Nonlinear dynamic analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under external pressure and surrounded by an elastic medium.

*(English)*Zbl 1406.74471Summary: A semi-analytical approach eccentrically stiffened functionally graded circular cylindrical shells surrounded by an elastic medium subjected to external pressure is presented the elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffeners technique and Galerkin method, this paper deals the nonlinear dynamic problem. The approximate three-term solution of deflection shape is chosen and the frequency-amplitude relation of nonlinear vibration is obtained in explicit form. The nonlinear dynamic responses are analyzed by using fourth order Runge-Kutta method and the nonlinear dynamic buckling behavior of stiffened functionally graded shells is investigated according to Budiansky-Roth criterion. Results are given to evaluate effects of stiffener, elastic foundation and input factors on the frequency-amplitude curves, natural frequencies, nonlinear responses and nonlinear dynamic buckling loads of functionally graded cylindrical shells.

##### MSC:

74K25 | Shells |

74A40 | Random materials and composite materials |

74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |

74G60 | Bifurcation and buckling |

##### Keywords:

functionally graded material; nonlinear dynamic analysis; stiffened circular cylindrical shell
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\textit{D. Van Dung} and \textit{V. H. Nam}, Eur. J. Mech., A, Solids 46, 42--53 (2014; Zbl 1406.74471)

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##### References:

[1] | Bagherizadeh, E.; Kiani, Y.; Eslami, M. R., Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation, Compos. Struct., 93, 3063-3071, (2011) |

[2] | Baruch, M.; Singer, J., Effect of eccentricity of stiffeners on the general instability of stiffened cylindrical shells under hydro-static pressure, J. Mech. Eng. Sci., 5, 23-27, (1963) |

[3] | Bich, D. H.; Nam, V. H.; Phuong, N. T., Nonlinear postbuckling of eccentrically stiffened functionally graded plates and shallow shells, Vietnam J. Mech., 33, 132-147, (2011) |

[4] | Bich, D. H.; Dung, D. V.; Nam, V. H., Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels, Compos. Struct., 94, 2465-2473, (2012) |

[5] | Bich, D. H.; Dung, D. V.; Nam, V. H., Nonlinear dynamic analysis of eccentrically stiffened imperfect functionally graded doubly curved thin shallow shells, Compos. Struct., 96, 384-395, (2013) |

[6] | Brush, D. O.; Almroth, B. O., Buckling of bars, plates and shells, (1975), Mc Graw-Hill New York · Zbl 0352.73040 |

[7] | Budiansky, B.; Roth, R. S., Axisymmetric dynamic buckling of clamped shallow spherical shells, (1962), NASA technical note D_510 |

[8] | Darabi, M.; Darvizeh, M.; Darvizeh, A., Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading, Compos. Struct., 83, 201-211, (2008) |

[9] | Deniz, A.; Sofiyev, A. H., The nonlinear dynamic buckling response of functionally graded truncated conical shells, J. Sound Vib., 332, 978-992, (2013) |

[10] | Dung, D. V.; Hoa, L. K., Nonlinear buckling and post-buckling analysis of eccentrically stiffened functionally graded circular cylindrical shells under external pressure, Thin-Walled Struct., 63, 117-124, (2013) |

[11] | Dung, D. V.; Hoa, L. K., Research on nonlinear torsional buckling and post-buckling of eccentrically stiffened functionally graded thin circular cylindrical shells, Compos. B, 51, 300-309, (2013) |

[12] | Hong, C. C., Thermal vibration of magnetostrictive functionally graded material shells, Eur. J. Mech. A/Solids, 40, 114-122, (2013) · Zbl 1406.74296 |

[13] | Huang, H.; Han, Q., Buckling of imperfect functionally graded cylindrical shells under axial compression, Eur. J. Mech. A/Solids, 27, 1026-1036, (2008) · Zbl 1151.74356 |

[14] | Huang, H.; Han, Q., Nonlinear elastic buckling and postbuckling of axially compressed functionally graded cylindrical shells, Int. J. Mech. Sci., 51, 500-507, (2009) |

[15] | Huang, H.; Han, Q., Nonlinear buckling and postbuckling of heated functionally graded cylindrical shells under combined axial compression and radial pressure, Int. J. Non-Linear Mech., 44, 209-218, (2009) · Zbl 1203.74044 |

[16] | Huang, H.; Han, Q., Research on nonlinear postbuckling of FGM cylindrical shells under radial loads, Compos. Struct., 92, 1352-1357, (2010) |

[17] | Huang, H.; Han, Q., Nonlinear buckling of torsion-loaded functionally graded cylindrical shells in thermal environment, Eur. J. Mech. A/Solids, 29, 42-48, (2010) |

[18] | Huang, H.; Han, Q., Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to a time-dependent axial load, Compos. Struct., 92, 593-598, (2010) |

[19] | Najafizadeh, M. M.; Hasani, A.; Khazaeinejad, P., Mechanical stability of functionally graded stiffened cylindrical shells, Appl. Math. Model, 54, 1151-1157, (2009) · Zbl 1168.74392 |

[20] | Najafov, A. M.; Sofiyev, A. H.; Kuruoglu, N., Torsional vibration and stability of functionally graded orthotropic cylindrical shells on elastic foundations, Meccanica, 48, 829-840, (2013) · Zbl 1293.74193 |

[21] | Najafov, A. M.; Sofiyev, A. H., The non-linear dynamics of FGM truncated conical shells surrounded by an elastic medium, Int. J. Mech. Sci., 66, 33-44, (2013) |

[22] | Paliwal, D. N.; Pandey, R. K.; Nath, T., Free vibration of circular cylindrical shell on Winkler and Pasternak foundation, Int. J. Pres. Ves. Pip., 69, 79-89, (1996) |

[23] | Reddy, J. N.; Starnes, J. H., General buckling of stiffened circular cylindrical shells according to a layerwise theory, Comput. Struct., 49, 605-616, (1993) · Zbl 0797.73019 |

[24] | Sewall, J. L.; Clary, R. R.; Leadbetter, S. A., An experimental and analytical vibration study of a ring-stiffened cylindrical shell structure with various support conditions, (1964), NASA TN D-2398 |

[25] | Sewall, J. L.; Naumann, E. C., An experimental and analytical vibration study of thin cylindrical shells with and without longitudinal stiffeners, (1968), NASA technical note D-4705 |

[26] | Shen, H. S., Post-buckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and thermal loading, Int. J. Mech., 40, 339-355, (1998) · Zbl 0904.73019 |

[27] | Shen, H. S., Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments, Eng. Struct., 25, 487-497, (2003) |

[28] | Shen, H. S., Postbuckling of axially-loaded FGM hybrid cylindrical shells in thermal environments, Compos. Sci. Technol., 65, 1675-1690, (2005) |

[29] | Shen, H. S., Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium, Int. J. Mech. Sci., 51, 372-383, (2009) |

[30] | Shen, H. S., Torsional buckling and postbuckling of FGM cylindrical shells in thermal environments, Int. J. Non-Linear Mech., 44, 644-657, (2009) · Zbl 1203.74053 |

[31] | Shen, H. S.; Yang, J.; Kitipornchai, S., Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium, Eur. J. Mech. A/Solids, 29, 448-460, (2010) |

[32] | Sheng, G. G.; Wang, X., Thermomechanical vibration analysis of a functionally graded shell with flowing fluid, Eur. J. Mech. A/Solids, 27, 1075-1087, (2008) · Zbl 1151.74364 |

[33] | Sofiyev, A. H., Dynamic buckling of functionally graded cylindrical shells under non-periodic impulsive loading, Acta Mech., 165, 151-163, (2003) · Zbl 1064.74100 |

[34] | Sofiyev, A. H., The stability of functionally graded truncated conical shells subjected to aperiodic impulsive loading, Int. J. Solids Struct., 41, 3411-3424, (2004) · Zbl 1119.74431 |

[35] | Sofiyev, A. H.; Schnack, E., The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading, Eng. Struct., 26, 1321-1331, (2004) |

[36] | Sofiyev, A. H., The stability of compositionally graded ceramic-metal cylindrical shells under aperiodic axial impulsive loading, Compos. Struct., 69, 247-257, (2005) |

[37] | Sofiyev, A. H., The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure, Compos. Struct., 89, 356-366, (2009) |

[38] | Sofiyev, A. H.; Avcar, M.; Ozyigit, P.; Adigozel, S., The free vibration of non homogeneous truncated conical shells on a Winkler foundation, Int. J. Eng. Appl. Sci., 1, 34-41, (2009) |

[39] | Sofiyev, A. H., Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation, Mech. Res. Commun., 37, 539-544, (2010) · Zbl 1272.74209 |

[40] | Sofiyev, A. H., Non-linear buckling behavior of FGM truncated conical shells subjected to axial load, Int. J. Non-Linear Mech., 46, 711-719, (2011) |

[41] | Sofiyev, A. H., Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells, Int. J. Mech. Sci., 53, 753-761, (2011) |

[42] | Sofiyev, A. H., Thermal buckling of FGM shells resting on a two-parameter elastic foundation, Thin-Walled Struct., 49, 1304-1311, (2011) |

[43] | Sofiyev, A. H., The non-linear vibration of FGM truncated conical shells, Compos. Struct., 94, 2237-2245, (2012) |

[44] | Sofiyev, A. H.; Kuruoglu, N., Non-linear buckling of an FGM truncated conical shell surrounded by an elastic medium, Int. J. Pres. Ves. Pip., 107, 38-49, (2013) |

[45] | Volmir, A. S., Non-linear dynamics of plates and shells, (1972), Science Edition M. (in Russian) |

[46] | Zozulya, V. V.; Zhang, Ch, A high order theory for functionally graded axisymmetric cylindrical shells, Int. J. Mech. Sci., 60, 12-22, (2012) |

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