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Structural Engineering and Mechanics Volume 44, Number 5, December10 2012 , pages 681-704 DOI: https://doi.org/10.12989/sem.2012.44.5.681 |
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Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads |
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Giuseppe Piccardo and Federica Tubino
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| Abstract | ||
| The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses. | ||
| Key Words | ||
| closed form solution; Euler-Bernoulli beams; harmonic moving loads; vibrations | ||
| Address | ||
| Giuseppe Piccardo and Federica Tubino: DICCA, University of Genoa, Via Montallegro 1, 16145 Genoa, Italy | ||