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Home  >  Transactions ... 2017)

15. Vibration of Uniform Rayleigh Beam Clamped-Clamped Carrying Concentrated Masses Undergoing Tractions BY Saheed Oluwatoyin AJIBOLA Transactions NAMP vol 5, (September and November, 2017), pp 113 – 126
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This paper  is sequel to previous study where 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 the previous study. Except that in some other study, 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 presented 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.

Keyword: Rayleigh Beam, Moving force, Moving mass, Velocity, Time-Department and Resonance