Fourier Sine Transform Method for the Free Vibration of Euler-Bernoulli Beam Resting on Winkler Foundation
- Charles Chinwuba Ike, Enugu State University of Science and Technology, Enugu State, Nigeria, firstname.lastname@example.org
In this study, the fourth order homogeneous partial differential equation (PDE) governing the free vibrations of Euler -Bernoulli
beams on Winkler foundation with prismatic cross-sections was solved using the finite Fourier sine integral transformation
method. Euler-Bernoulli beam theory was used to model the beam while Winkler foundation model was used for the foundation.
The beam of length l was assumed to be simply supported at the ends x = 0, and x = l. The PDE was decoupled by the assumption
of harmonic vibration. Application of the finite Fourier sine integral transformation on the decoupled equation resulted in the
transformation of the problem to an algebraic eigenvalue problem. The condition for non-trivial solutions resulted to the
characteristic frequency equation which was expressed in terms of a non-dimensional frequency parameter Wn'. The frequency
equation which was observed to be the exact frequency equation obtained in the literature using the Navier series method, was
solved to obtain the non-dimensional frequencies. Numerical values of the non-dimensional frequencies were computed for the
case where 4B^4=1, l = 1, and for n = 1, 2, 3, 4, 5. It was found that exact values of the non-dimensional frequencies were obtained
using the present method.