An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using an Analytical Approach

Valentin Fogang

doi:10.20944/preprints202101.0501.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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)

This study presents an analytical solution to the free vibration analysis of a uniform Timoshenko beam. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. A material law combining bending, shear, curvature, and natural frequency is presented. This complete study is based on this material law and closed-form solutions are found. The free vibration response of single-span systems, as well as that of spring-mass systems, is analyzed. Closed-form formulations of matrices expressing the boundary conditions are presented; the natural frequencies are determined by solving the eigenvalue problem. First-order dynamic stiffness matrices in local coordinates are determined. Finally, second-order analysis of beams resting on an elastic Winkler foundation is conducted.

Timoshenko beam; rotary inertia; bending shear curvature natural frequency relationship; spring mass system vibration; closed-form solutions; first-order dynamic stiffness matrix; second-order vibration analysis

ENGINEERING, Automotive Engineering

Your full name

Your affiliation information (e.g., name of your university/institution/organization)

Not displayed online.

Your Email address (not made public)

Please leave your comment to this article below.

Mathematical equations can be typed in either LaTeX formats \\[ ... \\] or $$ ... $$, or MathML format <math> ... </math>. Try the LaTeX or MathML example.

Type equation:

Preview:

Copy equation into message below

Close menu

Please click a symbol to insert it into the message box below:

Please enter the link here:

Optionally, you can enter text that should appear as linked text:

Copy link into message below

Close menu

Please enter or paste the URL to the image here (please only use links to jpg/jpeg, png and gif images):

Copy image into message below

Close menu

Type author name or keywords to filter the list of references in this group (you can add a new citation under Bibliography):

No existing citations in Discussion Group

Wikify editor is a simple editor for wiki-style mark-up. It was written by MDPI for Sciforum in 2014. The rendering of the mark-up is based on Wiky.php with some tweaks. Rendering of mathematical equations is done with MathJax. Please send us a message for support or for reporting bugs.

Close menu

Please declare any conflicts of interest you may have with this paper, financial or otherwise.

I do not have a conflict of interest

I would like to declare a conflict of interest

Display my name on the website I want to get recognition for my comment on Publons

[what’s this?]. Link your accounts here

Captcha

Renew

I accept the following conditions:

Comments must follow the standards of professional discourse and should focus on the scientific content of the article. Insulting or offensive language, personal attacks and off-topic remarks will not be permitted. Comments must be written in English. Preprints reserves the right to remove comments without notice. Readers who post comments are obliged to declare any competing interests, financial or otherwise.

Notify me about updates to this article or when a peer-reviewed version is published.

Upload a Image(max file size 2MB)

An Exact Solution to the Free Vibration Analysis of a Uniform Timoshenko Beam Using an Analytical Approach

Abstract

Keywords

Subject

Comments (0)