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

Title & Authors
ON POSITIVENESS AND CONTRACTIVENESS OF THE INTEGRAL OPERATOR ARISING FROM THE BEAM DEFLECTION PROBLEM ON ELASTIC FOUNDATION
CHOI, SUNG WOO;

Abstract
We provide a complete proof that there are no eigenvalues of the integral operator $\small{{\mathcal{K}}_l}$ outside the interval (0, 1/k). $\small{{\mathcal{K}}_l}$ 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;$\small{L^2}$-norm;
Language
English
Cited by
1.
Spectral analysis of the integral operator arising from the beam deflection problem on elastic foundation II: eigenvalues, Boundary Value Problems, 2015, 2015, 1
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