Investigation of the propagation of free waves in a rod in the design of building structures

This article investigates the dispersion dependences of waves propagating in a system consisting of an elastic rod immersed in a linear elastic medium. The phase velocities of a wave with a length λ, which propagate under stationary conditions, are investigated. It was found that for a sufficiently small η (a/λ), i.e., for relatively large wavelengths, no waves can propagate in the system under stationary conditions, i.e. there are critical values of η below which no real values of the phase velocity are possible.