SOLID BODY OSCILLATIONS UNDER THE INFLUENCE OF GROUP VIBRATION LOADS - Ikhtierovich, Boltaev Zafar; brohimovich, Safarov IsmoilI; Razzokovich, RuzievTulkin (International Journal of Psychosocial Rehabilitation, 2020)
The article considers oscillations of a dissipative mechanical system with a finite number of degrees of freedom when exposed to group vibration loads. As an example, a dissipative mechanical system with two degrees of freedom is considered. The considered bodies are mounted on viscoelastic supports whose rigidity is described by the integral Boltzmann – Walter relations.The resulting integro-differential equations are solved by the method of complex amplitudes of the theory of oscillations (or analytically).Investigated before the resonance, resonance and after resonance regions of the mechanical system under consideration. Found by the condition in the form of inequality when self-synchronization occurs. With sufficient maximum possible values of the vibrational moments, self-synchronization can take place even in the case when the partial angular velocities differ significantly from one another. Knowing the distribution law of a random variable, we can calculate the probability of inequality, that is, the probability of the presence of self-synchronization. It has been established that for sufficient maximum possible values of the vibrational moments, self-synchronization can take place even in the case when the partial angular velocities differ significantly from one another. It was also determined that the amplitude of the basement oscillations decreases by a factor of five compared with the amplitude of oscillations in the absence of self-synchronization. Thus, the mathematical formulation and methods for solving the problem of dynamic stability of a viscoelastic mechanical system with a finite number of degrees of freedom are developed. Comparison of calculated values with known results. Taking into account the viscous properties of the material has a noticeable effect on the areas of dynamic stability. Viscous properties play a stabilizing factor for parametric oscillations of mechanical systems. Geometrically, the sizes of the regions of dynamic instability corresponding to the main parametric resonances are reduced and shifted above the abscissa axis.