Low-frequency vibrations of a high-contrast orthotropic lattice

The study of long-wave propagation in lattices or in composite and layered structures is usually carried out using a single small parameter characterising the ratio of the wavelength to some characteristic size. Ratios of rigidity or density parameters are assumed to be of the order of unity. In reality, this is a multi-parameter problem, and the play of parameters often makes it possible to single out non-trivial limit systems. In particular, for high-contrast composite and layered structures, low-frequency regime, in which stiffer components do not prevent wave propagation across the thickness of weaker ones, has been revealed, in addition to the more traditional global low-frequency regime. This paper is devoted to the investigation of the existence of such regimes for a high-contrast plane orthotropic lattice. The ratios of masses and stiffness's of springs are analysed, under which the existence of in-phase and anti-phase modes of vibrations in the same frequency range is possible.