Homogeneous Solutions of a Skew-Symmetric Problem with Mixed Boundary Conditions for a Piezoceramic Layer

On the basis of a modified scheme of homogeneous solutions significantly simplifying the Lur'e scheme, we construct homogeneous solutions for a piezoceramic layer with mixed boundary conditions imposed on its faces. We consider an electroelastic state skew-symmetric about the median plane of the layer. It is shown that the corresponding homogeneous solutions do not contain biharmonic terms and the components of the conjugate electroelastic field in the layer have the form of Fourier series with respect to the coordinate x₃.