[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2015.52.4.1225

ON POSITIVENESS AND CONTRACTIVENESS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION

CHOI, SUNG WOO (DEPARTMENT OF MATHEMATICS DUKSUNG WOMEN'S UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.52, no.4, 2015 , pp. 1225-1240 More about this Journal

Abstract

We provide a complete proof that there are no eigenvalues of the integral operator ${\mathcal{K}}_l$ outside the interval (0, 1/k). ${\mathcal{K}}_l$ arises naturally from the deflection problem of a beam with length 2l resting horizontally on an elastic foundation with spring constant k, while some vertical load is applied to the beam.

Keywords

beam; deflection; elastic foundation; integral operator; eigenvalue; $L^2$ -norm;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

1	E. Alves, E. A. de Toledo, L. A. P. Gomes, and M. B. de Souza Cortes, A note on iterative solutions for a nonlinear fourth order ode, Bol. Soc. Parana. Mat. (3) 27 (2009), no. 1, 15-20.
2	F. W. Beaufait and P. W. Hoadley, Analysis of elastic beams on nonlinear foundations, Comput. Struct. 12 (1980), 669-676. DOI ScienceOn
3	S. W. Choi, Spectral analysis of the integral operator arising from the beam deflection problem on elastic foundation I: positiveness and contractiveness, J. Appl. Math. Inform. 30 (2012), no. 1-2, 27-47. DOI
4	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), no. 6, 27pp. DOI
5	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), no. 5, 24 pp. DOI ScienceOn
6	M. Galewski, On the nonlinear elastic simply supported beam equation, An. Stiint. Univ. "Ovidius" Constanta Ser. Mat. 19 (2011), no. 1, 109-119.
7	M. D. Greenberg, Foundations of Applied Mathematics, Prentice-Hall Inc., 1978.
8	M. R. Grossinho and A. I. Santos, Solvability of an elastic beam equation in presence of a sign-type Nagumo control, Nonlinear Stud. 18 (2011), no. 2, 279-291.
9	M. Hetenyi, Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, Mich., 1946.
10	Y. H. Kuo and S. Y. Lee, Deflection of non-uniform beams resting on a nonlinear elastic foundation, Comput. Struct. 51 (1994), 513-519. DOI ScienceOn
11	C. Miranda and K. Nair, Finite beams on elastic foundation, ASCE. I. Struct. Div. 92 (1966), 131-142.
12	S. P. Timoshenko, Statistical and dynamical stress in rails, Proceedings of the International Congress on Applied Mechanics (Zurich), 407-418, 1926.
13	S. P. Timoshenko, Strength of Materials: part 1 & part 2, 3rd ed., Van Nostrand, Princeton, NJ, 1955.
14	B. Y. Ting, Finite beams on elastic foundation with restraints, ASCE. J. Struct. Div. 108 (1982), 611-621.