Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Pliska Studia Mathematica Bulgarica, Vol. 25, No 1, (2015), 183p-192p
Piezoelectrical material with heterogeneities of nano-inclusions is considered in the case when it is subjected to time harmonic electro-mechanical load. The model is defined by the system of two partial differential equations and the boundary conditions for the generalized stress. On the exterior boundary, boundary conditions prescribe traction on the part of the boundary and prescribe displacement on the complemented part. We construct Cellular Nonlinear/Nanoscale Network (CNN) architecture for the boundary value problem. The dynamics of the obtained CNN model is studied via harmonic balance method. Traveling wave solutions are obtained numerically. The simulations are provided which illustrate the theoretical results. The obtained results are applicable in the field of non-destructive testing and fracture mechanics of multi-functional materials and structural elements based on them. 2010 Mathematics Subject Classification: 92B20, 74F15, 35K57, 35Q68.