References
- F. W. Beaufait and P. W. Hoadley, Analysis of elastic beams on nonlinear foundations, Comput. Struct. 12 (1980), no. 5, 669-676. https://doi.org/10.1016/0045-7949(80)90168-6
- A. Cabada, J. Fialho, and F. Minhos, Extremal solutions to fourth order discontinuous functional boundary value problems, Math. Nachr. 286 (2013), no. 17-18, 1744-1751. https://doi.org/10.1002/mana.201100239
- S. W. Choi, On positiveness and contractiveness of the integral operator arising from the beam deflection problem on elastic foundation, Bull. Korean Math. Soc. 52 (2015), no. 4, 1225-1240. https://doi.org/10.4134/BKMS.2015.52.4.1225
- S. W. Choi, Spectral analysis of the integral operator arising from the beam deflection problem on elastic foundation II: eigenvalues, Bound. Value Probl. 2015 (2015), 6, 27 pp. https://doi.org/10.1186/s13661-014-0268-2
- S. W. Choi, Existence and uniqueness of finite beam deflection on nonlinear non-uniform elastic foundation with arbitrary well-posed boundary condition, Bound. Value Probl. 2020 (2020), Paper No. 113, 23 pp. https://doi.org/10.1186/s13661-020-01411-7
- S. W. Choi and T. S. Jang, Existence and uniqueness of nonlinear deflections of an infinite beam resting on a non-uniform nonlinear elastic foundation, Bound. Value Probl. 2012 (2012), 5, 24 pp. https://doi.org/10.1186/1687-2770-2012-5
- M. Galewski, On the nonlinear elastic simply supported beam equation, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 19 (2011), no. 1, 109-119.
- M. Hetenyi, Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, Mich., 1946.
- Y. H. Kuo and S. Y. Lee, Deflection of nonuniform beams resting on a nonlinear elastic foundation, Comput. Struct. 51 (1994), no. 5, 513-519. https://doi.org/10.1016/0045-7949(94)90058-2
- X. Ma, J. W. Butterworth, and G. C. Clifton, Static analysis of an infinite beam resting on a tensionless Pasternak foundation, Eur. J. Mech., A, Solids 28 (2009), no. 4, 697-703. https://doi.org/10.1016/j.euromechsol.2009.03.003
- C. Miranda and K. Nair, Finite beams on elastic foundation, ASCE. J. Struct. Div. 92 (1966), 131-142.
- I. Stakgold and M. Holst, Green's functions and boundary value problems, third edition, Pure and Applied Mathematics (Hoboken), John Wiley & Sons, Inc., Hoboken, NJ, 2011. https://doi.org/10.1002/9780470906538
- S. P. Timoshenko, History of strength of materials. With a brief account of the history of theory of elasticity and theory of structures, McGraw-Hill Book Company, Inc., New York, 1953.
- B. Y. Ting, Finite beams on elastic foundation with restraints, ASCE. J. Struct. Div. 108 (1982), 611-621. https://doi.org/10.1061/JSDEAG.0005906
- J. Valle, D. Fernandez, J. Madrenas, Closed-form equation for natural frequencies of beams under full range of axial loads modeled with a spring-mass system, Int. J. Mech. Sci. 153-154 (2019), 380-390. https://doi.org/10.1016/j.ijmecsci.2019.02.014