Abstract
A method is proposed for calculating vibrations of plastic structures with distributed parameters. The frequency dependence of the elastic properties and hysteresis losses of the plastics is taken into account in the calculation. The equation of motion of the system, simplified by a number of transformations and assumptions, is solved asymptotically by the Krylov-Bogolyubov method (Pisarenko method) in the first approximation. Since a rigorous solution with the use of the Krylov-Bogolyubov method proved to be complex, the possibility of taking into account the specific nature of the elastic and damping properties of plastics in such problems by other methods is investigated in this work.
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