Harmonic vibrations of static response of a finite beam resting on elastic foundation subjected to an asymmetric load

In this study, the response of a finite beam resting on a tensionless Pasternak foundation, subjected to an asymmetric vertical load is investigated. In obtaining the governing differential equations, it is assumed that the Bernoulli-Euler hypotesis is valid and that the beam is partially in contact with the foundation. By considering the asymmetric loading case, differential equations are obtained for both the contact and noncontact regions. The coordinates of the lift-off points (contact length) and the variation of them with respect to some parameters, for symmetric and asymmetric loading cases are studied with the aid of graphics. In the first chapter, various kinds of foundation models and the studies dealing with the subject are given. In the second chapter, the differential equations for the contact and noncontact regions are obtained, and the boundary conditions of the problem is given. In the third chapter, the solution of the differential equations which depends on the various values of the frequency parameter is given. In the fourth chapter, the variation of the contact length with respect to some parameters are studied with the aid of graphics. Keywords: Elastic foundation, assymetric load, harmonic vibration, finite beam