Free Vibration Analysis of Bidirectional Functionally Graded Conical/Cylindrical Shells and Annular Plates on Nonlinear Elastic Foundations, Based on a Unified Differential Transform Analytical Formulation
Subject Areas : EngineeringM Molla-Alipour 1 , M Shariyat 2 , M Shaban 3
1 - Department of Mechanical Engineering, University of Mazandaran, Babolsar , Iran
2 - Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
3 - Mechanical Engineering Department, Bu-Ali Sina University, Hamadan, Iran
Keywords:
Abstract :
[1] Qatu M.S., 2004, Vibration of Laminated Shells and Plates, San Diego, Elsevier.
[2] Reddy J.N., 2003, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Florida, CRC Press.
[3] Shen H-S., 2009, Functionally Graded Materials: Nonlinear Analysis of Plates and Shells, Taylor & Francis Group, LLC.
[4] Carrera E., Brischetto S., Nali P., 2011, Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis, John Wiley & Sons.
[5] Tornabene F., Fantuzzi N., 2014, Mechanics of Laminated Composite Doubly-Curved Shell Structures, Società Editrice Esculapio, Milan.
[6] Efraim E., Eisenberger M., 2007, Exact vibration analysis of variable thickness thick annular isotropic and FGM plates, Journal of Sound and Vibration 29: 720-738.
[7] Hosseini-Hashemi Sh., Fadaee M., Es’haghi M., 2010, A novel approach for in-plane/out-of-plane frequency analysis of functionally graded circular/annular plates, International Journal of Mechanical Sciences 52: 1025-1035.
[8] Nie G.J., Zhong Z., 2010, Dynamic analysis of multi-directional functionally graded annular plates, Applied Mathematical Modelling 34: 608-616.
[9] Malekzadeh P., Golbahar Haghighi M.R., Atashi M.M., 2011, Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment, Meccanica 46: 893-913.
[10] Jodaei A., Jalal M., Yas M.H., 2012, Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN, Composites Part B: Engineering 43: 340-353.
[11] Dong C.Y., 2008, Three-dimensional free vibration of functionally graded annular plates using the Chebyshev-Ritz method, Materials & Design 29: 1518-1525.
[12] Shariyat M., Alipour M.M., 2011, Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations, Archive of Applied Mechanics 81(9): 1289-1306.
[13] Alipour M.M., Shariyat M., 2011, A power series solution for free vibration of variable thickness Mindlin circular plates with two-directional material heterogeneity and elastic foundations, Journal of Solid Mechanics 3(2): 183-197.
[14] Alipour M.M., Shariyat M., 2010, Stress analysis of two-directional FGM moderately thick constrained circular plates with non-uniform load and substrate stiffness distributions, Journal of Solid Mechanics 2(4): 316-331.
[15] Shariyat M., Alipour M.M., 2013, A power series solution for vibration and complex modal stress analyses of variable thickness viscoelastic two-directional FGM circular plates on elastic foundations, Applied Mathematical Modelling 37(5): 3063-3076.
[16] Shariyat M., Alipour M.M., 2014, A novel shear correction factor for stress and modal analyses of annular FGM plates with non-uniform inclined tractions and non-uniform elastic foundations, International Journal of Mechanical Sciences 87: 60-71.
[17] Lezgy-Nazargah M., 2015, Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach, Aerospace Science and Technology 45: 154-164.
[18] Shariyat M., Jafari A.A., Alipour M.M., 2013, Investigation of the thickness variability and material heterogeneity effects on free vibration of the viscoelastic circular plates, Acta Mechanica Solida Sinica 26(1): 83-98.
[19] Alipour M.M., Shariyat M., Shaban M., 2010, A semi-analytical solution for free vibration and modal stress analyses of circular plates resting on two-parameter elastic foundations, Journal of Solid Mechanics 2(1): 63-78.
[20] Lezgy-Nazargah M., Cheraghi N., 2017, An exact Peano Series solution for bending analysis of imperfect layered FG neutral magneto-electro-elastic plates resting on elastic foundations, Mechanics of Advanced Materials and Structures 24(3): 183-199.
[21] Lezgy-Nazargah M., Meshkani Z., 2018, An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations, Structural Engineering and Mechanics 66(5): 665-676.
[22] Najafizadeh M.M., Isvandzibaei M.R., 2007, Vibration of functionally graded cylindrical shell based on higher order shear deformation plate theory with ring support, Acta Mechanica 191: 75-91.
[23] Matsunaga H., 2008, Free vibration and stability of functionally graded circular cylindrical shells according to a 2D higher-order deformation theory, Composite Structures 88: 519-531.
[24] Santos H., MotaSoares C.M., MotaSoares C.A., Reddy J.N., 2009, A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials. Composite Structures 91: 427-432.
[25] Zhao X., Lee Y.Y., Liew K.M., 2009, Thermoelastic and vibration analysis of functionally graded cylindrical shells, International Journal of Mechanical Sciences 51: 694-707.
[26] Vel S.S., 2010, Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells, Composite Structures 92: 2712-2727.
[27] Shen H.S., 2012, Nonlinear vibration of shear deformable FGM cylindrical shells surrounded by an elastic medium, Composite Structures 94: 1144-1154.
[28] Ebrahimi M.J., Najafizadeh M.M., 2014, Free vibration analysis of two-dimensional functionally graded cylindrical shells, Applied Mathematical Modelling 38: 308-324.
[29] Ng T.Y., He X.Q., Liew K.M., 2002, Finite element modeling of active control of functionally graded shells in frequency domain via piezoelectric sensors and actuators, Computational Mechanics 28: 1-9.
[30] Pradhan S.C., Loy C.T., Lam K.Y., Reddy J.N., 2000, Vibration characteristics of functionally graded cylindrical shells under various boundary conditions, Applied Acoustics 61:111-129.
[31] Viola E., Rossetti L., Fantuzzi N., 2012, Numerical investigation of functionally graded cylindrical shells panels using the generalized unconstrained third order theory coupled with the stress recovery, Composite Structures 94: 3736-3758.
[32] Bhangale R.K., Ganesan N., Chandramouli P., 2006, Linear thermoelastic buckling and free vibration behavior of functionally graded truncated conical shells, Journal of Sound and Vibration 292: 341-371.
[33] Tornabene F., 2009, Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution, Computer Methods in Applied Mechanics and Engineering 198: 2911-2935.
[34] Tornabene F., Viola E., Inman D.J., 2009, 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures, Journal of Sound and Vibration 328: 259-290.
[35] Qu Y.G., Long X.H., Yuan G.Q., Meng G., 2013, A unified formulation for vibration analysis of functionally graded shells of revolution with arbitrary boundary conditions, Composites Part B: Engineering 50: 381-402.
[36] Sofiyev A.H., 2009, The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure, Composite Structures 89: 356-366.
[37] Sofiyev A.H., 2011, On the vibration and stability of clamped FGM conical shells under external loads, Journal of Composite Materials 45: 771-788.
[38] Malekzadeh P., Fiouz A.R., Sobhrouyan M., 2012, Three-dimensional free vibration of functionally graded truncated conical shells subjected to thermal environment, International Journal of Pressure Vessels and Piping 89: 210-221.
[39] Sofiyev A.H., 2012, The non-linear vibration of FGM truncated conical shells, Composite Structures 94: 2237-2245.
[40] Najafov A.M., Sofiyev A.H., 2013, The non-linear dynamics of FGM truncated conical shells surrounded by an elastic medium, International Journal of Mechanical Sciences 66: 33-44.
[41] Malekzadeh P., Heydarpour Y., 2013, Free vibration analysis of rotating functionally graded truncated conical shells, Composite Structures 97: 176-188.
[42] Sofiyev A.H., 2014, On the dynamic buckling of truncated conical shells with functionally graded coatings subject to a time dependent axial load in the large deformation, Composites: Part B 58: 524-533.
[43] Sofiyev A.H., 2014, The combined influences of heterogeneity and elastic foundations on the nonlinear vibration of orthotropic truncated conical shells, Composites: Part B 61: 324-339.
[44] Xiang X., Guoyong J., Tiangui Y., Zhigang L., 2014, Free vibration analysis of functionally graded conical shells and annular plates using the Haar wavelet method, Applied Acoustics 85: 130-142.
[45] Zhu S., Guoyong J., Shuangxia Sh., Tiangui Y., Xingzhao J., 2014, A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions, International Journal of Mechanical Sciences 80: 62-80.
[46] Zhu S., Guoyong J., Tiangui Y., 2014, Three-dimensional vibration analysis of thick functionally graded conical, cylindrical shell and annular plate structures with arbitrary elastic restraints, Composite Structures 118: 432-447.
[47] Tornabene F., Fantuzzi N., Bacciocchi M., 2014, Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories, Composites: Part B 67: 490-509.
[48] Sofiyev A.H., Kuruoglu N., 2015, On a problem of the vibration of functionally graded conical shells with mixed boundary conditions, Composites: Part B 70: 122-130.