참고문헌
- Abu-Hilal, M. (2003), "Forced vibration of Euler-Bernoulli beams by means of dynamic Green functions", J. Sound Vibr., 267(2), 191-207. https://doi.org/10.1016/S0022-460X(03)00178-0
- Asghar, S., Zaman, F.D. and Ahmad, M. (1991), "Field due to a point source in a layer over an inhomogeneous medium", Nuovo Cim., 5, 569-573.
- Burlon, A., Failla, G. and Arena, F. (2016), "Exact frequency response analysis of axially loaded beams with viscoelastic dampers", Int. J. Mech. Sci., 115-116, 370-384.
- Duque, D. (2015), "A derivation of the beam equation", Eur. J. Phys., 37(1).
- Ebrahimi, F. and Barati, M.R. (2018), "Stability analysis of porous multi-phase nanocrystalline nonlocal beams based on a general higher-order couple-stress beam model", Struct. Eng. Mech., 65(4).
- Failla, G. (2016), "An exact generalized function approach to frequency response analysis of beams and plane frames with the inclusion of viscoelastic damping", J. Sound Vibr., 360, 171-202. https://doi.org/10.1016/j.jsv.2015.09.006
- Ghosh, M.L. (1970), "Love waves due to a point source in an inhomogeneous medium", Gerlands Beitr. Geophys., 79, 129-141.
- Graef, J.R., Henderson, J. and Yang, B. (2009), "Positive solutions to a fourth order three-point boundary value problem", Discret. Contin. Dyn. Syst., 269-275.
- Graef, J.R., Yang, B. and Yang, B. (1999), "On a nonlinear boundary value problem for fourth order equations", Appl. Anal., 72(3-4), 439-448. https://doi.org/10.1080/00036819908840751
- Gupta, C.P. (1988), "Existence and uniqueness theorems for the bending of an elastic beam equation", Appl. Anal., 26(4), 289-304. https://doi.org/10.1080/00036818808839715
- Han, S.M., Benaroya, H. and Wei, T. (1999), "Dynamics of transversely vibrating beams using four engineering theories", J. Sound Vibr., 225(5), 935-988. https://doi.org/10.1006/jsvi.1999.2257
- Huang, Y., Chen, C.H., Keer, L.M. and Yao, Y. (2017), "A general solution to structural performance of pre-twisted Euler beam subject to static load", Struct. Eng. Mech., 64(2).
- Kukla, S. and Zamojska, I. (2007), "Frequency analysis of axially loaded stepped beams by Green's function method", J. Sound Vibr., 300, 1034-1041. https://doi.org/10.1016/j.jsv.2006.07.047
- Li, X.Y., Zhao, X. and Li, Y.H. (2014), "Green's functions of the forced vibration of Timoshenko beams with damping effect", J. Sound Vibr., 333, 1781-1795. https://doi.org/10.1016/j.jsv.2013.11.007
- Lindell, I.V. and Olyslager, F. (2001), "Polynomial operators and green functions", Prog. Electromagn. Res., 30, 59-84. https://doi.org/10.2528/PIER00031305
- Logan, J.D. (2007), Pure and Applied Mathematics in An Introduction to Nonlinear Partial Differential Equations, 2nd Edition, Hoboken, John Wiley & Sons, New Jersey, U.S.A.
- Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., 59(3).
- Morrison, S.M. (2007), Application of the Green's Function for Solutions of Third Order Nonlinear Boundary Value Problems, Tennessee, Knoxville, U.S.A.
- Nejad, M.Z., Hadi, A. and Farajpour, A. (2017), "Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials", Struct. Eng. Mech., 63(2).
- Orucoglu, K. (2005), "A new green function concept for fourth-order differential equations", Electron. J. Differ. Equat., (28), 1-12.
- Pietramala, P. (2011), "A note on a beam equation with nonlinear boundary conditions", Bound. Value Probl., 1-14.
- Rizov, V.I. (2017), "Fracture analysis of functionally graded beams with considering material non-linearity", Struct. Eng. Mech., 64(4).
- Stakgold, I. and Holst, M.J. (2011), Green's Functions and Boundary Value Problems, John Wiley & Sons, New York, U.S.A.
- Stuwe, H.C. and Werner, P. (1996), "A Green's function approach to wave propagation and potential flow around obstacles in infinite cylindrical channels", Math. Meth. Appl. Sci., 19(8), 607-638. https://doi.org/10.1002/(SICI)1099-1476(19960525)19:8<607::AID-MMA785>3.0.CO;2-O
- Teterina, O.A. (2013), The Green's Function Method for Solutions of Fourth Order Nonlinear Boundary Value Problem, University of Tennessee, Knoxville, U.S.A.
- Truesdell, C. (1983), Rational Mechanics, Academic Press, New York, U.S.A.
- Webb, J.R.L., Infante, G. and Franco, D. (2008), "Positive solutions of nonlinear fourth-order boundaryvalue problems with local and non-local boundary conditions", Proceedings of the Royal Society of Edinburgh.
- Zaman, F.D., Asghar, S. and Ahmad, M. (1990), "Love-type waves due to a line source in an inhomogeneous layer trapped between two half spaces", Boll. Di Geofis. Teor. Ed Appl., XXXII(N), 127-128.
- Zaman, F.D. and Al-Zayer, R.M. (2004), "Dispersion of Love waves in a stochastic layer", Nuovo Cimento-Socista Ital. Di Fis. Sez., C(27), 143-154.
- Zaman, F.D., Masood, K. and Muhiameed, Z. (2006), "Inverse scattering in multilayer inverse problem in the presence of damping", Appl. Math. Comput., 176(2), 455-461. https://doi.org/10.1016/j.amc.2005.09.034