The forced resonant vibrations and vibrational heating of viscoelastic plates with actuators are modeled considering geometrical nonlinearity and transverse shear. An approximate analytical solution of the problem is obtained for a hinged rectangular plate by the Bubnov–Galerkin method. The effect of geometrical nonlinearity and shear deformations on the efficiency of active damping of vibrations with piezoelectric actuators is analyzed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. F. Bulat, V. I. Dyrda, V. G. Karnaukhov, E. L. Zvyagil’skii, and A. S. Kobets, Forced Vibrations and Dissipative Heating of Elastic Bodies, Vol. 3 of the four-volume series Applied Mechanics of Elastic-Hereditary Media [in Russian], Naukova Dumka, Kiev (2014).
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 Elements [in Russian], Naukova Dumka, Kiev (1989).
V. G. Karnaukhov and I. F. Kirichok, Electrothermoviscoelasticity, Vol. 4 of the five-volume series Mechanics of Coupled Fields in Structural Elements [in Russian], Naukova Dumka, Kiev (1988).
V. G. Karnaukhov and V. V. Mikhailenko, Nonlinear Thermal Mechanics of Piezoelectric Inelastic Bodies under Monoharmonic Loading [in Russian], ZhGTU, Shitomir (2005).
V. G. Karnaukhov, V. I. Kozlov, and T. V. Karnaukhova, “Thermal failure of inelastic hinged rectangular plate with piezoelectric sensors and actuators under forced resonant bending vibrations,” Byul. Dnepropetrovsk Univ., Ser. Mekh., 2, No. 5 (15), 68–75 (2011).
V. V. Matveev Damping of Vibrations of Deformable Bodies [in Russian], Naukova Dumka, Kiev (1985)
A. N. Guz (ed.), Mechanics of Composites [in Russian], in 12 vols., A.S.K., Kiev (1992).
Yu. A. Mitropolsky, Nonlinear Mechanics, Single-Frequency Vibrations [in Russian], Inst. Mat. NAS Ukrainy, Kiev (1997).
A. Nashif, J. Jones, and J. Henderson, Vibrations Damping, New York, Wiley (1985).
Yu. N. Rabotnov, Elements of Hereditary Solid Mechanics [in Russian], Nauka, Moscow (1977).
G. S. Agnes, “Development of a modal model for simultaneous active and passive piezoelectric vibration suppression,” J. Intell. Mater. Syst. Struct., 6, No. 4, 482–487 (1995).
G. S. Bae, M. K. Kwak, and D. J. Inman, “Vibration suppression of a cantilever beam using eddy current of damper,” J. S. V., 284, No. 3–5, 805–814 (2005).
U. Gabbert and H. S. Tzou, Smart Structures and Structronic Systems, Kluwer Academic Pub., Dordrecht (2001).
I. A. Guz, Y. A. Zhuk, and M. Kashtalyan, “Dissipative heating and thermal fatigue life prediction for structures containing piezoactive layers,” Techn. Mech., 32, No. 2–5, 238–250 (2012).
Mel Schwartz (ed.), Encyclopedia of Smart Materials, 1–2, Wiley & Sons, New York (2002).
D. I. Jones, Handbook of Viscoelastic Vibration Damping, Wiley & Sons, New York (2001).
J. F. He and D. A. Ma, “Analysis of flexural vibration of viscoellastically damped sandwich plates,” J. Sound Vibr., 126, No. 1, 37–47 (1988).
V. L. Karlash, “Influence of electric loading conditions on the vibrations of piezoceramic resonators,” Int. Appl. Mech., 53, No. 2, 220–227 (2017).
V. L. Karlash, “Phase–frequency characteristics of the longitudinal and transverse vibrations of planar piezoceramic transformers,” Int. App. Mech., 53, No. 3, 349–355 (2017).
V. L. Karlash, “Effect of split or partial electrodes on the forced vibrations of bear-type piezoceramic transducers”, Int. Appl. Mech., 52, No. 5, 535–546 (2016).
T. V. Karnaukhova, “Thermal depolarization of a piezoelectric layer under harmonic quasistatic electric loading,” Int. Appl. Mech., 34, No. 4, 373–376 (1998).
V. G. Karnaukhov, “Thermomechanics of coupled fields in passive and piezoactive inelastic bodies under harmonic deformations (review),” J. Therm. Stress., 28, No. 6–7, 783–815 (2005).
V. G. Karnaukhov, T. V. Karnaukhova, and O. McGillicaddy, “Thermal failure of flexible rectangular viscoelastic plates with distributed sensors and actuators,” J. Eng. Math., 78, No. 1, 199–212 (2013).
V. G. Karnaukhov, I. F. Kirichok, and V. I. Kozlov, “Thermomechanics of inelastic thin-walled structural members with piezoelectric sensors and actuators under harmonic loading (review),” Int. Appl. Mech., 53, No. 1, 6–59 (2017).
I. F. Kirichok, “Damping the radial vibrations and self-heating of viscoelastic shell elements with piezoelectric sensor and actuator,” Int. Appl. Mech., 52, No. 4, 354–358 (2016).
J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, CRC, Boca Raton (2007).
J. Tani, T. Takagi, and J. Qui, “Intelligent material systems: Application of functional materials,” Appl. Mech. Rev., 51, No. 8, 505–521 (1998).
H. S. Tzou, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer Academic Publishers, Boston (1993).
H. S. Tzou and L. A. Bergman, Dynamics and Control of Distributed Systems, Cambridge University Press, Cambridge (1998).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 54, No. 1, pp. 101–110, January–February, 2017.
Rights and permissions
About this article
Cite this article
Karnaukhov, V.G., Kozlov, V.N. & Karnaukhova, T.V. Forced Vibrations and Dissipative Heating of Hinged Flexible Viscoelastic Rectangular Plates with Actuators Under Shear Deformation. Int Appl Mech 54, 85–93 (2018). https://doi.org/10.1007/s10778-018-0862-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-018-0862-6