Investigation of forced oscillations viscoelastic shells

The paper proposes a new method for solving integral-differential equation of forced oscillations of linear viscoelastic shells built on the basis of the operational calculus for arbitrary hereditary functions at a low viscosity. The solution is built as a series, the first member of which is the solution of this problem, obtained by averaging method and it is shown that at low impacts of amplitude true fluctuations remain finite. Fundamental results that at low frequencies the effect of subsequent terms slightly and they increase with increasing frequency. It is shown that in the particular case of certain values influence the amplitude of the oscillation frequency of the second term is 20-25% of the amplitude of the first term and the amplitude of all the members of the series over time fit exponentially, and the phases are shifted.