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Free vibration analysis of non-uniform Euler–Bernoulli beams by means of Bernstein pseudospectral collocation

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Abstract

The eigenvalue problem related to the free vibration of Euler–Bernoulli beams of variable cross-section is solved using a collocation technique based on Bernstein polynomials. The properties of the non-orthogonal Bernstein basis allow the construction of the pseudospectral stiffness matrix by recursive formulation and the straightforward enforcement of essential and natural boundary conditions. The approach is tested in benchmark problems of modal analysis, showing high accuracy and exponential convergence rates.

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Acknowledgments

The author wishes to thank the support and collaboration of Safran Group.

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  1. Safran Engineering Services (Safran Group), Calle Arnaldo de Vilanova, 5, 28906, Getafe, Madrid, Spain

    D. Garijo

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  1. D. Garijo
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Garijo, D. Free vibration analysis of non-uniform Euler–Bernoulli beams by means of Bernstein pseudospectral collocation. Engineering with Computers 31, 813–823 (2015). https://doi.org/10.1007/s00366-015-0401-6

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