magazinelogo

Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 163992 Total View: 1912643
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
Email: jamc@hillpublisher.com
Article Open Access http://dx.doi.org/10.26855/jamc.2018.08.004

Dynamic Response of Non-Uniform Rayleigh Beam Subjected to Harmonically Varying Moving Load

Jimoh, A.1,*, Ajoge, E. O.2

1Department of Mathematical Sciences Kogi State University, Anyigba, Nigeria 

2Centre for Energy Research and Development Obafemi Awolowo University, Ile-Ife, Nigeria

*Corresponding author: Jimoh, A.

Published: August 27,2018

Abstract

This paper investigates the effect of axial force and rotatory inertial on the dynamic motion of non-uniform Rayleigh beam resting on Pasternak foundation transverseby harmonically varying magnitude moving loads. The versatile Galerkin’smethod and the integral transform techniques were employed to treat the fourth order partial differential equation governing the motion of the vibrating system. Analytical solution was obtained for the transverse displacement response of the non-uniform Rayleigh beam. Analytical and numerical results show that as the values of axial force (N) and rotatory inertial ( ) increases the deflection profile of the non-uniform Rayleigh beam decreases. It is also found that as the values of the other structural parameter such as shear module (G), foundation modulus (K) and damping coefficient ( ) increases lead to decreases in the deflection profile of the beam. Finally, it is observed that the effect of rotatory inertia is significant compared to that of the axial force.

References

[1] A.N Krylor: Mathematic collection of papers of the Academy of Sciences, Vol. 61, Piterburg 1905. 

[2] S. Timoshenko: On the Correction for shear of the differential equation for transverse vibration of prismatic bars, Phil Mag. S. 6 Vol. 41. PP. 744-776, 1921 

[3] J. Kenny: Steady state vibrations of a beam on an elastic foundation for a moving load. J. Appl. Mech. Vol. pp 359 -364, 1954. 

[4] S.T Oni and B. Omolofe: Dynamic Analysis of a Prestressed elastic beam with general boundary condition under moving loads at varying velocities. Journal of Engineering & Technology, FUTA. Vol. 4 No. 1 pp 55 – 72, 2005. 

[5] S.T. Oni and T. Awodola: Dynamic Response to moving concentrated masses of uniform Rayleigh beams resting on variable winkler elastic foundation. Journal of the Nigerian Association of Mathematical Physics. Vol. 9, pp 151 – 162, 2005. 

[6] B. Omolofe, S. T. Oni and J. M. Tolorunshagba: On the transverse motions of non-prismatic deep beam under the actions of variable magnitude moving loads. Latin American Journal of Solid and Structures. Vol 6 pp 153 – 167, 2009. 

[7] R. R Misra: Free vibration analysis of isotrophical plate using multi-quadric radial basis function. International of Science, Environment and Technology. Vol. 1 (2), pp 99 – 107 2012. 

[8] M.H HSU: Vibration analysis of non-uniform beam resting on elastic foundation using the sine collocation method. Tankang Journal of Science and Engineering. Vol. 12 (2), pp 113 -122, 2009 

[9] M. F. Liu and T. P. Chang: Closed from expression for the vibration problem of a transversely isotropic magneto -electro elastic plate. Journal of Applied Mechanic Transactions of the ASME. Vol. 77 (2) pp 025502-1-0245-2-8. 

[10] K. Achawakorn and T. Jearsin-Pongjul: Vibration analsyis of exponential cross-section beam using Galerkkin’s method. International Journal of Applied Sciences and Technology. Vol. 2 (6), 2010 

[11] A. D. Kerr: Elastic and visco-elastic foundation models. Journal of Applied Mechanics 86, pp, 491-49, 1964 

[12] G. L. Anderson: The influence of a weghardt type elastic foundation on a stability of some beams subjected to distributed tangential forces. Journal of Sound and Vibrations, 44 (1), pp 103 = 118, 1976. 

[13] A. Jimoh and E. O. Ajoge: Influence of damping coefficient and rotatory inertia on the dynamic response to moving load of non-uniform Rayleigh beam. International Journal of Science, Engineering and Technology. pp 139 – 149, 2018 

[14] S. T. Oni and A. Jimoh: On the dynamic response of moving concentrated loads of prestressed Bernoulli-Euler beam resting on Bi-parametric subgrades with other boundary conditions. Journal of Mathematical Sciences. National Mathematical Centre F.C.T Abuja. Vol. 4 No 1 pp 826 – 880. 2016. 

[15] A. Jimoh and E.O Ajoge: Effect of rotatory inertial and damping coefficient on the transvers motion of uniform Rayleigh beam under moving loads of constant magnitude. American Journal of Engineering Research. Vol. 7. Issue 1, pp 313 – 319. 

[16] L. Frybal: Vibrations of solids an structures under moving loads. Gromingen, Noordhoff. 1972 

[17] C. Bilello and L.A. Bergman: Vibration of damaged beams under a moving mass, theory and experimental validation. Journal of Sound and Vibration, 274: 567 – 582, 2004. 

[18] M. Dafarma, N. Jalli and E. Esmailzadeh: A comparative study of the Gaterkin approximation utilised in the Timoshenko beam theory. Journal of Sound and Vibration, 280: 1132 – 1142, 2005. 

[19] E. Savin: Dynamic amplification factor and response spectrum for the evaluation of vibrations of beams under successive moving loads. Journal of Sound and Vibration, 248 (2), 267 – 288.

How to cite this paper

Dynamic Response of Non-Uniform Rayleigh Beam Subjected to Harmonically Varying Moving Load

How to cite this paper: Jimoh, A., Ajoge, E. O. (2018) Dynamic Response of Non-Uniform Rayleigh Beam Subjected to Harmonically Varying Moving LoadJournal of Applied Mathematics and Computation2(8), 345-356.

DOI: http://dx.doi.org/10.26855/jamc.2018.08.004