On positiveness and contractiveness of the integral operator arising from the beam deflection problem on elastic foundation
Bull. Korean Math. Soc. 2015 Vol. 52, No. 4, 1225-1240
Printed July 31, 2015
Sung Woo Choi
Duksung Women's University
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
MSC numbers : Primary 34L15, 47G10, 74K10
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd