This paper presents the results of a numerical study of synchronization of pendulums, chronometers, and mechanical clocks suspended from a common movable beam. An auxiliary problem is considered about the oscillations of a pendulum with a swinging weight, then the mutual synchronization of free vibrations of two and four pendulums (and pendulums with the supply of a moment pulse-clock) on a common movable spring-loaded beam. It is shown that in the considered simplest configuration, mutual synchronization (equality of frequencies or oscillation periods) is performed with high efficiency. The frequency of synchronized oscillations of the pendulums is close to the frequency of vibrations of the platform in a wide range of changes in its rigidity. The degree of connectivity of pendulums and synchronization of their oscillations is determined by the Strouhal number. Synchronization of clocks does not guarantee the accuracy of their movement, which is achieved only when the Strouhal number is equal to one.
One of important problems of closed-loop hydraulic systems is ability of self-oscillations. Linear simulation shows unlimited growth of amplitude, but self-oscillations appear in a real hydraulic drive because of wastages, limits of endurance and oscillation energy. Main purpose of the research is to make a numerical simulation to correspond main parameters of self-oscillations of electro-hydraulic servo drive with characteristics of drive. Results of numerical simulation could be improved with transition to nondimensional variables. In this case several nondimensional complexes present whole hydraulic system instead of many variables and parameters in case of dimensional model. Main result is stability and amplitude of self-oscillations of electro-hydraulic servo drive depends of nondimensional variable Sh, if hydraulic time constant is more than mechanical time constant, then less oscillation energy applies to drive. Simulation model in this research is quite far from real electro-hydraulic servo drive, so improvement of simulation is purpose for the future researches.
A numerical study of the self-oscillation of the Froude friction pendulum is presented. For comparison with approximate analytical or graphical solutions, the cubic approximation is used as one of the approximations of the friction characteristic; changes in the case of other approximations are shown.By results of the conducted computational experiment was built characteristics of the amplitude of self-oscillations from dimensionless ratios, complexes of similarity, which showed the convergence of the estimated and actual (obtained by numerical integration) values of the amplitudes of oscillation for small values of friction and slope characteristics; if you increase the moment amplitude is also increased.It is noted that the results of computer modeling will significantly depend on the design, manufacturing technology and operating conditions of the device in question.
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