Response of Timoshenko Beams on Winkler Foundation Subjected To Dynamic Load

Abstract - In this study, the dynamic response of a uniform deep beam resting on a Winkler elastic foundation and excited by a moving load is considered. The solution technique discussed involves the use of finite Fourier transform and the resulting simultaneous equations are reduced to simple algebraic equations via Laplace transform. Analytical and numerical solutions depict that as the values of the elastic foundation moduli increases, the amplitudes of transverse vibration of the beam decreases.

REFERENCES

[1] Fryba, L.: Vibrations of solids and structures under moving loads. Thomas Telford, London. 1999

[2] Gbadeyan, J.A. and Oni, S.T.: Dynamic behaviour of beams and rectangular plates under moving loads. Journal of Sound and Vibrations. 182(5): 677-695,1995

[3] Alev, K., Tugba Tan, H. and Kaya, M.O.: Free vibration of beams on variable winkler elastic foundation by using the differential transforms method. Mathematical and Computational Analysis, Vol. 16, No 3 Pp773-783, 2011

[4] Huang, M.H. and Thambiratnam, D.P.: Deflection response of a plate on Winkler foundation to moving accelerated loads. Engineering Structures, 23, 1134-1141, 2001.

[5] Timoshenko, S.: On the correction for shear of the differential equation for transverse vibration of prismatic bars, Phil. Mag. Ser. 6 vol. 41, Pp. 744-776, 1921.

[6] Lowan, A.N.: On transverse oscillations of beams under the action of moving variable loads: Phil. Mag. Ser. 7, vol. 19, N0.27, Pp. 708-715, 1935.

[7] Adams, G.G.: Critical speeds and the response of a tensioned beam on an elastic foundation to repetitive moving loads: Int. J. Mech. Science Vol. 37, No 7, Pp. 773-781, 1995.

[8] Kolsky, H,: Stress waves in Solids. New York: Dover, 1963.

[9] Djondjorov, P.A.: On the critical velocities of pipes on variable elastic foundations. Journal of Theoretical and Applied Mechanics, Vol. 31, Pp. 73-81, 2001.

[10] Djondjorov,P.A.: Invariant properties of Timoshenko beam equations. International Journal of Engineering Science. Vol. 33, No. 4, Pp. 2103-2114, 1995