Harmonic Vibrations of the Simplest Shell Models Loaded with a Periodic System of Localised Masses

The free harmonic vibrations of two types of simplest shells are studied: Bernoulli-Euler beam on Winkler base and Kirchhoff-Love type shell. The axisymmetric vibrations of the latter are considered. Both shells are loaded by a periodic system of localized masses. The exact analytical solution of these problems in the form of Floquet wave is investigated. On the basis of exact analytical solutions, vibration fields, pass bands (PBs), energy fluxes and its components both in the vicinity of localized masses and outside them are analyzed. The influence of the magnitude of the reduced concentrated masses and relative stiffnesses of Winkler base on the nature of the wave processes is analyzed. The effect of attenuation of the energy flux in the first pass band is investigated. Calculations showing that in some cross-sections of the both models it is possible to zero the work of the shear force on displacements of the shells or to zero the work of the moment on rotations of elementary elements of the shells are given. The vibration fields and components of energy fluxes at the boundaries of the transmission bands are particularly investigated.