Abstract
This paper presents a mathematical model of a new multi-striker eccentric shock-vibration mechanism (ESVM) with a crank-sliding bar vibration exciter (CSVE) and an arbitrary number of pistons. Analytical solutions for the parameters of the model are obtained to determine the regions of existence of stable periodic motions. Under the assumption of an absolutely inelastic collision of the piston, we derive equations that single out a bifurcational unattainable boundary in the parameter space, which has a countable number of arbitrarily complex stable periodic motions in its neighborhood. We present results of numerical simulations, which illustrate the existence of periodic and stochastic motions. The methods proposed in this paper for investigating the dynamical characteristics of the new crank-type conrod mechanisms allow practitioners to indicate regions in the parameter space, which allow tuning these mechanisms into the most efficient periodic mode of operation, and to effectively analyze the main changes in their operational regimes when the system parameters are changed.
Highlights
Alongside with shock-vibration mechanisms with unbalance vibration exciters, eccentric shock-vibration mechanisms (ESVM) with a crank-sliding bar vibration exciter (CSVE) [1, 2] have come to be widely used in civil engineering
The work presents a mathematical model of multi-striker ESVM with CSVE with and without account for the motion of the processed medium, describes the structure of the phase space of model and, based on this and using the point mapping method, determines analytical relations for finding in the parameter space the boundaries of the regions of existence and stability of periodical motion modes
Using numerical computations with the help of a software complex developed in the Borland C++ Builder 6, bifurcation diagrams were obtained which make it possible to monitor the main changes of the motion modes of the mechanisms
Summary
Alongside with shock-vibration mechanisms with unbalance vibration exciters, eccentric shock-vibration mechanisms (ESVM) with a crank-sliding bar vibration exciter (CSVE) [1, 2] have come to be widely used in civil engineering. It concerns bifurcations related to the expansion of the phase trajectory of a periodical solution stitched up of separate portions beyond the sub-regions of its definition and having no counterparts in analytical systems In this connection, the work presents a mathematical model of multi-striker ESVM with CSVE with and without account for the motion of the processed medium, describes the structure of the phase space of model and, based on this and using the point mapping method, determines analytical relations for finding in the parameter space the boundaries of the regions of existence and stability of periodical motion modes. Using numerical computations with the help of a software complex developed in the Borland C++ Builder 6, bifurcation diagrams were obtained which make it possible to monitor the main changes of the motion modes of the mechanisms
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