Dynamics of heavy beams: Closed-form vibrations of gravity-loaded Rayleigh–Timoshenko columns

Bizzi, Arthur Augusto Coutinho; Fortaleza, Eugênio; Guenka, Tomé S.N.

doi:10.1016/j.jsv.2021.116259

Cited by 6 publications

(1 citation statement)

References 26 publications

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“…Both techniques yield the same results. An exact solution is provided for the mode-shape equation of self-weight loaded columns and cables in [3]. The mode shapes are given by a family of complex Hankel-Airy functions.…”

Section: Introductionmentioning

confidence: 99%

Vibration of an axially loaded heterogeneous fixed–fixed beam with an intermediate roller support

Kiss

Szeidl

Messaoudi

2022

J Braz. Soc. Mech. Sci. Eng.

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The present paper investigates how an axial load can change the natural frequencies of heterogeneous fixed–fixed beams with an intermediate roller support. The problem is treated as a three-point boundary value problem (eigenvalue problem) that is paired with homogeneous boundary conditions. The Green functions are determined for the unloaded and pre-loaded beams as well—in the later case, both for compression and tension. With these, the eigenvalue problems can be transformed into eigenvalue problems governed by a homogeneous Fredholm integral equations. It is then replaced by an algebraic eigenvalue problem, that is solved numerically with an effective solution algorithm which is based on the boundary element method.

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Section: Introductionmentioning

confidence: 99%

Vibration of an axially loaded heterogeneous fixed–fixed beam with an intermediate roller support

Kiss

Szeidl

Messaoudi

2022

J Braz. Soc. Mech. Sci. Eng.

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Green functions for three-point boundary value problems governed by differential equation systems with applications to Timoshenko beams

Kiss

Szeidl

2023

Acta Mech

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The present paper is devoted to the issue of the Green function matrices that belongs to some three-point boundary- and eigenvalue problems. A detailed definition is given for the Green function matrices provided that the considered boundary value problems are governed by a class of ordinary differential equation systems associated with homogeneous boundary and continuity conditions. The definition is a constructive one, i.e., it provides the means needed for calculating the Green function matrices. The fundamental properties of the Green function matrices—existence, symmetry properties, etc.—are also clarified. Making use of these Green functions, a class of three-point eigenvalue problems can be reduced to eigenvalue problems governed by homogeneous Fredholm integral equation systems. The applicability of the novel findings is demonstrated through a Timoshenko beam with three supports.

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Green functions for four-point boundary value problems with applications to heterogeneous beams

Messaoudi,

Kiss,

Szeidl

2024

Applications in Engineering Science

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Dynamics of heavy beams: Closed-form vibrations of gravity-loaded Rayleigh–Timoshenko columns

Cited by 6 publications

References 26 publications

Vibration of an axially loaded heterogeneous fixed–fixed beam with an intermediate roller support

Vibration of an axially loaded heterogeneous fixed–fixed beam with an intermediate roller support

Green functions for three-point boundary value problems governed by differential equation systems with applications to Timoshenko beams

Green functions for four-point boundary value problems with applications to heterogeneous beams

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