Vibration of Uniform Rayleigh Beam Clamped-Clamped Carrying Concentrated Masses Undergoing Tractions

Abstract

This paper is sequel to [1], the initial –boundary –value problem of vibration of a uniform Rayleigh beam resting on a constant elastic foundation and with axial force and traversed by masses travelling at a uniform velocity is investigated. The dynamical problem, methods of solution and its closed form solution are as alluded to in [1]. Except that in [1], a simply-supported boundary condition was illustrated this is the simplest and the commonest boundary condition in literature. The novelty in this paper is that we considered boundary condition other than simply-supported one. One of the known but cumbersome boundary conditions in literature is the clamped-clamped boundary condition. A closed form solution of our dynamical problem with clamped –clamped boundary condition is obtained , numerical calculations and discussions of results reveals that; the response amplitude of the uniform Rayleigh beam clamped at both ends decreases as the value of the axial force N increases. It is further observed that higher values of an axial force N and foundation modulli when the rotatory   inertial  (r) is  fixed are required for a more noticeable effect in the case of clamped-clamped time dependent boundary condition than those of simply supported boundary conditions as in [1,3] for both moving force and moving mass problems. Conclusively, this study has shed more light on the reliability of the moving force solution as a safe approximation to the moving mass problem.