We analyze a classical problem of oscillations arising in an elastic base caused by rotor vibrations of an asynchronous driver near the critical angular velocity. The nonlinear coupling between oscillations of the elastic base and rotor takes place naturally due to unbalanced masses. This provides typical frequency-amplitude patterns, even let the elastic properties of the base be linear one. As the measure of energy dissipation increases, the effect of bifurcated oscillations can disappear. The latter circumstance indicates the efficiency of using vibration absorbers to stabilize the dynamics of the electromechanical system. The second section of this paper presents results of theoretical studies inspired by the problem of reducing the noise and vibrations by using hydraulic absorbers as dampers to dissipate the energy of oscillations in railway electric equipments. The results of experimental trials over this problem and some theoretical calculations, discussed in the text, are demonstrated the ability to customize the damping properties of hydraulic absorbers to save an electric power and to protect the equipment itself due to utilizing the synchronous modes of rotation of the rotors.

This short contribution considers the essentials of nonlinear wave properties in typical mechanical systems such as an infinite straight bar, a circular ring, and a flat plate. It is found that nonlinear resonance is experienced in all the systems exhibiting continuous and discrete spectra, respectively. Multiwave interactions and the stability of coupled modes with respect to small perturbations are discussed. The emphasis is placed on mechanical phenomena, for example, stress amplification, although some analogies with some nonlinear optical systems are also obvious. The nonlinear resonance coupling in a plate within the Kirchhoff-Love approximation is selected as a two-dimensional example exhibiting a rich range of resonant wave phenomena. This is originally examined by use of Whitham's averaged Lagrangian method. In particular, the existence of three basic resonant triads between longitudinal, shear, and bending modes is shown. Some of these necessarily enter cascade wave processes related to the instability of some mode components of the triad under small perturbations.

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