ABSTRACT
This chapter analyzes the problems of wave propagation in heterogeneous materials and structures and existing approaches for their effective solutions. It describes general ideas of higher- order homogenization based on a simple case study. The chapter analyzes the relations between numerical and analytical solutions. Composite materials are materials consisting of several components with different physical and mechanical characteristics. Elastic waves of deformations which propagate in the microinhomogeneous composites are typically associated with various effects of nonlinearity, dispersion and dissipation. The ability of forming and propagation of localized nonlinear waves under initial perturbation with conservation of the form and velocity can be employed to detect defects in engineering constructions. Peculiar dynamical features of non-homogeneous medias can be employed while fabricating new materials for various technical applications including antinoise and antivibration layers, vibration dampers, acoustic filters, ultrasonic transmitters and receivers, wave-guides, and so on. Depending on the sources of generation, solid bodies exhibit the following nonlinearities: Geometric, Physical, and Structural.
