The construction of a model of frequency independent damping using the amplitude characteristic of the absorption coefficient

Relations are obtained which connect the stresses and strains accompanying oscillations with the absorption coefficient and a procedure for modelling the frequency-independent scattering of energy is constructed based on them. Account is taken of the fact that damping lowers the resonance frequency and the accumulation of residual stresses and strains is not observed during oscillation. The models obtained using this procedure can be employed for any changes, including unsteady changes, in the load with respect to time. The case of a power dependence of the absorption coefficient on the amplitude, which is important in practice, is investigated in detail. The forced, transverse oscillations of a rod are considered as an example. Asymptotic and numerical solutions of the problem are obtained in the single-mode approximation.