Vibrations of nonlinear elastic lattices: low- and high-frequency dynamic models, internal resonances and modes coupling.

ABSTRACT: We aim to study how the interplay between the effects of nonlinearity and heterogeneity can influence on the distribution and localization of energy in discrete lattice-type structures. As the classical example, vibrations of a cubically nonlinear elastic lattice are considered. In contrast with many other authors, who dealt with infinite and periodic lattices, we examine a finite-size model. Supposing the length of the lattice to be much larger than the distance between the particles, continuous macroscopic equations suitable to describe both low- and high-frequency motions are derived. Acoustic and optical vibrations are studied asymptotically by the method of multiple time scales. For numerical simulations, the Runge-Kutta fourth-order method is employed. Internal resonances and energy

SUBMITTER: Andrianov IV 

PROVIDER: S-EPMC7209152 | biostudies-literature | 2020 Apr

REPOSITORIES: biostudies-literature