The basic relations of the thermomechanics of thin-walled viscoelastic plates with distributed piezoelectric sensors under monogarmonic mechanical loading are presented. To describe the thermomechanical behavior of materials, the concept of complex characteristics is used. Numerical and variational methods are used to study the forced resonant vibrations of viscoelastic plates with distributed piezoelectric sensors. The effect of dissipative heating on the readings of the sensors of a circular viscoelastic plate undergoing axisymmetric resonant bending vibrations is analyzed as an example
References
V. G. Karnaukhov, “Thermal failure of polymeric structural elements under monoharmonic deformation,” Int. Appl. Mech., 40, No. 6, 622–655 (2004).
V. G. Karnaukhov and V. V. Mikhailenko, Nonlinear Thermomechanics of Piezoelectric Bodies under Monoharmonic Loading [in Russian], ZhTTU, Zhitomir (2005).
V. G. Karnaukhov and Ya. V. Tkachenko, “Damping the vibrations of a rectangular plate with piezoelectric actuators,” Int. Appl. Mech., 44, No. 2, 182–187 (2008).
T. V. Karnaukhova and E. V. Pyatetskaya, “Basic equations for thermoviscoelastic plates with distributed actuators under monoharmonic loading,” Int. Appl. Mech., 45, No. 2, 200–214 (2009).
T. V. Karnaukhova and E. V. Pyatetskaya, “Damping the resonant flexural vibration of a hinged plate with actuators,” Int. Appl. Mech., 45, No. 4, 448–456 (2009).
T. V. Karnaukhova and E. V. Pyatetskaya, “Damping the flexural vibration of a clamped viscoelastic rectangular plate with piezoelectric actuators,” Int. Appl. Mech., 45, No. 5, 546–557 (2009).
I. F. Kirichok, “Flexural vibrations and vibrational heating of a ring plate with thin piezoceramic pads under single-frequency electromechanical loading,” Int. Appl. Mech., 44, No. 2, 200–207 (2008).
I. F. Kirichok, E. V. Pyatetskaya, and M. V. Karnaukhov, “Bending vibrations and dissipative heating of a circular viscoelastc plate with piezoelectric actuators under electromechanical monoharmonic loading,” Visn. Kyiv. Univ., Ser. Fiz. Mat. Nauky, No. 2, 84–92 (2006).
I. F. Kirichok and M. V. Karnaukhov, “Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading,” Int. Appl. Mech., 44, No. 1, 65–72 (2008).
I. F. Kirichok and M. V. Karnaukhov, “Monoharmonic vibrations and vibrational heating of an electromechanically loaded circular plate with piezoelectric actuators subject to shear strain,” Int. Appl. Mech., 44, No. 9, 1041–1049 (2008).
W. P. Mason (ed.), Physical Acoustics. Principles and Methods, Vol. 2, Part B. Properties of Polymers and Nonlinear Acoustics, Academic Press, New York–London (1965).
N. A. Shul’ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies [in Russian], Naukova Dumka, Kyiv (1990).
O. P. Chervinko, I. K. Senchenkov, and N. N. Yakimenko, “Vibrations and self-heating of a viscoelastic prism with cylindrical inclusion,” Int. Appl. Mech., 43, No. 6, 647–653 (2007).
V. A. Dolya, O. P. Chervinko, and I. K. Senchenkov, “Vibrations and self-heating of a layered viscoelastic rectangular prism under a vibrating punch,” Int. Appl. Mech., 43, No. 8, 886–892 (2007).
V. L. Karlash, “Planar electroelastic vibrations of a piezoceramic plate and a half-disk,” Int. Appl. Mech., 43, No. 5, 547–553 (2007).
V. L. Karlash, “Evolution of the planar vibrations of a rectangular plate as its aspect ratio is changed,” Int. Appl. Mech., 43, No. 7, 786–793 (2007).
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Translated from Prikladnaya Mekhanika, Vol. 45, No. 6, pp. 100–112, June 2009.
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Karnaukhova, T.V., Pyatetskaya, E.V. Basic relations of the theory of thermoviscoelastic plates with distributed sensors. Int Appl Mech 45, 660–669 (2009). https://doi.org/10.1007/s10778-009-0213-8
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DOI: https://doi.org/10.1007/s10778-009-0213-8