Abstract
A mathematical formulation of a new nonlinear problem for active vibration damping (ACD) of thin viscoelastic plates by distributed piezoelectric sensors and actuators is given. The influence of dissipative heating on ACD is considered. The nonlinearity of the problem is caused by the temperature dependence of the material properties and the nonlinearity of the dissipative function. The thermomechanical behavior of the materials under harmonic loading is described by the concept of complex characteristics. Numerical and analytical methods are used for solving this problem. As an example, the influence of dissipative heating on damped axisymmetric bending vibrations of a circular viscoelastic plate is investigated. It is shown that this influence can be significant in the case of ACD of polymeric plates.
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References
Birman V (1996) Thermal effects on measurements of dynamic processes in composite structures using piezoelectric sensors. Smart Mater Struct 5: 379–385
Heidary F, Eslami NR (2005) Pyroelectric effect on dynamic response of coupled distributed piezothermoelastic composite plate. J Therm Stresses 28: 285–300
Tzou HS, Howard RV (1994) A piezothermoelastic thin shell theory applied to active structures. J Vibration Acoust 116: 295–302
Tzou HS, Ye R (1994) Piezothermoelasticity and precision control of piezoelectric systems: theory and finite element analysis. J Vibration Acoust 116: 489–495
Tauchert TR, Ashida F (2003) Control of transient response in intelligent piezothermoelastic strustures. J Therm Stresses 26: 559–582
Lu X, Hanagud SV (2004) Extended irreversible thermodynamics modeling for self-heating and dissipation in piezoelectric ceramics. IEEE Trans Ultrason Ferroelectr Freq Control 51: 1582–1592
Mauk LD, Lynch CS (2003) Thermo-electro-mechanical behavior of ferroelectric materials. Part I: a computational micromechanical model versus experimental results. J Intell Mater Syst Struct 14: 587–602
Mauk LD, Lynch CS (2003) Thermo-electro-mechanical behavior of ferroelectric materials. Part II: Introduction of rate and self-heating effects. J Intell Mater Syst Struct 14: 605–620
Grinchenko VT, Ulitko AF, Shul’ga NA (1989) Electroelasticity. Naukova Dumka, Kiev, p 290
Karnaukhov VG, Kirichok IF (1989) Electrothermoviscoelasticity. Naukova Dumka, Kiev, p 320
Karnaukhov VG (1993) Modeling vibrations and dissipative heating of inelastic bodies. Prikl Mekh 29: 70–76
Karnaukhov VG (1982) Coupled problems of thermoviscoelasticity. Naukova Dumka, Kiev, p 260
Karnaukhov VG, Kirichok IF (1986) Coupled problems of theory of viscoelastic plates and shells. Naukova Dumka, Kiev, p 220
Karnaukhov VG, Mikhailenko VV (2005) Nonlinear thermomechanics of piezoelectric nonelastic bodies under monoharmonic loading. ZTU, Zytomyr, p 428
Tzou HS, Bao Y (1997) Nonlinear piezothermoelasticity and multi-field actuations, part 1. Nonlinear anisotropic piezothermoelastic shell laminates. J Vibration Acoust 119: 374–381
Tzou HS, Zhou YH (1997) Nonlinear piezothermoelasticity and multi-field actuations, part 2. Control of nonlinear deflection, buckling and dynamics. J Vibration Acoust 119: 382–389
Gabbert U, Tzou HS (2001) Smart structures and structronic systems. Kluwer Academic Publication, Dordrecht, p 384
Tani J, Takagi T, Qiu J (1998) Intelligent material systems: applications of functional materials. Appl Mech Rev 51: 505–521
Tzou HS, Bergman LA (1998) Dynamics and control of distributed systems. Cambridge University Press, Cambridge, p 400
Tzou HS (1993) Piezoelectric shells (Distributed sensing and control of continua). Kluwer Academic Publication, Dordrecht, p 400
Karnaukhov VG, Kirichok IF (2000) Forced harmonic vibrations and dissipative heating-up of viscoelastic thin-walled elements. Int Appl Mech 36: 174–196
Karnaukhov VG, Kirichok IF, Kozlov VI (2001) Electromechanical vibrations and dissipative heating of viscoelastic thin-walled piezoelements. Int Appl Mech 37: 182–212
Senchenkov IK, Zhuk Ya A, Karnaukhov VG (2004) Modelling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading. Int Appl Mech 40: 3–34
Karnaukhov VG, Mikhailenko VV (2002) Nonlinear single-frequency vibrations and dissipative heating of inelastic piezoelectric bodies. Int Appl Mech 38: 521–547
Karnaukhov VG (2004) Thermal failure of polymeric structural elements under monoharmonic deformation. Int Appl Mech 40: 3–30
Karnaukhov VG (2005) Thermomechanics of coupled fields in passive and piezoactive inelastic bodies under harmonic deformations. J Therm Stresses 28: 783–815
Grigorenko Ya M, Vasilenko AT (1981) Theory of variable stiffness shells. Naukova Dumka, Kiev, p 544
Mason WP (ed) (1985) Physical acoustics, principles and methods. Properties of polymers and nonlinear acoustics, Vol II. Part B. Academic Press, New York, p 420
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Karnaukhov, V.G., Kirichok, I.F. & Karnaukhov, M.V. The influence of dissipative heating on active vibration damping of viscoelastic plates. J Eng Math 61, 399–411 (2008). https://doi.org/10.1007/s10665-008-9217-3
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DOI: https://doi.org/10.1007/s10665-008-9217-3