Transverse Motions of Bernoulli-euler Beam Resting on Elastic Foundation and under Two Concentrated Moving Loads

Main Article Content

A. Adedowole

Abstract

Aims/Objectives: The aim is to obtain a closed form solutions of single-dimensional structural element of continuously supported by an elastic foundation. Thereafter, we classify the effects of the space d connecting the loads on the relevant partial differential equations governing the motion of the structural members. The study also analysis circumstances under which resonance occur in the dynamical systems involving structural members.

Study Design: The single-dimensional structural element is a partial differential equation of order fourth order place on elastic Winkler foundation. The Bernoulli-Euler beam traversed by two moving loads.

Place and Duration of Study: Department of Mathematical Sciences, Adekunle Ajasin University P.M.B. 01, Akungba-Akoko, Nigeria, between May 2019 and September 2019.

Methodology: The principal equation of the single -dimensional beam model is governing by partial differential equation of the order four. For the single -dimensional beam problem, the solution techniques are based on the Fourier sine transformation. The governing partial differential equation of the order four was reduced to sequence of second order ordinary differential equations.

Keywords:
Beam, elastic foundation, prestressed, concentrated loads, harmonic load.

Article Details

How to Cite
Adedowole, A. (2020). Transverse Motions of Bernoulli-euler Beam Resting on Elastic Foundation and under Two Concentrated Moving Loads. Journal of Advances in Mathematics and Computer Science, 34(6), 1-21. https://doi.org/10.9734/jamcs/2019/v34i630228
Section
Original Research Article

References

Kenny J. Steady state vibrations of a beam on an elastic foundation for a moving load. Journal of Applied Mechanics. 1954;76:359-364.
Available:https://www.worldscientific.com/doi/abs/10.1142/S0219455415500066

Stanisic MM, Hardin JC, Lou YC. On the response of the plate to a multi-masses moving system. Acta Mechanical. 1968;5:37-53.
Available:https://www.researchgate.net/publication/244996692

Oni ST. Response of non-uniform beam resting on an elastic foundation to several moving masses. Abacus Journal of Mathematical Association of Nigeria. 1996;24(2):72–88.
Available:https://www.academia.edu/35129217

Ozkaya E. Non-linear transverse vibration of a simply supported beam carrying concentrated masses. J Sound Vib. 2002;257(3):413–424.
Available:https://doi.org/10.1006/jsvi.2002.5042

Dasa SK, Rayb PC, Pohit G. Free vibration analysis of a rotating beam with non-linear spring and mass system. J. Sound Vib. 2007;301:165–188.
Available:https://www.researchgate.net/publication/223278948_Free_Vibration_Analysis_Of_A_
Rotating_Beam_With_Non-Linear_Spring_And_Mass_System

Lin HY, Tsai YC. Free vibration analysis of a uniform multi-span carrying multiple spring-mass systems. J Sound Vib. 2007;302:442–456.
Available:https://doi.org/10.1016/j.jsv.2006.06.080

Oni ST, Adedowole A. Influence of prestress on the response to moving loads of rectangular plates incorporating rotatory inertia correction factor. Journal of the Nigerian Association of Mathematical Physics. 2008;13:127-140.
Available:http://e.nampjournals.org/product-info.php%3Fpid718.html

Yusuf Yesilce, Oktay Demirdag, Seval Catal. Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems. Sadhana. 2008;33(4):385–401.
Available:https://www.mendeley.com/catalogue/free-vibration-piles-embedded-soil-having-different-modulus-
subgrade-reaction/

Hosking RJ, Husain SA, Milinazzo F. Natural flexural vibrations of a continuous beam on discrete elastic supports. Journal of Sound and Vibration. 2004;272(1-2):169-185.
Available:https://www.hindawi.com/journals/mpe/2014/840937/ref/

Yesilce Y, Catal HH. Free vibration of piles embedded in soil having different modulus of subgrade reaction. Appl. Math. Modelling. 2008;32:889–900.
Available:https://www.mendeley.com/catalogue/free-vibration-piles-embedded-soil-having-different-modulus-
subgrade-reaction/

Oni ST, Ogunyebi SN. Dynamical analysis of finite prestressed Bernoulli-Euler beams with general boundary conditions under travelling distributed loads. Journal of the Nigerian Association of Mathematical Physics. 2008;12:87-102.
Available:https://www.ajol.info/index.php/jonamp/article/view/45492

Jimoh SA. Analysis of non-uniformly prestressed tapered beams with exponentially varying thickness resting on Vlasov foundation under variable harmonic load moving with constant velocity. International Journal of Advanced Research and Publications. 2017;1(5):135-142.
Available:www.ijarp.org/published-research-papers/nov2017/Analysis-Of-Non-uniformly-Prestressed-Tapered Beams-With-Exponentially-Varying-
Thickness-Resting-On-Vlasov-Foundation-Under-Variable-Harmonic-Load

Jafarzadeh Jazi A, Shahriari B, Torabi K. Exact closed form solution for the analysis of the transverse vibration mode of a nano-Timoshenko beam with multiple concentrated masses. Int J Mech Sci. 2017;131–132:728–743.
Available:https ://doi.org/10.1016/j.ijmecsci.2017.08.023

Bakhshi Kaniki H. Vibration analysis of rotating nanobeam systems using Eringen’s two-phase local/nonlocal model. Phys E. 2018;92:310–319.
Available:https://doi.org/10.1016/j.physe .2018.02.008

Malesela KM, Sarp A. Fundamental frequencies of a torsional cantilever nano beam for dynamic atomic force microscopy (DAFM) in tapping mode. Microsystem Technologies. 2019;25:1087–1098.
Available:https://doi.org/10.1007/s00542-018-4166-x

Omolofe B, Adedowole A. Transverse response of a structural member with time dependent boundary conditions to moving distributed mass. Journal of Applied Nonlinear Dynamics. 2019;8(2):167-187.
Available:https://lhscientificpublishing.com/Journals/JAND-Default.aspx

Jimoh A, Ajoge EO. Exponentially varying load on Rayleigh beam resting on Pasternak foundation. Journal of Advances in Mathematics. 2019;16:8449-8458.
Available:https://rajpub.com/index.php/jam, https://doi.org/10.24297/jam.v16i0.8219

Alireza P, Keivan T, Hassan A. free vibration analysis of a rotating non‑uniform nanocantilever carrying arbitrary concentrated masses based on the nonlocal Timoshenko beam using DQEM. INAE Letters. 2019;4:45–58.
Available:https://doi.org/10.1007/s41403-019-00065-x