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The analytical solution is obtained for the vibrations and dissipative heating of a hollow piezoceramic sphere polarized across the thickness, with thermal depolarization taken into account. The sphere is subjected to a quasistatic potential difference varying harmonically with time. The inside surface is heat-insulated and the outside surface is involved in convective heat exchange with the environment. A numerical analysis is made and the depolarization conditions and the effect of the depolarized region on the stress–strain state and heating temperature are analyzed.

The results of studying the electromechanical response of thin-walled viscoelastic piezoactive elements under harmonic loading are generalized. The nonlinear electrothermoviscoelastic problem for a harmonically deformed body is formulated in a simplified form with regard for the facts that the mechanical, thermal, and electric fields are coupled, the material is physically nonlinear, and its properties depend on temperature. Classical and refined electromechanical models of single-layer and multilayer shells and plates under general and harmonic loading are reviewed. The models consider that the electromechanical characteristics of the material depend on temperature and physical and geometrical nonlinearities. Methods for solving nonlinear coupled electrothermoviscoelastic problems are discussed. Analytical and numerical solutions are given to specific quasistatic and dynamic electrothermoviscoelastic problems for thin-walled elements such as rods, plates, and shells of various shapes under harmonic electric loading. The effect of dissipation, the temperature dependence of the material properties, and physical and geometrical nonlinearities on the harmonic and parametric vibrations and stability of piezoelectric elements is studied

The paper presents a review of scientific studies on development, of the classical and refined models of the thermomechanical behavior of thin-walled single- and multilayer viscoelastic elements. Allowance is made for the temperature dependence of the properties of the material and physical and geometrical nonlinearities in the case of monoharmonic strain as one of the most typical types of deformation. Methods of solution of nonlinear connected problems of thermoviscoelasticity and results of solution of some specific problems on vibrations and heating-up of thin-walled rods, plates, and shells in quasistatic and dynamic formulations are discussed. A number of thermomechanical effects are noted. They are due to the coupling of mechanical and thermal fields and physical and geometrical nonlinearities, taken into account either separately or jointly.

Abstract: The oscillation and dissipative heating of an infinitely long piezoceramic cylinder polarized along the radius is considered in the case of partial heat depolarization, with harmonic quasi-static loading of the cylinder by a potential difference. The inner surface of the cylinder is thermally insulated; there is heat transfer at the outer surface. An analytical solution is obtained, and numerical calculations are performed for a TsTStBS-2 piezoceramic. The conditions in which the depolarized zone appears are examined, along with the stress-strain state of the cylinder.

Abstract: The paper deals with a conjugate problem of harmonic electromechanical vibrations and dissipative heating of a thin closed spherical and an infinitely long cylindrical piezoelectric shells with allowance for the temperature dependence of the viscoelastic properties and the phenomenon of thermal depolarization. The presence of an acoustic medium inside and outside the shell is taken into account. An explicit expression is derived for the critical electrical load for the case of constant electromechanical characteristics. Using a spherical shell as an example, we study the effect that the frequency of the harmonic load, the geometric parameters, and the external acoustic medium have on the critical electrical load as well as the temperature dependence of the electromechanical properties, including the Curie point, on the temperature-frequency characteristics.

Use of the quasilinearization method is proposed for the solution of coupled dynamic (particularly, quasistatic) problems of thermoviscoelasticity under cyclic loading. The coupled problems under consideration here include vibrations of a one-dimensional body (beam, plate, shell) and shear vibrations of a hollow cylinder made of a material with temperature-dependent properties, with the principle of temperature-time analogy applicable in the latter case. The quasilinearization method is shown to be a fast converging one when applied to the solution of these problems.