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Modal coupling in one-dimensional electromechanical structured continua

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Summary

A passive continuously distributed control of mechanical vibrations is proposed. The piezoelectric actuators are interconnected by a linear electric transmission line. We introduce coupling and internal resonance criteria to determine the optimal choices for electric parameters. These criteria can be found decomposing the differential operator appearing in the linear evolutions according to a partition of the state vector into mechanical and electrical parts. The results we find allow for the design of an experimental set up.

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References

  1. Eringen, A. C., Maugin, G. A.: Electrodynamics of continua I–II. New York: Springer 1990.

    Google Scholar 

  2. Fuller, C. R., Elliott, S. J., Nelson, P. A.: Active control of vibration. London: Academic Press 1996.

    Google Scholar 

  3. Guran, A., Inman, D. J.: Wave motion, intelligent structures and nonlinear mechanics. Singapore: World Scientific 1995.

    Google Scholar 

  4. Proceedings of SPIE: Smart materials and structures, Vol. 3241.

  5. dell'Isola, F., Vidoli, S.: Continuum modelling of piezoelectro-mechanical truss beams: an application to vibration damping. Arch. Appl. Mech.68, 1–19 (1998).

    Google Scholar 

  6. dell'Isola, F., Vidoli, S.: Damping of bending-waves in truss beams by electrical transmission line with PZT actuators. Arch. Appl. Mech.68, 626–636 (1997).

    Google Scholar 

  7. Di Carlo, A.: A non-standard format for continuum mechanics. In: Contemporary research in the mechanics and mathematics of materials (Batra, R. C., Beatty, M. F., eds.) pp. 263–268. CIMNE: Barcelona 1996.

    Google Scholar 

  8. Maugin, G. A.: The method of virtual power in continuum mechanics: application to coupled fields. Acta Mech.35, 1–70 (1980).

    Google Scholar 

  9. Capriz, G.: Continua with microstructure. New York: Springer 1989.

    Google Scholar 

  10. Euler, L.: Methodus inveniendi lineas curvas maximi minimive proprietati gaudentes. Lausanne (1744). German Translation in: Opera Omnia I (24), Berna (1952). Bernoulli, J.: Specimen alterum calculi differentialis... una cum additamento quodam ad problema funicularum, aliisque. Acta Eruditorum (1691).

  11. Di Carlo, A.: Bodies with affine structure. Lecture held at the 31st Polish Solid Mechanics Conference. Mierki, Sept. 1996.

  12. Gurtin, M. E.: An introduction to continuum mechanics. New York: Academic Press 1981.

    Google Scholar 

  13. Chua, L. O., Desoer, C. A., Kuh, E. S.: Linear and nonlinear circuits. New York: McGraw-Hill 1987.

    Google Scholar 

  14. Reed, M., Simon, B.: Methods of modern mathematical physics. Boston: Academic Press 1980.

    Google Scholar 

  15. Krasnov, M. L., Kiselev, A. I., Makarenko, G. I.: Equazioni integrali. Moscow: Mir 1976.

    Google Scholar 

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Vidoli, S., dell'Isola, F. Modal coupling in one-dimensional electromechanical structured continua. Acta Mechanica 141, 37–50 (2000). https://doi.org/10.1007/BF01176806

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  • DOI: https://doi.org/10.1007/BF01176806

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