The paper addresses the forced flexural vibrations and dissipative heating of a circular viscoelastic plate with piezoactive actuators under axisymmetric loading. A refined formulation of this coupled problem is considered. The viscoelastic behavior of materials is described using the concept of complex moduli dependent on the temperature of dissipative heating. The electromechanical behavior of the plate is modeled based on the Timoshenko hypotheses for the mechanical variables and analogous hypotheses for the electric-field variables in the piezoactive layers of the actuator. The temperature is assumed constant throughout the thickness. The nonlinear problem is solved by a time stepping method using, at each step, the discrete-orthogonalization and finite-difference methods to solve the elastic and heat-conduction equations, respectively. A numerical study is made of the effect of the shear strain, the temperature dependence of the material properties, fixation conditions, and geometrical parameters of the plate on the vibrational characteristics and the electric potential applied to the actuator electrodes to balance the mechanical load
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ya. M. Grigorenko (ed.), Algorithms and Programs for Solving Problems of Solid Mechanics [in Russian], Naukova Dumka, Kyiv (1976), pp. 157–170.
A. M. Bolkisev, V. L. Karlash, and N. A. Shul'ga, “Temperature dependence of the properties of piezoelectric ceramics,” Int. Appl. Mech., 20, No. 7, 650–653 (1984).
Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells of Varying Thickness [in Russian], Naukova Dumka, Kyiv (1981).
Ya. M. Grigorenko and A. P. Mukoid, Computer Solution of Linear and Nonlinear Problems in Shell Theory [in Russian], Lybid', Kyiv (1992).
V. T. Grinchenko, A. F. Ulitko, and N. A. Shul'ga, Electroelasticity, Vol. 5 of the six-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1989).
V. G. Karnaukhov and I. F. Kirichok, Electrothermoviscoelasticity, Vol. 4 of the six-volume series Mechanics of Coupled Fields in Structural Members [in Russian], Naukova Dumka, Kyiv (1988).
V. G. Karnaukhov, T. V. Karnaukhova, and O. V. P'yatets'ka, “Effect of dissipative heating temperature on the active damping of forced axisymmetric vibrations of a circular plate with a piezoelectric actuator,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk, No. 3, 107–114 (2004).
V. G. Karnaukhov, V. I. Kozlov, and O. V. P'yatets'ka, “Active damping of axisymmetric resonant vibrations of a circular plate with piezoelectric inclusions,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk, No. 2, 81–85 (2003).
V. G. Karnaukhov and V. V. Mikhailenko, “Nonlinear single-frequency vibrations and dissipative heating of inelastic piezoelectric bodies,” Int. Appl. Mech., 38, No. 5, 521–547 (2002).
I. F. Kirichok, O. V. P'yatets'ka, and M. V. Karnaukhov, “Flexural vibrations and dissipative heating of a viscoelastic circular plate with piezoelectric actuators under electromechanical monoharmonic loading,” Visn. Kyiv. Univ., Ser. Fiz.-Mat. Nauk, No. 2, 84–92 (2006).
N. P. Nesterenko, O. P. Chervinko, and I. K. Senchenkov, “Modeling ultrasonic heating of structural members of fibrous polymeric composites under normal loading,” Vest. Nats. Tekhn. Univ. KhPI, No. 9, 3–8 (2002).
V. L. Karlash, “Planar electroelastic vibrations of piezoceramic rectangular plate and half-disk,” Int. Appl. Mech., 43, No. 5, 547–553 (2007).
V. L. Karlash, “Evolution of the planar vibrations of a rectangular piezoceramic plate as its aspect ratio is changed,” Int. Appl. Mech., 43, No. 7, 786–793 (2007).
V. G. Karnaukhov and Yu. V. Revenko, “Dissipative heating of a viscoelastic cylinder steadily rolling over a rigid foundation,” Int. Appl. Mech., 42, No. 1, 51–60 (2006).
I. F. Kirichok, “Resonant flexural vibrations and dissipative heating of a piezoceramic ring plate with nonuniformly electroded surfaces,” Int. Appl. Mech., 42, No. 3, 336–341 (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, “Flexural vibrations and vibrational heating of a ring plate with thin piezoceramic pads under single-frequency electromechanical loading,” Int. Appl. Mech., 44, No. 2, 100–207 (2008).
H. S. Tzou, Piezoelectric Shells (Distributed Sensing and Control of Continua), Kluwer, Dordrecht-Boston-London (1993).
H. S. Tzou and L. A. Bergman, Dynamics and Control of Distributes Systems, Cambridge Univ. Press, Cambridge (1998).
Author information
Authors and Affiliations
Additional information
Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 104–114, September 2008.
Rights and permissions
About this article
Cite this article
Kirichok, I.F., Karnaukhov, M.V. Monoharmonic vibrations and vibrational heating of an electromechanically loaded circular plate with piezoelectric actuators subject to shear strain. Int Appl Mech 44, 1041–1049 (2008). https://doi.org/10.1007/s10778-009-0112-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-009-0112-z