 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| Adara E.O. and Omolofe B., "Dynamic Analysis of Bernoulli-Euler Beams under Compressive Axial Force and Traversed by Masses Travelling at Varying Velocity," Mech. Solids. 57 (1), 178-192 (2022) |
| Year |
2022 |
Volume |
57 |
Number |
1 |
Pages |
178-192 |
| DOI |
10.3103/S0025654422010071 |
| Title |
Dynamic Analysis of Bernoulli-Euler Beams under Compressive Axial Force and Traversed by Masses Travelling at Varying Velocity |
| Author(s) |
Adara E.O. (Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA, eoadara@crimson.ua.edu)
Omolofe B. (Department of Mathematical Sciences,The Federal University of Technology, P.M.B.704, Akure, Ondo State, Nigeria, bomolofe@futa.edu.ng) |
| Abstract |
This paper investigates the vibration characteristics of a beam under compressive axial force and accelerating point-like mass. The problem is prescribed by a partial differential equation of order four with singular and variable coefficients. This study proposes a procedure for obtaining an approximate analytical solutions to this beam-load complex interactions problem. The solution technique involved a versatile technique popularly known as Galerkin's Method which is used to transform the equation of motion to a system of second order ordinary differential equations. This is followed by the application of an asymptotic method due to Struble to simplify the resulting system of equations called Galerkin's equations. Duhamel Integral Transform (also known as Impulse Response Function) is finally used to obtain solutions representing the response of this structural member to accelerating loads. Dynamic characteristics exhibited by the beam-mass system are extensively investigated and effects of various structural parameters of interests are scrutinized. It is discovered that incorporating these parameters sufficiently into the governing equation of motion of the beam-load system enhances the dynamic stability of a beam subjected to a compressive axial force and accelerating masses. It is also found that as the travelling velocity of the moving mass increases, the response amplitude of the vibrating uniform beam increases and also the amplitude of vibration of the beam decreases as the span length increases. |
| Keywords |
beam-mass system, response characteristics, simply supported, moving load, Duhamel’s integral, Galerkin's method |
| Received |
10 May 2021 | Revised |
24 August 2021 | Accepted |
22 September 2021 |
| Link to Fulltext |
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