Abstract

The consequences of a uniform Bernoulli-Euler beam resting on a Pasternak foundation under the action of a focussed moving load with a damping term were investigated in this paper using the merely support, clamped-clamped, and clamped-free classical boundary conditions. The Laplace transform method, the extended finite integral transform, and Struble's asymptotic methodology were used to solve the governing equation after the Dirac delta function was expressed as a Fourier cosine series. The dynamic responses of the beam and their corresponding resonance condition were obtained using the simply support, clamped-clamped, and clamped-free conditions after the equations defining the transverse displacement for the moving force and moving mass issues were obtained. The uniform beam's deflection profiles were then calculated, and MATLAB was used to display the corresponding graphs for various damping coefficient, axial force, foundation modulus, and shear modulus values. The graphs for these boundary conditions showed that, for the moving force and moving mass problems, the response amplitude of the beam decreases as the axial force, foundation modulus, shear modulus, and damping term values rise. The influence of the damping term was however, more noticeable than other parameters. In addition, the transverse displacement of the simply support beam was generally higher for the moving force and moving mass problems, followed by the clamped-free condition with the clamped-clamped showing the least displacement. Furthermore, the highest deflection of the simply support condition concentrated at the mid-points of the graphs for the moving force problem whereas, the case of the moving mass is not significantly noticeable. On the other hand, the clamped-clamped and clamped-free conditions generally had their peak deflections at the ends of the graphs.  Furthermore, the moving mass problem cannot be safely approximated using the moving force problem. These results are consistent with previous research.

Key Words:Bernoulli-Euler beam, Classical boundary conditions, Concentrated moving load, Damping term, Pasternak foundation.

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