.1016/S0020-7403(01)00021-2Search in Google Scholar

[51] Y.C. Zhou, G.W. Wei, DSC analysis of rectangular plates with non-uniform boundary conditions, J. Sound Vib., 255(2) (2002), 203-228.10.1006/jsvi.2001.4150Search in Google Scholar

[52] Y. Hou, G.W. Wei, Y. Xiang, DSC-Ritz method for the free vibration analysis of Mindlin plates, Int. J. Numer. Meth. Eng., 62 (2005), 262–288.10.1002/nme.1186Search in Google Scholar

[53] C.W. Lim, Z.R. Li, G.W. Wei, DSC-Ritz method for high-mode frequency analysis of thick shallow shells, Int. J. Numer. Methods Eng., 62 (2005), 205-232.10.1002/nme.1179Search in Google Scholar

[54] Ö. Civalek, A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight-sided quadrilateral plates, Appl. Math. Model., 33(1) (2009), 300-314.10.1016/j.apm.2007.11.003Search in Google Scholar

[55] Ö. Civalek, Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method, Int. J. Mech. Sci., 49 (2007), 752-765.10.1016/j.ijmecsci.2006.10.002Search in Google Scholar

[56] Ö. Civalek, M.H. Acar, Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations, Int. J. Press. Vessel. Pip., 84 (2007), 527-535.10.1016/j.ijpvp.2007.07.001Search in Google Scholar

[57] Ö. Civalek, Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method, Appl. Math. Model., 33(10) (2009), 3825-3835.10.1016/j.apm.2008.12.019Search in Google Scholar

[58] Ö. Civalek, Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method, Finite Elem. Anal. Des., 44(12-13) (2008), 725-731.10.1016/j.finel.2008.04.001Search in Google Scholar

[59] Ö. Civalek, A.K. Korkmaz, Ç. Demir, Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two opposite edges, Adv. Eng. Softw., 41 (2010), 557-560.10.1016/j.advengsoft.2009.11.002Search in Google Scholar

[60] Ö. Civalek, Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory, J. Compos. Mater. 42 (2008), 2853-2867.10.1177/0021998308096952Search in Google Scholar

[61] A. Seçkin, A.S. Sarıgül, Free vibration analysis of symmetrically laminated thin composite plates by using discrete singular convolution (DSC) approach: Algorithm and verification, J. Sound Vib., 315 (2008), 197-211.10.1016/j.jsv.2008.01.061Search in Google Scholar

[62] A. Seçkin, Modal and response bound predictions of uncertain rectangular composite plates based on an extreme value model, J. Sound Vib., 332 (2013), 1306–1323.10.1016/j.jsv.2012.09.036Search in Google Scholar

[63] L. Xin, Z. Hu, Free vibration of layered magneto-electro-elastic beams by SS-DSC approach, Compos. Struct., 125 (2015), 96–103.10.1016/j.compstruct.2015.01.048Search in Google Scholar

[64] L. Xin, Z. Hu, Free vibration of simply supported and multilayered magneto-electro-elastic plates, Compos. Struct., 121 (2015), 344-350.10.1016/j.compstruct.2014.11.030Search in Google Scholar

[65] X. Wang, S. Xu, Free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution, J. Sound Vib., 329(10) (2010), 1780–1792.10.1016/j.jsv.2009.12.006Search in Google Scholar

[66] X. Wang, Y. Wang, S. Xu, DSC analysis of a simply supported anisotropic rectangular plate, Compos. Struct. 94(8) (2012), 2576–2684.10.1016/j.compstruct.2012.03.005Search in Google Scholar

[67] G. Duan, X. Wang, C. Jin. Free vibration analysis of circular thin plates with stepped thickness by the DSC element method, Thin. Wall. Struct., 85 (2014), 25-33.10.1016/j.tws.2014.07.010Search in Google Scholar

[68] A.K. Baltacıoglu, Ö. Civalek, B. Akgöz, F. Demir, Large deflection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution, Int. J. Pres. Ves. Pip., 88 (2011), 290-300.10.1016/j.ijpvp.2011.06.004Search in Google Scholar

[69] Ö. Civalek, B. Akgöz, Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix, Comp. Mater. Sci.,77 (2013), 295-303.10.1016/j.commatsci.2013.04.055Search in Google Scholar

[70] M. Gürses, Ö. Civalek, A. Korkmaz, H. Ersoy, Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory, Int. J. Numer. Meth. Eng., 79 (2009), 290-313.10.1002/nme.2553Search in Google Scholar