Abstract
A coupled dynamic problem of thermoelectromechanics for thin-walled multilayer elements is formulated based on a geometrically nonlinear theory and the Kirchhoff–Love hypotheses. In the case of harmonic loading, an approximate formulation is given using the concept of complex moduli to characterize the cyclic properties of the material. The model problem on forced vibrations of sandwich beam, whose core layer is made of a passive physically nonlinear material, and face layers, of a viscoelastic piezoactive material, is considered as an example to demonstrate the possibility of damping the vibrations by applying harmonic voltage to the oppositely polarized layers of the beam. Substantiation is given for a linear control law with a complex coefficient for the electric potential, which provides damping of vibrations in the first symmetric mode at the linear and nonlinear stages of deformation. The stress–strain state and dissipative-heating temperature are studied
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REFERENCES
V. I. Gololobov, "Elastic relations for thin-walled shells with piezoceramic layers," Prikl. Mekh., 20, No. 6, 117–120 (1984).
Ya. M. Grigorenko and A. P. Mukoed, Computer Solution of Linear and Nonlinear Problems for Shells[in Ukrainian], Lybid', Kiev (1992).
V. T. Karnaukhov and I. F. Kirichok, "Thermoelectromechanical behavior of viscoelastic piezoceramic bodies under harmonic excitation," Tepl. Napryazh. Élem. Konstr., 14, 121–126 (1974).
V. T. Karnaukhov and I. F. Kirichok, Coupled Problems in the Theory of Viscoelastic Plates and Shells[in Russian], Naukova Dumka, Kiev (1986).
N. A. Shul'ga and A. M. Bolkisev, Vibrations of Piezoelectric Bodies[in Russian], Naukova Dumka, Kiev (1990).
V. V. Matveev, Damping Vibrations of Solids[in Russian], Naukova Dumka, Kiev (1985).
Yu. N. Shevchenko and I. V. Prokhorenko, The Theory of Elastoplastic Shells under Nonisothermal Loading, Vol. 3 of the five-volume series Methods of Shell Design[in Russian], Naukova Dumka, Kiev (1981).
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).
S. I. Pugachev, Handbook of Piezoceramic Transducers[in Russian], Sudostroenie, Leningrad (1984).
I. K. Senchenkov, Ya. A. Zhuk, G. A. Tabieva, and O. P. Chervinko, "Simplified models of the thermoviscoplastic behavior of bodies under harmonic loading," Prikl. Mekh., 33, No. 9, 24–33 (1997).
Y. Bao, H. S. Tzou, and V. B. Venkayya, "Analysis of non-linear piezothermoelastic laminated beams with electric and temperature effects," J. Sound Vibr., 209, No. 3, 505–518 (1998).
A. Blanguernon, F. Lene, and M. Bernadou, "Active control of a beam using a piezoceramic element," Smart Mater.Struct., 8, 116–124 (1999).
M. Brennan, S. Elliott, and R. Pinnington, "The dynamic coupling between piezoceramic actuators and a beam," JASA, 102, No. 4, 1931–1942 (1997).
E. Crawley and K. Lazarus, "Induced strain actuation of isotropic and anisitropic plates," AIAA J., 29, 944 (1991).
C. Fuller and J. Jones, "Experiments on reduction of propeller induced interior noise by active control of cylinder vibration," J. Sound Vib., 112, 389 (1987).
S. Gopinathan, V. V. Varadan, and V. K. Varadan, "A review and critique of theories for piezoelectric laminates," SmartMater. Struct., 9, 24–48 (2000).
S. Kokorowski, "Analysis of adaptive optical elements made from piezoelectric bimorphs," J. Opt. Soc. Am., 69, 181 (1979).
H. S. Tzou and R. Ye, "Piezothermoelasticity and precision control of piezoelectric systems: Theory and finite element analysis," Trans. ASME, J. Vibr. Acoust., 116, 489–495 (1994).
Ya. A. Zhuk, I. K. Senchenkov, G. A. Tabieva, and O. P. Chervinko, "Axisymmetric vibrations and dissipative heating of a laminated inelastic disk," Int. Appl. Mech., 38, No. 1, 95–102 (2002).
Ya. A. Zhuk and I. K. Senchenkov, "Study of the resonant vibrations and dissipative heating of thin-walled elements made of physically nonlinear materials," Int. Appl. Mech., 38, No. 4, 463–471 (2002).
Ya. A. Zhuk and I. K. Senchenkov, "Approximate model of thermomechanically coupled inelastic strain cycling," Int.Appl. Mech., 39, No. 3, 300–306 (2003).
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Zhuk, Y.A., Senchenkov, I.K. Modelling the Stationary Vibrations and Dissipative Heating of Thin-Walled Inelastic Elements with Piezoactive Layers. International Applied Mechanics 40, 546–556 (2004). https://doi.org/10.1023/B:INAM.0000037302.96867.2c
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DOI: https://doi.org/10.1023/B:INAM.0000037302.96867.2c