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On the response of small buildings to vibrations

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Abstract

In this work, the analysis the response to vibrations of a small building equipped with an electromechanical vibration absorber is investigated. In the first part, the case of harmonic excitation with constant or time dependent frequencies is considered, and in the second part, the case of random earthquakes, respectively. The cross correlation functions and the mean square displacements are calculated for the structure when it is equipped with an electromechanical vibration absorber. The stochastic process which characterizes the earth movements is coupled to the cnoidal method, which delivers the analytical solutions of the nonlinear problem. The interaction between the structure and the energy source is analyzed via the Sommerfeld effect inside the resonance region. The resonance capture and the vibration reduction are displayed by the time history responses of the displacement and angular velocities above the resonance.

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Acknowledgements

This research was elaborated through the PN-II-PT-PCCA-2011-3.1-0190. Project Nr. 149/2012 UEFISCSU, Romania. The authors acknowledge the similar and equal contributions to this article.

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Authors and Affiliations

  1. Institute of Solid Mechanics, Romanian Academy, Ctin Mille 15, 010141, Bucharest, Romania

    Ligia Munteanu, Veturia Chiroiu & Tudor Sireteanu

Authors
  1. Ligia Munteanu
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  2. Veturia Chiroiu
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  3. Tudor Sireteanu
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Corresponding author

Correspondence to Veturia Chiroiu.

Appendix

Appendix

Table 1 Values m jk , \(\tilde{\beta} _{jk}\), j=1,2,3,4 for the first problem
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Table 2 Values m jk , \(\tilde{\beta} _{jk}\), j=1,2,3,4 for the second problem
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Munteanu, L., Chiroiu, V. & Sireteanu, T. On the response of small buildings to vibrations. Nonlinear Dyn 73, 1527–1543 (2013). https://doi.org/10.1007/s11071-013-0883-y

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