Dynamic Response of Uniform Cantilever Beams on Elastic Foundation

Abstract:

The problem of the flexural vibrations of a uniform cantilever Bernoulli-Euler beams resting on an elastic foundation is studied in this paper. The analytical solution is based on the expression of the Heaviside function as a Fourier series and the fourth order partial differential equation of beam vibration under fixed and free end boundary conditions is transformed to second order ordinary differential equation by the generalized finite integral transform. The method of Struble’s asymptotic technique is then used to simplify the resulting equation and make it amenable to the methods of Laplace and convolution theory. The effects of velocity of the load, axial force and flexural stiffness on the natural frequencies of the beam model are studied. The solutions obtained are verify first and then used to investigate the significance of different parameters on the beam behaviour.