Stability of Heterogeneous Beams with Three Supports—Solutions Using Integral Equations

It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated wi...

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Bibliographic Details
Published in:Applied Mechanics 2023-03, Vol.4 (1), p.254-286
Main Authors: Kiss, László, Messaoudi, Abderrazek, Szeidl, György
Format: Article
Language:English
Subjects:
critical load
eigenvalue problem
Eigenvalues
Green function
heterogeneous beam
Integral equations
Investigations
Ordinary differential equations
stability
three point BVP
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Summary:It is our main objective to find the critical load for three beams with cross sectional heterogeneity. Each beam has three supports, of which the intermediate one is a spring support. Determination of the critical load for these beams leads to three point boundary value problems (BVPs) associated with homogeneous boundary conditions—the mentioned BVPs constitute three eigenvalue problems. They are solved by using a novel solution strategy based on the Green functions that belong to these BVPs: the eigenvalue problems established for the critical load are transformed into eigenvalue problems governed by homogeneous Fredholm integral equations with kernels that can be given in closed forms provided that the Green function of each BVP is known. Then the eigenvalue problems governed by the Fredholm integral equations can be manipulated into algebraic eigenvalue problems solved numerically by using effective algorithms. It is an advantage of the way we attack these problems that the formalism established and the results obtained remain valid for homogeneous beams as well. The numerical results for the critical forces can be applied to solve some stability problems in the engineering practice.
ISSN:2673-3161
2673-3161
DOI:10.3390/applmech4010015