Relations of electroelasticity for piezoceramic shells of revolution

Theoretical analysis on shear-bending deflection of a ring-shape piezoelectric plate

“…A flexure displacement formula for one-dimensional beam equation was firstly derived by Mason. 10 Models of isolated piezoelectric plates were developed by Boriseiko 11 and Antonyak. 12 On this basis, Crawley 13 established an integral models and solutions for isotropic and anisotropic plates with a Rayleigh-Ritz technique.…”

The vibrations of a rotating thin piezoceramic cylindrical shell

“…It has been established that for thin-walled shells with thickness polarization in the presence of electrode coverings the electric field can be determined independently of the solution of the mechanical problem in accordance with (1), that is, by means of the theory of a simple capacitor. The coupling of the fields is expressed in the change in the bending stiffness of the shell and in the supplementary equations of motion due to volume forces uniformly distributed over the thickness of the shell, which represent the action of the interior electric field.…”

“…As is known [1], the basis of applied theories of deformation of thin-walled piezoceramic elements with various types of polarization is Kirchhoff's hypothesis for the mechanical variables and the adequate hypothesis for the electrical variables of a coupled electroelastic field. It has been established that for thin-walled shells with thickness polarization in the presence of electrode coverings the electric field can be determined independently of the solution of the mechanical problem in accordance with (1), that is, by means of the theory of a simple capacitor.…”

“…Since elements made of piezoceramic materials are frequently proposed for practical use [1,2,9], it is reasonable to return to Bryan's problem and carry out a more detailed mathematical a,.~lysis of the solution taking account of assumptions on the perturbation of the vibrations that are feasible in practice and realistic mechanical properties of ceramic materials. As will be seen from the following discussion, such an analysis does not allow us to regard the effect of rotational motion of shells as consistent with the model proposed by Bryan for precession of the normal vibration modes.…”

General dynamic equations of electromagnetomechanics for dielectrics and piezoelectrics

“…The mathematical basis of such studies is the balance equations of continuum mechanics incorporating ponderomotive forces, Maxwell's equations, and the simultaneous equations of state for mechanical and electromagnetic parameters [5,8,9,28,29]. The noninvariance of Maxwell's equations under the Galilean transformations and Michelson's null result (failure to detect the ether wind [11]) resulted in Einstein's special relativity theory, which requires that the mechanical and electromagnetic equations should generally be formulated in relativistic form.Due to the increasing use of piezoelectric materials in technology, static and dynamic problems of electroelasticity have become especially important in solid mechanics [3,4,6,13,19,22,23,29,30]. The original electroelastic equations [3,6] include the static or dynamic equations for an elastic body, the electrostatic equation (acoustic approximation), the equations of state relating the stress tensor and the electric-displacement vector with the strain tensor and electric-field vector, and the Cauchy relations.…”