1 |
Buchanan, G.R. and Rich, B.S. (2002), "Effect of boundary conditions on free vibration of thick isotropic spherical shells", J. Vib. Control, 8, 389-403.
DOI
|
2 |
Chang, Y.C. and Demkowicz, L. (1995), "Vibrations of a spherical shell: comparison of 3D elasticity and Kirchhoff shell theory", Comput. Assi. Mech. Eng. Sci., 2(3), 187-206.
|
3 |
Chree, C. (1889), "The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solutions and application", Tran. Cambrid. Phil. Soc. Math. Phys. Sci., 14, 250-269.
|
4 |
Cohen, H. and Shah, A.H. (1972), "Free vibrations of a spherically isotropic hollow sphere", Acustica, 26, 329-340.
|
5 |
Ding, H. and Chen, W. (1996), "Nonaxisymmetric free vibrations of a spherically isotropic spherical shell embedded in an elastic medium", Int. J. Solid. Struct., 33 (18), 2575-2590.
DOI
|
6 |
Fadaee, M., Atashipour, S.R. and Hosseini-Hashemi, S. (2013), "Free vibration analysis of Levy-type functionally graded spherical shell panel using a new exact closed-form solution", Int. J. Mech. Sci., 77, 227-238.
DOI
|
7 |
Fazzolari, F.A. (2014), "A refined dynamic stiffness element for free vibration analysis of cross-ply laminated composite cylindrical and spherical shallow shells", Compos. PartB: Eng., 62, 143-158.
DOI
|
8 |
Ghavanloo, E and Fazelzadeh, S.A. (2013), "Nonlocal elasticity theory for radial vibration of nanoscale spherical shells", Eur. J. Mech. A Solid., 41, 37-42.
DOI
|
9 |
Grigorenko, Y.M. and Kilina, T.N. (1990), "Analysis of the frequencies and modes of natural vibration of laminated hollow sphere in two- and three-dimensional formulations", Soviet Appl. Mech., 25(12), 1165-1171.
DOI
|
10 |
Jaerisch, P. (1880), Journal of Mathematics (Crelle) Bd. 88.
|
11 |
Jiang, H., Young, P.G. and Dickinson, S.M. (1996), "Natural frequencies of vibration of layered hollow spheres using exact three-dimensional elasticity equations", J. Sound Vib., 195 (1), 155-162.
DOI
|
12 |
Kang, J.H. (2012), "Vibrations of hemi-spherical shells of revolution with eccentricity from a threedimensional theory", J. Vib. Control, 18(13), 2017-2030.
DOI
|
13 |
Lamb, H. (1882), Proceedings, London Mathematical Society, 13, 189-212.
|
14 |
Kang, J.H. (2013), "Vibration analysis of hemispherical shells of revolution having variable thickness with and without axial conical holes from a three-dimensional theory", J. Eng. Mech., 139(7), 925-927.
DOI
|
15 |
Kang, J.H. and Leissa, A.W. (2004), "Three-dimensional vibration analysis of solid and hollow hemispheres having varying thickness with and without axial conical holes", J. Vib. Control, 10(2), 199-214.
DOI
|
16 |
Kantorovich, L.V. and Krylov, V.I. (1958), Approximate Methods of Higher Analysis, Noordhoff, Groningen.
|
17 |
McGee, O.G. and Leissa, A.W. (1991), "Three-dimensional free vibrations of thick skewed cantilever plates", J. Sound Vib., 144, 305-322.
DOI
|
18 |
McGee, O.G. and Spry, S.C. (1997), "A three-dimensional analysis of the spheroidal and toroidal elastic vibrations of thick-walled spherical bodies of revolution", Int. J. Numer. Meth. Eng., 40, 1359-1382.
DOI
|
19 |
Panda, S.K. and Singh, B.N. (2009), "Nonlinear free vibration of spherical shell panel using higher order shear deformation theory-A finite element approach", Int. J. Press. Ves. Pip., 86(6), 373-383.
DOI
|
20 |
Poisson, S.D. (1829), "Memoire sur l'equilibre et le mouvement des corps elastiques", Memoires de t'Academie des Sciences, Paris, 8.
|
21 |
Qatu, M.S. (2002), "Recent research advances in the dynamic behavior of shells: 1989-2000, part 2: homogeneous shells", Appl. Mech. Rev., 55, 415-34.
DOI
|
22 |
Sahoo, S. (2014) "Laminated composite stiffened shallow spherical panels with cutouts under free vibration-A finite element approach", Eng. Sci. Tech., 17(4), 247-259.
|
23 |
Su, Z., Jin, G., Shi, S. and Ye, T. (2014), "A unified accurate solution for vibration analysis of arbitrary functionally graded spherical shell segments with general end restraints", Compos. Struct., 111, 271-284.
DOI
|
24 |
Sato, Y. and Usami, T. (1962), "Basic study on the oscillation of a homogeneous elastic sphere. Part II: Distribution of displacement", Geoph. Mag., 31, 25-47.
|
25 |
Shah, A.H., Ramkrishnan, C.V. and Datta, S.K. (1969), "Three-dimensional and shell theory analysis of elastic waves in a hollow sphere", J. Appl. Mech., 36, 431-444.
DOI
|
26 |
Sokolnikoff, I.S. (1956), Mathematical Theory of Elasticity, 2nd Edition, McGraw-Hill Book Co., New York.
|
27 |
Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: The free vibration analysis", Compos. Struct., 116, 637-660.
DOI
|
28 |
Ye, T., Jin, G. and Su, Z. (2014), "Three-dimensional vibration analysis of laminated functionally graded spherical shells with general boundary conditions", Compos. Struct., 116, 571-588.
DOI
|