Version 1
: Received: 22 January 2021 / Approved: 25 January 2021 / Online: 25 January 2021 (14:09:44 CET)
Version 2
: Received: 15 September 2021 / Approved: 15 September 2021 / Online: 15 September 2021 (15:33:01 CEST)
Version 3
: Received: 6 October 2022 / Approved: 7 October 2022 / Online: 7 October 2022 (10:34:31 CEST)
How to cite:
Fogang, V. An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using a Moment-Shear Force-Circular Frequency-Curvature Relationship. Preprints2021, 2021010501. https://doi.org/10.20944/preprints202101.0501.v3
Fogang, V. An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using a Moment-Shear Force-Circular Frequency-Curvature Relationship. Preprints 2021, 2021010501. https://doi.org/10.20944/preprints202101.0501.v3
Fogang, V. An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using a Moment-Shear Force-Circular Frequency-Curvature Relationship. Preprints2021, 2021010501. https://doi.org/10.20944/preprints202101.0501.v3
APA Style
Fogang, V. (2022). <strong></strong>An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using a Moment-Shear Force-Circular Frequency-Curvature Relationship. Preprints. https://doi.org/10.20944/preprints202101.0501.v3
Chicago/Turabian Style
Fogang, V. 2022 "<strong></strong>An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using a Moment-Shear Force-Circular Frequency-Curvature Relationship" Preprints. https://doi.org/10.20944/preprints202101.0501.v3
Abstract
This study presents an exact solution to the free vibration analysis of a uniform Timoshenko beam, with a harmonic vibration being assumed. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. In this paper, a moment-shear force-circular frequency-curvature relationship was presented. The complete study was based on this relationship and closed-form expressions of efforts and deformations were derived. The free vibration response of single-span systems and spring-mass systems was analyzed; closed-form formulations of matrices expressing the boundary conditions were presented and the natural frequencies were determined by solving the eigenvalue problem. Systems with intermediate mass, spring, or spring-mass system were also analyzed. Furthermore, first-order dynamic stiffness matrices in local coordinates were derived. Finally, a second-order analysis of beams resting on an elastic Winkler foundation was conducted. The results obtained in this paper were in good agreement with those of other studies.
Keywords
Timoshenko beam; rotary inertia; moment shear force circular frequency curvature relationship; spring mass system; closed-form solutions; first-order dynamic stiffness matrix; second-order vibration analysis
Subject
Physical Sciences, Applied Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Valentin Fogang
Commenter's Conflict of Interests: Author
Abstract