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Transverse free vibration of non uniform rotating Timoshenko beams with elastically clamped boundary conditions

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Abstract

In the present paper the Differential Quadrature Method, DQM, and the domain decomposition are used to carry out the free transverse vibration analysis of non-uniform multi-span rotating Timoshenko beams with perfect and not perfect boundary conditions. The cross section could vary in a continuous or discontinuous fashion along the beam length. The material of the beam could be different in each beam span. The influence of elastically clamped boundary conditions at hub end are studied and discussed. The effect of an arbitrary hub radius is considered. The governing differential equations of motion for rotating Timoshenko beams come from the derivation of Hamilton’s principle. The first six natural frequencies of vibration are obtained for many particular situations and for some of them the mode shapes are also available. The examples of applications of the method indicated its effectiveness. The results for particular cases are in excellent agreement with published results and results obtained by means of the finite element method.

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Acknowledgements

The authors wish to express their gratitude to the Universidad Nacional del Sur and the Consejo Nacional de Investigaciones Científicas y Técnicas for the financial support which enable this work to be conducted.

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Authors and Affiliations

  1. Instituto de Mecánica Aplicada, IMA, Departamento de Ingeniería, Universidad Nacional del Sur, UNS, Bahía Blanca, Argentina

    D. V. Bambill, C. A. Rossit, R. E. Rossi, D. H. Felix & A. R. Ratazzi

  2. Consejo Nacional de Investigaciones Científicas y Técnicas, CONICET, Bahía Blanca, Argentina

    D. V. Bambill & C. A. Rossit

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  1. D. V. Bambill
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  2. C. A. Rossit
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  3. R. E. Rossi
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  4. D. H. Felix
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  5. A. R. Ratazzi
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Correspondence to D. V. Bambill.

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Bambill, D.V., Rossit, C.A., Rossi, R.E. et al. Transverse free vibration of non uniform rotating Timoshenko beams with elastically clamped boundary conditions. Meccanica 48, 1289–1311 (2013). https://doi.org/10.1007/s11012-012-9668-5

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  • DOI: https://doi.org/10.1007/s11012-012-9668-5

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