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Abstract
Accuracy of numerical modeling of any discontinuous dynamical system plays an important role in the proper use of the tools applied for its analysis. No less important in this matter is the numerical estimation of the phase trajectories, bifurcation diagrams, and Lyapunov exponents. This paper meets these expectations presenting application of Hénon’s method to obtain good numerical estimations of the stick–slip transitions existing in the Filippov-type discontinuous dynamical systems with dry friction. Subsequent sections are focused on the problem definition, block diagrams of the numerical procedure coded in Python, application of the method that was originally proposed for Poincaré maps, its use in estimation of phase trajectories, bifurcation diagrams of tangent points, and on estimation of the Lyapunov exponents for a selected two-dimensional system with stick–slip effect.
Highlights
In nonsmooth systems it is possible for trajectories to collide with some discontinuity zone in phase space
Paper [8] deals with the techniques for solving ordinary differential equations with essential nonlinearity arising from the representation of frictional force by the sign function of the relative velocity. This problem is connected with dynamic behavior studies of baseisolated structures with dry friction effects
Equation (3) describes the dynamics of the excited vibrations that occur during the dry friction between contacting surfaces of mass m and the movable belt
Summary
In nonsmooth systems it is possible for trajectories to collide with some discontinuity zone in phase space. They are formed on the basis of a sequence of consecutive slides (slips) and sticks of connected to each other and vibrating solid bodies An example of such dynamic analysis of a discontinuous system with two degrees of freedom and friction is found in [10]. Contact friction described by a model of friction existing between the ideal surfaces of cooperating bodies’ is a source of excited stick–slip vibrations Occurrence of such type of vibrations is the cause of exposing by the system of a variety of bifurcations between the stick and slip modes. Paper [8] deals with the techniques for solving ordinary differential equations with essential nonlinearity arising from the representation of frictional force by the sign function of the relative velocity This problem is connected with dynamic behavior studies of baseisolated structures with dry friction effects. A numerical algorithm for the dynamic analysis of base-isolated structures with dry friction has been proposed
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