Study on propagation regularity of harmonic waves in periodic structures of beams

The wide application of elements with periodic configuration in dynamically loaded structures stimulates a study of the propagation phenomenon of harmonic waves in mechanical systems of a periodic structure. The absolute majority of investigations of the wave propagation phenomenon in periodic structures concern one-dimensional and quasi-one-dimensional systems. Therefore, it is of certain interest to study the regularities in the distribution of the "transparency windows" of a mechanical system of a periodic structure with continuously changing parameters, which can be obtained by passing through the limit from the corresponding system with the threshold-type irregularities. Besides, the non-homogeneity in these systems is of a discrete, i.e. threshold type. The article presents the research results of propagation of harmonic waves along unfixed beams of a periodic structure. In addition two beam configurations are considered: with a constant cross section in individual segments and a continuous change in the cross section along the beam axis. The solution of the two problems has been made on the basis of the Floquet theory. As a result of the solution of this problem, frequency bands of the waves for both types of beams were found, and a comparative analysis of their propagation was carried out.