A two-layer (metal–piezoceramic) beam with hinged ends under a nonstationary distributed load is considered. A method for solving the problem of active damping of the nonstationary flexural vibrations of this structure is proposed. The shape of the electric signal applied to the electrode of the electroelastic layer to keep the beam almost undeformed is identified. The solution is obtained using the Laplace transform with respect to time. Numerical results are presented and analyzed
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References
A. E. Babaev, Nonstationary Waves in Continua with Reflecting Surfaces [in Russian], Naukova Dumka, Kyiv (1990).
A. E. Babaev, A. A. Babaev, and I. V. Yanchevskii, “Nonstationary vibrations of a bimorph beam with direct and inverse piezoelectric effect,” in: Important Aspects of Physical and Mechanical Research: Acoustics and Waves [in Ukrainian], Naukova Dumka, Kyiv (2007), pp. 16–27.
A. E. Babaev and Yu. B. Moseenkov, “Nonstationary vibrations of a thin electroelastic strip,” Dokl. AN Ukrainy, No. 12, 54–58 (1994).
V. T. Grinchenko, A. F. Ulitko, and N. A. Shul’ga, Electroelasticity, Vol. 5 of the five-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).
V. A. Ditkin and A. P. Prudnikov, Handbook of Operational Calculus [in Russian], Vyssh. Shk., Moscow (1965).
S. I. Pugachev (ed.), Piezoceramic Transducers [in Russian], Sudostroenie, Leningrad (1984).
N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).
H. J. Ding, H. M. Wang, and P. F. Hou, “The transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems,” Int. J. Solids Struct., 40, 105–123 (2003).
A. N. Guz, V. D. Kubenko, and A. E. Babaev, “Dynamics of shell systems interacting with a liquid,” Int. Appl. Mech., 38, No. 3, 260–301 (2002).
S. I. Rudnitskii, V. M. Sharapov, and N. A. Shul’ga, “Vibrations of a bimorphic disk transducer of the metal–piezoceramic type,” Int. Appl. Mech., 26, No. 10, 973–980 (1990).
N. A. Shul’ga and L. O. Grigorieva, “Method of characteristics in analysis of the propagation of electroelastic thickness oscillations in a piezoceramic layer under electric excitation,” Int. Appl. Mech., 44, No. 10, 1093–1097 (2008).
N. A. Shul’ga and L. O. Grigorieva, “Propagation of two-dimensional nonstationary vibrations in an electrically excited piezoceramic prismatic body,” Int. Appl. Mech., 44, No. 11, 1258–1264 (2008).
H. M. Wang, H. J. Ding, and Y. M. Chen, “Dynamic solution of multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems,” Int. J. Solids Struct., 42, 85–109 (2005).
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Translated from Prikladnaya Mekhanika, Vol. 46, No. 7, pp. 84–92, July 2010.
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Babaev, A.E., Babaev, A.A. & Yanchevskii, I.V. Active damping of the nonstationary flexural vibrations of a bimorph beam. Int Appl Mech 46, 806–811 (2010). https://doi.org/10.1007/s10778-010-0370-9
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DOI: https://doi.org/10.1007/s10778-010-0370-9