Axisymmetrical Vibrations and Vibroheating of a Thermoviscoelastic Cylindrical Shell with Piezoactuators and Shear Defor
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International Applied Mechanics, Vol. 56, No. 3, May, 2020
AXISYMMETRICAL VIBRATIONS AND VIBROHEATING OF A THERMOVISCOELASTIC CYLINDRICAL SHELL WITH PIEZOACTUATORS AND SHEAR DEFORMATION TAKEN INTO ACCOUNT* I. F. Kirichok1 and O. A. Chernyushok2
The problem of the forced resonance vibrations and dissipative heating of a hinged thermoviscoelastic cylindrical shell with a piezoelectric actuator with deformation of transverse shear and temperature dependency of electromechanical characteristics taken into account is stated. The influence of temperature, transverse-shear deformation, and heat-exchange conditions on the amplitude- and temperature-frequency characteristics of the forced vibrations of the shell is studied. The thermal failure of the system and possibility of active damping of the bending mode of the vibrations using the piezoelectric actuators are analyzed as well. Keywords: resonance vibrations, dissipative heating, inelastic material, piezoelectric actuators Introduction. Thin-walled elastic cylindrical shells are widely used as load-bearing members of modern engineering. Frequently they are acted upon by intensive harmonic loads with frequency close to resonance. Due to hysteresis losses, the inelastic materials undergo dissipative heating [2, 3]. The resonance vibrations and dissipative heating may cause loss of operating capacity of a member due to fatigue failure, high level of dynamic stresses, vibroheating temperature, etc. To decrease the stress level, deflection amplitudes, and temperature of dissipative heating, the active methods of active damping of forced vibrations of thin-walled structure members are employed along with passive methods. A piezoelectric component is embedded into the structure to act as an actuator after applying voltage to it compensating the mechanical loading [3, 6, 18]. Advances in active control of forced vibrations of structural members with piezoactivators and sensors using an isothermal problem statement are outlined in [6, 8, 9, 17, 18, etc.]. Electromechanical models of laminated thin-walled members made of inelastic passive (without the piezoeffect) and piezoactive materials are considered in [4, 13–16, etc.]. In these publications, the effect of dissipative heating, geometric and physical nonlinearities on their dynamic behavior is studied in detail in solving specific problems [10, 11]. The publications devoted to study of the effect of the vibroheating temperature on the operating capacity of piezoelectric sensors and actuators in damping the forced vibrations of thin-walled beams, plates, and shells made of passive viscoelastic materials are discussed in [12]. The results obtained within the framework of the Kirchhoff–Love classical shell theory in studying the forced vibrations and vibroheating of viscoelastic cylindrical shells and their damping by piezoactive actuators and sensors are considered in [4, 14, 16]. The problem of damping by piezoactuators of a rectangular flexible plate with allowance for transverse-shear deformation was solved by the Bubnov–
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