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Home  >  Transactions ... 2017)

14. Transient Loads Of Structurally Prestressed Non- Uniform Simply Supported Rayleigh Beam With Time-Dependent Boundary Conditions For Moving Force BY Saheed Oluwatoyin AJIBOLA Transactions NAMP vol 5, (September and November, 2017), pp 101 – 112
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Abstract


The transverse vibration of a prismatic non-uniform simply supported Rayleigh beam resting on an elastic foundation and continuously acted upon by concentrated masses moving with non-uniform velocity is studied. A procedure involving Mindlin-Goodman’s method to transform, the use of the expression of the Dirac delta function in series form, and the use of Generalized Galakin's method (GGM) is employed to simplify the governing fourth order partial differential equation with singular and variable coefficients. The resulting Galerkin’s equations are solved via the use of modified Struble’s asymptotic techniques to treat this dynamical beam problems, hence, the analytical solutions for moving force  models which is valid for all variants of classical boundary conditions was obtained. We are invariably interested in predicting the response of the dynamical beam model. The proposed analytical procedure is illustrated by examples of some practical engineering interest in which the effects of some important parameters such as boundary conditions, pre-stressed function, mass ratio and elastic foundation are investigated in depth. Resonance phenomenon of the vibrating system is carefully investigated and the condition under which this may occur is clearly scrutinized. The results presented in this paper shows good agreement when compared with that of existing literature.

Keyword:  Non-uniform Rayleigh beam, resonance phenomenon, rotatory inertia, concentrated moving loads, dynamic responses.



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