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Theoretical Basis of the Structural Modeling Method. A 2D Lattice with Dense Packing of the Particles. A Two-Dimensional Lattice with Non-dense Packing of Particles. Application of the 2D Models of Media with Dense and Non-dense Packing of the Particles for Solving the Parametric Identification Problems. Nonlinear Models of Microstructured Media. A Cubic Lattice of Spherical Particles. Propagation and Interaction of Nonlinear Waves in Generalized Continua. Discussion of the Results. Appendices