Dynamical behavior of integro-differential boundary value problem arising in nano-structures via Cellular Nanoscale Network approach

Piezoelectrical solid with nano-holes under time-harmonic anti-plane load is studied in the paper. The model is defined by the system of two partial differential equations and the boundary conditions which define the generalized stress. We reduce the model into an integro-differential boundary value problem and construct Cellular Nanoscale Network (CNN) architecture. Dynamical behavior of the obtained CNN model is studied by means of describing function technique. The simulations are provided which illustrate the theoretical results. The results of this paper are applicable in the field of non-destructive testing and fracture mechanics of multi-functional materials and structural elements based on them.