The problem of the influence of the temperature of dissipative heating on active damping of forced resonance vibrations of flexible simply supported viscoelastic cylindrical panels by piezoelectric actuators is considered. For the solution of the nonlinear problem, we use the analytic Bubnov–Galerkin method and the numerical finite-element methods together with the method of harmonic balance. In both cases, the problem is reduced to nonlinear algebraic equations that are solved numerically. Equating the maximum temperature of dissipative heating to the Curie temperature, we determine the critical value of the parameter of mechanical load after achievement of which control over panel vibrations is unrealizable due to the loss of piezoeffect by the active material.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 54, No. 1, pp. 175–188, January–March, 2011.
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Karnaukhov, V.G., Kozlov, V.I. & Karnaukhova, T.V. Influence of dissipative heating on active damping of forced resonance vibrations of a flexible viscoelastic cylindrical panel by piezoelectric actuators. J Math Sci 183, 205–221 (2012). https://doi.org/10.1007/s10958-012-0807-2
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DOI: https://doi.org/10.1007/s10958-012-0807-2