A comparative study on the response of prismatic and non-prismatic timoshenko beams to accelerating loads

Abstract eng:
The Dynamic response of Timoshenko beams of uniform and non-uniform crosssections resting on elastic foundation whose rigidity is of a linear function and subjected to fast traveling concentrated loads of constant and varying magnitude is scrutinized using an elegant analytical approach. In particular, the spectral generalized Galerkin’s method in conjunction with Integral transform method is used to treat the problem of the coupled system of partial differential equations describing the transverse motion of the vibrating system. The specific aim is to compare the dynamic stability of Timoshenko beams of uniform and non-uniform cross-sections when under the actions of moving concentrated loads of constant and varying magnitudes. The closed-form solutions for both beam problems are obtained. Analytical and numerical Results show that as the foundation parameter K0 increases the response amplitudes for both beam decrease. Results also show that foundation parameter K0 produces a more noticeable effect on the deflection of a non-uniform beam than on a uniform beam when subjected to variable magnitude loads. It is equally established that, for higher values of foundation modulus, the risk of resonance is sufficiently reduced for both uniform and non-uniform Timoshenko beams resting on variable elastic foundation and under the actions of concentrated moving loads of any magnitude.

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