A general approach for antiresonance assignment in undamped vibrating systems exploiting auxiliary systems

  • D. RichiedeiEmail author
  • I. Tamellin
  • A. Trevisani
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


This paper proposes a method for antiresonance assignment in undamped vibrating systems, formulated as an inverse eigenvalue problem of the adjunct system. The method exploits both the addition of auxiliary systems, as in the well-known tuned mass damper, and modifications of the existing parameters. The approach handles arbitrary topology of modifications and provide a general formulation of the problem. Constraints on the feasible modifications can be included. The antiresonance assignment is solved exploiting the homotopy global optimization. The proposed method is validated on a continuum system.


dynamic structural modification antiresonance assignment inverse eigenvalue problem vibration absorber 


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The second Author acknowledges the financial support of the Cariparo foundation (“Fondazione Cassa di Risparmio di Padova e Rovigo”) through a Ph.D. scholarship.


  1. 1.
    Richiedei, D., Trevisani, A.: Simultaneous active and passive control for eigenstructure assignment in lightly damped systems. Mechanical Systems and Signal Processing, 85, 556-566 (2017).CrossRefGoogle Scholar
  2. 2.
    Belotti, R., Richiedei, D.: Dynamic structural modification of vibrating systems oriented to eigenstructure assignment through active control: A concurrent approach. Journal of Sound and Vibration, 422, 358-372 (2018).CrossRefGoogle Scholar
  3. 3.
    Frahm, H.: Device for damping vibrations of bodies. U.S. Patent No. 989,958 (1911).Google Scholar
  4. 4.
    Den Hartog, J. P.: Mechanical Vibrations, McGraw Hill, NY, Chap. 3 (1934).Google Scholar
  5. 5.
    Ram, Y. M., Sylvan, E.: The theory of a multi-degree-of-freedom dynamic absorber. Journal of Sound and Vibration, 195.4, 607-616 (1996).CrossRefGoogle Scholar
  6. 6.
    Ozer, M. B., Royston, T. J.: Extending Den Hartog’s vibration absorber technique to multi-degree-of-freedom systems. Journal of Vibration and Acoustics 127(4), 341-350 (2005).CrossRefGoogle Scholar
  7. 7.
    Stăncioiu, D., Ouyang, H.: Structural modification formula and iterative design method using multiple tuned mass dampers for structures subjected to moving loads. Mechanical Systems and Signal Processing, 28, 542-560 (2012).CrossRefGoogle Scholar
  8. 8.
    Tsai, S., Ouyang H., Chang, J.: Inverse structural modifications of a geared rotor-bearing system for frequency assignment using measured receptances. Mechanical Systems and Signal Processing, 110, 59-72 (2018).CrossRefGoogle Scholar
  9. 9.
    Belotti R., Richiedei D., Tamellin I.: A Novel Approach for Antiresonance Assignment in Undamped Vibrating Systems. In: Gasparetto A., Ceccarelli M. (eds) Mechanism Design for Robotics. MEDER 2018. Mechanisms and Machine Science, vol 66, pp.276-283. Springer, Cham (2018).Google Scholar
  10. 10.
    Belotti, R., Caracciolo, R., Palomba, I., Richiedei, D., Trevisani, A.: An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System. Shock and Vibration, 2018, (2018).Google Scholar
  11. 11.
    Belotti R., Richiedei D., Trevisani A.: Optimal Design of Vibrating Systems Through Partial Eigenstructure Assignment. Journal of Mechanical Design 138.7, (2016).CrossRefGoogle Scholar
  12. 12.
    Belotti, R., Richiedei, D.: Designing auxiliary systems for the inverse eigenstructure assignment in vibrating systems. Archive of Applied Mechanics, 87.2, 171-182, (2017).CrossRefGoogle Scholar
  13. 13.
    Mottershead, J. E.: Structural modification for the assignment of zeros using measured receptances. Journal of applied mechanics, 68.5, 791-798 (2001).CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Università degli Studi di PadovaVicenzaItaly

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