Продольные волны в структурно неоднородных вязко-упругих твёрдых телах с квадратично-бимодульной нелинейностью, уменьшающейся с ростом частоты

We study theoretically the propagation of longitudinal acoustic waves in structurally inhomogeneous viscoelastic solids with a quadratic-bimodular nonlinearity decreasing with increasing frequency. Exact solutions for stationary waves propagating without changing their shape are obtained. Analytical and numerical solutions for the evolution of an initially harmonic wave are presented, and amplitude-frequency dependences of nonlinear effects in such media are revealed.