Flexural Vibrations of Prismatic Rayleigh Beam on Vlasov Supple Foundation Underneath Fast Travelling Multiple Loads
Abstract
Transverse vibration of prismatic Rayleigh beam subjected to several point loads on Vlasov flexible foundation has been investigated in this study. The technique based on the Fourier sine transformation was used to obtain the closed form solution of the fourth order partial differential equation with singular and variable coefficients is obtained through. Thereafter, use is also made of Integral transformation and convolution theory. The results obtained are presented in plotted curves. The results illustrated that the response amplitudes of the prismatic Rayleigh beam on Vlasov foundation decrease as the foundation modulli k0 increases. Furthermore, the displacements of prismatic Rayleigh beam resting on Vlasov flexible foundation, for fixed values of foundation modulli k0, shear modulli k1 and point loads decrease as the axial force N increases. Moreover, the transverse deflections of the Rayleigh beam decrease as the distances between the point loads increase under the actions of moving loads. The state of resonance of the vibrating systems was also analyzed.
References
2. Oni, S.T. & Adedowole, A. (2008).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, vol 13,pp.127-140,. http://e.nampjournals.org/product-info.php%3Fpid718.html
3. Dehestani, M. Mofid, M. & Vafai, A. (2009).Investigation of critical influential speed for moving mass problems on beams,” Applied Mathematical Modeling, vol. 33,pp. 3885–3895.
4. Sadiku, S. & Leipholz, H.H.E. (1987). On the dynamics of elastic systems with moving concentrated masses, Ingenieur-Arehive, vol. 57, pp. 223–242.
5. Stanisic, M.M. & Lafayette, W. (1985). On a new theory of the dynamic behavior of the structures carrying moving masses, Ingenieur-Archiv , vol.55, pp. 176–185.
6. Tan, G. J. Shan, J. H. Wu, C. L. and Wang, (2017). Free vibration analysis of cracked Timoshenko beams carrying springmass systems, Structural Engineering and Mechanics, Vol. 63, No. 4, pp. 551-565, DOI: 10.12989/sem.2017.63.4.551.
7. Frýba, L. (1999). Vibration of solids and structures under moving loads”, III edn. Academia, Academy of Sciences of the Czech Republic, Prague
8. Ozkaya, E. (2002). Non-linear transverse vibration of a simply supported beam carrying concentrated masses,” Journal of Sound Vibration, vol. 257, no3, pp. 413–424. https://doi.org/10.1006/jsvi.2002.5042
9. Dasa, S.K., Rayb, P.C.& Pohit, G. (2007). Free vibration analysis of a rotating beam with non-linear spring and mass system” .Jounal Sound Vibration, vol. 301. Pp.165–188. https://www.researchgate.net/publication/223278948_Free_Vibration_Analysis_Of_A_Rotating_Beam_With_Non-Linear_Spring_And_Mass_System
10. Lin, H.Y. & Tsai, Y.C. (2007). Free vibration analysis of a uniform multi-span carrying multiple spring-mass systems, .Jounal Sound Vibration, vol. 302, pp.442–456. https://doi.org/10.1016/j.jsv.2006.06.080
11. Cao Chang-Yong, Zhong Yang. (2008). Dynamic response of a beam on a Pasternak foundation and under a moving load. Chongqing University, Eng Ed. Vol.7, no.4 , pp.311-316, ISSN: 1671-8224
12. Awodola, T.O. (2005). “Influence of foundation and axial force on the vibration of thin beam under variable harmonic moving load” Journal of the Nigerian Association of Mathematical Physics.9:143- 150
13. Oni, S.T. & Awodola, T.O. (2010). Dynamic behavior under moving concentrated masses of elastically supported finite Bernoulli-Euler beam on Winkler elastic foundation, Latin American Journal of Solids and Structures (LAJSS), vol;7:2-20.
14. Ogunbanke O.K.(2014). Dynamic analysis of elastic structures resting on bi-parametric vlasov foundations and under distributed masses moving at varying velocities. Ph.D Thesis, Federal University of Technology, Akure.
15. Adedowole A. (2020).On The Transverse Vibrations of Rotating Timoshenko Beams Subjected to two Concentrated Moving Loads, The Coast Journal of The Faculty Of Science OSUSTECH Okitipupa 1(2) 211-221.
