Homogeneous solutions of the electroelasticity equations for piezoceramic layers in R3

Abstract

We present a procedure for the derivation of homogeneous solutions for piezoceramic layers within the framework of electroelasticity. The proposed approach simplifies considerably the Lurié (J Appl Math Mech 6:151–169, 1942) method. Two cases of mechanical boundary-conditions for piezoceramic layers are examined, namely, when the bases are (a) built in, and (b) free from the influence of forces. In both cases, the bases of the layer are assumed to be covered by grounded electrodes. It is shown that in the case of boundary conditions of the first type and for the symmetric, with respect to the mid-surface of the layer, electro-elastic state, the homogeneous solutions do not contain any biharmonic terms. We also calculate the distribution of the characteristic values of the corresponding spectrum problems for every given type of boundary conditions. The derived homogeneous solutions can be used for solving boundary-value problems for piezoceramic cylinders and layers within the framework of electroelasticity. We illustrate our approach through a practical example considering an oblique-symmetric boundary-value problem for layers which weaken due to a side to side elliptic cavity. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/22398