Analysis Of Non-Uniformly Prestressed Tapered Beams With Exponentially Varying Thickness Resting On Vlasov Foundation Under Variable Harmonic Load
Volume 1 - Issue 5, November 2017 Edition
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Author(s)
Jimoh Sule Adekunle
Keywords
non-uniformly prestressed tapered beams, exponentially varying thickness, Vlasov foundation, variable harmonic load.
Abstract
In this paper, the motion of non-uniformly prestressed tapered beams with exponentially varying thickness resting on Vlasov foundation under variable harmonic load moving with constant velocity is investigated. The governing equation is a fourth order partial differential equation. The solution technique is based on the method of Galerkin with series representation of Heaviside function, Struble's asymptotic method and Laplace transformation technique in conjunction with convolution theory. The result shows that, an increase in the values of the structural parameters such as foundation stiffnesses, axial force, moment of inertia of the beam and exponential factor reduces the response amplitude of the beam for the dynamic problem. Furthermore, it is found that the moving force solution is not always an upper bound for the accurate solution for the non-uniformly prestressed tapered beams.
References
[1] Krylov, A. N. Mathematical Collection of Papers of the Academy of Science, 1905.
[2] Timoshenko, S. "On the correction for shear of the differential equation for transverse vibration of prismatic bars." Phil. Mag.S.6, 1921: 5:46-74.
[3] Kenny, J. T. “Steady state vibrations of beams on an elastic foundation for a moving load,†Journal of Applied Mechanics. 1954: 76: 359-369.
[4] Steel, C. R. “Beam and Shells vibration with moving loads,†International Journal of solid and structures, 1971: 7: 1171-1198.
[5] Oni, S. T., "thick beams under the action of a variable travelling transverse load," Abacus, Journal of Mathematical Association of Nigeria. 1997: 2: 531-546.
[6] Gbadeyan, J. A. and Oni, S. T. "Dynamic behavior of beams and rectangular plates under moving loads." Journal of sound and vibration. 1995: 182(5): 677-695.
[7] Oni, S.T. "Response on non-uniform beam resting on an elastic foundation to several moving masses." Abacus. Journal of Mathematical association of Nigeria. 1996: 24(2):72-88.
[8] Nayfey, A.H. "Perturbation Methods" John Wiley and Sons, New York. 1973: 171-174.
[9] Sayad Boreyri, Pouya Mohtat, Mohamad Javad Ketabdari, Ali Moosavi. "Study vibration analyses of a tapered beam with exponentially varying thickness resting on Winkler foundation using the differential transform method." International Journal of Physics Research. 2014: 2(1): 10-15
[10] N. D. Kien, "Dynamic response of prestressed Timoshenko beams resting on two-parameter foundation to moving harmonic load," Technische Mechanik, 2008: 28(3): 237-258.
[11] Oni, S .T. and Awodola, T. O. "Vibrations of a simply supported plate under moving masses and resting on Pasternak elastic foundation with stiffness variation," Journal of Nigerian Mathematical society. JNMS Accepted in May 2012
