Investigation of free vibrations of viscoelastic bodies

The method of the solution of problems of free fluctuations of viscoelastic elements of designs from a linear viscoelastic material Is developed at any hereditary kernels. Expressions of frequency and factor of attenuation of viscoelastic fluctuations which an averaging method were approximately received for the first time by the outstanding scientist of the XX century A. A. Ilyyushin and his employees are specified. The method is based to an original approach of calculation of poles of subintegral function in Mellin's formula at any, not set analytically, hereditary kernel of a relaxation. It open a way of application of integrated transformation of Laplas to the solution of non-stationary dynamic problems of a viscoelastic with real rheological properties.