Theory of dynamic processes in mechanical systems and materials of regular structure

Abstract

The theory of vibrations and waves in natural and synthesized materials of regular structure is analyzed. Models based on different averaging and continualization methods are outlined. Emphasis is on periodically inhomogeneous structures. The exact solutions are obtained and analyzed using the closed-form solution of infinite algebraic systems, representing equations in Hamiltonian operator form and solving them based on the theory of differential equations with periodic coefficients, mode selection rule, and methods of drawing wave shapes at limit and arbitrary frequencies