Study of vibration shock processes of non-linear mechanical systems with distributed parameters - Gavasheli, Levan; Gavasheli, Anri (Annals of Mathematics and Physics, 2024)
In practice, under the conditions of perfection and constructive development of modern equipment and machines, nonlinear mechanical systems with distributed parameters are often encountered, which, depending on the principles of operation, are affected by vibration shock. Therefore, the study of vibration shock processes of the mentioned systems has great theoretical and practical importance and as a result to determine the optimal parameters of vibration protection devices to ensure their safe operation. In our case, the displacement field of two interacting non-linear mechanical systems with distributed parameters is considered, when their interaction is of vibration shock nature. Obviously, the mentioned events are more pronounced when the self-oscillation frequency of one or both systems momentarily approaches the frequency of forced vibration shock processes. In addition, critical moments are fixed during the phase shifts of forced oscillations of oscillatory systems, in this case, the frequencies of forced oscillations approach mutually opposing phase moments. By choosing the optimal parameters of hysteresis losses, it is possible to almost exclude sub-harmonic modes superimposed on the main resonance modes in vibration shock processes. During hysteresis losses of the parabolic type, the value of µ changes automatically in connection with impulsive loads, which will allow us to transfer the vibration shock processes to automatic modes and, accordingly, the practically safe operation of the mentioned systems.