[1] Timoshenko, S. and Woinowsky-Krieger, S. Theory of Plates and Shells, McGraw-Hill Book Company, Inc., New York (1959)
[2] Leissa, A. W. Vibration of Plates, NASA SP-169, Washington (1969)
[3] Irie, T., Yamada, G., and Aomura, S. Natural Frequencies of Mindlin circular plates. Journal of Applied Mechanics-Transactions of the ASME, 47, 652-655(1980)
[4] Liew, K. M., Han, J. B., and Xiao, Z. M. Vibration analysis of circular Mindlin plates using the differential quadrature method. Journal of Sound and Vibration, 205, 617-630(1997)
[5] Ding, H. J., Xu, R. Q., Chi, Y. W., and Chen, W. Q. Free axisymmetric vibration of transversely isotropic piezoelectric circular plates. International Journal of Solids and Structures, 36, 4629-4652(1999)
[6] Wang, Y., Xu, R. Q., and Ding, H. J. Free axisymmetric vibration of FGM circular plates. Applied Mathematics and Mechanics (English Edition), 30(9), 1077-1082(2009) DOI 10.1007/s10483-009-0901-x
[7] Nie, G. J. and Zhong, Z. Semi-analytical solutions for three-dimensional vibration of functionally graded circular plates. Computer Methods in Applied Mechanics and Engineering, 196, 4901-4910(2007)
[8] Ma, L. S. and Wang, T. J. Analytical relations between eigenvalues of circular plate based on various plate theories. Applied Mathematics and Mechanics (English Edition), 27(3), 279-286(2006) DOI 10.1007/s10483-006-0301-1
[9] Reddy, J. N., Wang, C. M., and Kitipornchai, S. Axisymmetric bending of functionally graded circular and annular plates. European Journal of Mechanics A-Solids, 18, 185-199(1999)
[10] Li, X. Y., Ding, H. J., and Chen, W. Q. Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk. International Journal of Solids and Structures, 45, 191-210(2008)
[11] Wang, Y. Z., Chen, W. Q., and Li, X. Y. Statics of FGM circular plate with magneto-electroelastic coupling:axisymmetric solutions and their relations with those for corresponding rectangular beam. Applied Mathematics and Mechanics (English Edition), 36(5), 581-598(2015) DOI 10.1007/s10483-015-1934-7
[12] Conway, H. D. Some special solutions for the flexural vibration of disks of varying thickness. Archive of Applied Mechanics, 26, 408-410(1958)
[13] Conway, H. D., Becker, E. C. H., and Dubil, J. F. Vibration frequencies of tapered bars and circular plates. Journal of Applied Mechanics, 31, 329-331(1964)
[14] Lenox, T. A. and Conway, H. D. An exact, closed form, solution for the flexural vibration of a thin annular plate having a parabolic thickness variation. Journal of Sound and Vibration, 68, 231-239(1980)
[15] Harris, G. Z. The normal modes of a circular plate of variable thickness. The Quarterly Journal of Mechanics and Applied Mathematics, 21, 321-327(1968)
[16] Prasad, C., Jain, R. K., and Soni, S. R. Axisymmetric vibrations of circular plates of linearly varying thickness. Journal of Applied Mathematics and Physics, 23, 941-948(1972)
[17] Elishakoff, I. and Storch, J. A. An unusual exact, closed-form solution for axisymmetric vibration of inhomogeneous simply supported circular plates. Journal of Sound and Vibration, 284, 1217-1228(2005)
[18] Elishakoff, I. Eigenvalues of Inhomogeneous Structures:Unusual Closed-Form Solutions, CRC Press, Boca Raton (2005)
[19] Wang, J. Generalized power series solutions of the vibration of classical circular plates with variable thickness. Journal of Sound and Vibration, 202, 593-599(1997)
[20] Duan, W. H., Quek, S. T., and Wang, Q. Generalized hypergeometric function solutions for transverse vibration of a class of non-uniform annular plates. Journal of Sound and Vibration, 287, 785-807(2005)
[21] Caruntu, D. I. Classical Jacobi polynomials, closed-form solutions for transverse vibrations. Journal of Sound and Vibration, 306, 467-494(2007)
[22] Deresiewicz, H., and Mindlin, R. D. Axially symmetric flexural vibrations of a circular disk. Journal of Applied Mechanics, 49, 633-638(1955)
[23] Mindlin, R. D. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics, 18, 31-38(1951)
[24] Xiang, Y. and Zhang, L. Free vibration analysis of stepped circular Mindlin plates. Journal of Sound and Vibration, 280, 633-655(2005)
[25] Yuan, J. H., Pao, Y. H., and Chen, W. Q. Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section. Acta Mechanica, 227, 2625-2643(2016)
[26] Von Kármán, T. and Biot, M. A. Mathematical Methods in Engineering, McGraw-Hill Book Company, Inc., New York (1940)
[27] Gradshteyn, I. S. and Ryzhik, I. M. Table of Integrals, Series, and Products, Elsevier, Singapore (2007)
[28] Gupta, U. S., Lal, R., and Sharma, S. Vibration of non-homogeneous circular Mindlin plates with variable thickness. Journal of Sound and Vibration, 302, 1-17(2007)
[29] Ronveaux, A. Heun's Differential Equations, Oxford University Press, Oxford (1995)
[30] Slavyanov, S. Y. and Lay, W. Special Functions:A Unified Theory Based on Singularities, Oxford University Press, Oxford (2000)
[31] Fiziev, P. P. Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order. Journal of Physics A-Mathematical and Theoretical, 43, 035203(2010)
[32] Hortacsu, M. Heun functions and their uses in Physics. Proceedings of the 13th Regional Conference on Mathematical Physics, Antalya (2010)
[33] Morgan, E. F., Bayraktar, H. H., and Keaveny, T. M. Trabecular bone modulus-density relationships depend on anatomic site. Journal of Biomechanics, 36, 897-904(2003)
[34] Woignier, T., Reynes, J., Alaoui, A. H., Beurroies, I., and Phalippou, J. Different kinds of structure in aerogels:relationships with the mechanical properties. Journal of Non-Crystalline Solids, 241, 45-52(1998)
[35] Pabst, W., Gregorová, E., and Tichá, G. Elasticity of porous ceramics-a critical study of modulus-porosity relations. Journal of the European Ceramic Society, 26, 1085-1097(2006)
[36] Roberts, A. P. and Garboczi, E. J. Elastic moduli of model random three-dimensional closed-cell cellular solids. Acta Materialia, 49, 189-197(2001)