참고문헌
- Chai, Y.B., Gong, Z.X. and Li, W. and Zhang, Q. (2017), "A smoothed finite element method for exterior Helmholtz equation in two dimensions", Eng. Anal. Bound. Elem., 84, 237-252. https://doi.org/10.1016/j.enganabound.2017.09.006.
- Cheung, Y.K., Au, F. T.K. and Zheng, D.Y. (2000), "Finite strip method for the free vibration and buckling analysis of plates with abrupt changes in thickness and complex support conditions", Thin. Wall. Struct., 36, 89-110. https://doi.org/10.1016/S0263-8231(99)00044-0.
- Cheung, Y. K. and Zhou, D. (2000), "Vibrations of rectangular plates with elastic intermediate line -supports and edge constraints", Thin. Wall. Struct., 37, 305-331. https://doi.org/10.1016/S0263-8231(00)00015-X.
- Duan, G. H. and Wang, X. W. (2013), "Free vibration analysis of multiple-stepped beams by the discrete singular convolution", Appl. Math. Comput., 219, 11096-11109. https://doi.org/10.1016/j.amc.2013.05.023.
- Duan, G.H. and Wang, X.W. (2014), "Vibration analysis of stepped rectangular plates by the discrete singular convolution algorithm", Int. J. Mech. Sci., 82, 100-109. https://doi.org/10.1016/j.ijmecsci.2014.03.004.
- Duan, G.H., Wang, X.W. and Jin, C.H. (2014), "Free vibration analysis of circular thin plates with stepped thickness by the DSC element method", Thin Wall. Struct., 85, 25-33. https://doi.org/10.1016/j.tws.2014.07.010.
- Fornberg, B. (1998), "Calculation of weights in finite difference formulas", SIAM Rev., 40, 685-691. https://doi.org/10.1137/S0036144596322507.
- Gu, H. and Wang, X.W. (1997), "On the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method", J. Sound Vib., 202(3), 452-459. https://doi.org/10.1006/jsvi.1996.0813.
- Khezri, M., Bradford, M.A. and Vrcelj, Z. (2015), "Application of RKP-FSM in the buckling and free vibration analysis of thin plates with abrupt thickness changes and internal supports", Int.J. Numer. Meth. Engng., 104, 125-156. https://doi.org/10.1002/nme.4936.
- Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vib., 31, 257-293. https://doi.org/10.1016/S0022-460X(73)80371-2.
- Li, Q.S. (2003), "An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support", Int. J. Mech. Sic., 45, 669-685. https://doi.org/10.1016/S0020-7403(03)00110-3.
- Li, W., Song, Z.W. and Chai, Y.B. (2015), "Discrete singular convolution method for dynamic stability analysis of beams under periodic axial forces", J. Eng. Mech., 141, 04015033-1-13. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000931.
- Li ,W., Song ,Z.W., He ,X.Q. and Xie , D. (2020), "A comparison study of HO-CFD and DSC-RSK for solving some classes of boundary-value and eigenvalue problems", Int. J. Comput. Methods, 17(6), 1950011-1-47. https://doi.org/10.1142/S0219876219500117.
- Liu, F.L. and Liew, K.M. (1999), "Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities", Comput. Methods Appl. Mech. Eng., 179, 407-423. https://doi.org/10.1016/S0045-7825(99)00049-3.
- Lu, C.F., Lee, Y.Y., Lim, C.W. and Chen, W.Q. (2006), "Free vibration of long-span continuous rectangular Kirchhoff plates with internal rigid line supports", J. Sound Vib., 297, 351-364. https://doi.org/10.1016/j.jsv.2006.04.007.
- Mizusawa, T., Kajita, T. and Naruoka, M. (1980), "Vibration and buckling analysis of plates of abruptly varying stiffness", Comput. Struct., 12, 689-693. https://doi.org/10.1016/0045-7949(80)90170-4.
- Ng, C.H.W., Zhao, Y.B. and Wei, G.W. (2004), "Comparison of discrete singular convolution and generalized differential quadrature for the vibration of analysis of rectangular plates", Comput. Meth. Appl. Mech. Eng., 193, 2483-2506. https://doi.org/10.1016/j.cma.2004.01.013.
- Rajasekaran, S. (2013), "Buckling and vibration of stepped rectangular plates by element -based differential transform method", Civil Struct. Eng., 6(1), 51-64. https://doi.org/10.1080/19373260.2012.732399.
- Shu, C. (2000), Differential Quadrature and its Application in Engineering, Springer, London, UK.
- Singhatanadgid, P. and Taranajetsada, P. (2014), "Vibration analysis of stepped rectangular plates using the extended Kantorovich method", Mech. Adv. Mater. Struct., 23, 201-215. https://doi.org/10.1080/15376494.2014.949922.
- Song, Z.W., Chen, Z.G., Li, W. and Chai, Y.B. (2017), "Parametric instability analysis of a rotating shaft subjected to a periodic axial force by using discrete singular convolution method", Meccanica, 52, 1159-1173. https://doi.org/10.1007/s11012-016-0457-4.
- Song, Z. W., Li, W., He, X.Q. and Xie, D. (2019), "Free vibration analysis of beams with various interfaces by using a modified matched interface and boundary method", Struct. Eng. Mech., 72(1), 1-17. https://doi.org/10.12989/sem.2019.72.1.001.
- Wang, C, and Unal, A. (2013), "Free vibration of stepped thickness rectangular plates using spectral finite element method", J. Sound Vib., 332, 4324-4338. https://doi.org/10.1016/j.jsv.2013.03.008.
- Wang, B., Xia, K.L. and Wei, G.W. (2015), "Second order solving 3D elasticity equations with complex interfaces", J. Comput. Phys., 294, 405-438. https://doi.org/10.1016/j.jcp.2015.03.053.
- Wei, G. W., Zhao, Y. B. and Xiang, Y. (2002), "A novel approach for the analysis of high-frequency vibrations", J. Sound Vib., 257(2), 207-246. https://doi.org/10.1006/jsvi.2002.5055.
- Wu, F., Zeng, W.L., Yao, L.Y. and Liu, G. R. (2018) "A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner-Mindlin plates", Appl. Math. Model., 53, 333-352. https://doi.org/10.1016/j.apm.2017.09.005.
- Wu, T. Y. and Liu, G. R. (2001), "Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule", Int. J. Solids Struct., 38, 7967-7980. https://doi.org/10.1016/S0020-7683(01)00077-4.
- Wu, T. Y., Wang, Y. Y. and Liu, G. R. (2002), "Free vibration analysis of circular plates using generalized differential quadrature rule", Comput. Methods Appl. Mech. Eng., 191, 5365-5380. https://doi.org/10.1016/S0045-7825(02)00463-2.
- Xiang, Y. and Wang, C. M. (2002), "Exact buckling and vibration solutions for stepped rectangular plates", J. Sound Vib., 250(3), 503-517. https://doi.org/10.1006/jsvi.2001.3922.
- Xiang, Y., Zhao, Y. B. and Wei, G. W. (2002), "Levy solutions for vibration of multi-span rectangular plates", Int. J. Mech. Sci., 44, 1195-1218. https://doi.org/10.1016/S0020-7403(02)00027-9.
- Yu, S. N., Xiang, Y. and Wei, G. W. (2009), "Matched interface and boundary (MIB) method for the vibration analysis of plates", Commun. Numer. Mech. Engng., 25, 923-950. https://doi.org/10.1002/cnm.1130.
- Yu, S. N., Zhou, Y. C. and Wei, G. W. (2007), "Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces", J. Comput. Phys., 224, 729-756. https://doi.org/10.1016/j.jcp.2006.10.030.
- Zhao, S. and Wei, G. W. (2004), "High order FDTD methods via derivative matching for Maxwell's equations with material interfaces", J. Comput. Phys., 200, 60-103. https://doi.org/10.1016/j.jcp.2004.03.008.
- Zhao, S., Wei, G.W. and Xiang, Y. (2005), "DSC analysis of free-edged beams by an iteratively matched boundary method", J. Sound Vib., 284, 487-493. https://doi.org/10.1016/j.jsv.2004.08.037.
- Zhao, S. and Wei, G.W. (2009), "Matched interface and boundary (MIB) for the implementation of boundary conditions in high order central finite differences", Int. J. Numer. Meth. Engng., 77, 1690-1730. https://doi.org/10.1002/nme.2473.
- Zhou, Y.C. and Wei, G.W. (2006), "On the fictitious-domain and interpolation formulations of the matched interface and boundary (MIB) method", J. Comput. Phys., 219, 228-246. https://doi.org/10.1016/j.jcp.2006.03.027.
- Zhou, X. Q., Yu, D. Y. and Shao, X.Y., Wang, S. and Tian, Y.H. (2014), "Band gap characteristics of periodically stiffened - thin-plate based on center finite difference method", Thin. Wall. Struct., 82,115-123. https://doi.org/10.1016/j.tws.2014.04.010.
- Zhou, Y.C., Zhao, S., Feig, M. and Wei, G.W. (2006), "High order matched interface and boundary (MIB) schemes for elliptic equations with discontinuous coefficients and singular sources", J. Comput. Phys., 213, 1-30. https://doi.org/10.1016/j.jcp.2005.07.022.
- Zienkiewicz, O.C. and Taylor, R.L. (1989), The Finite Element Method, McGraw-Hill, New York, USA.