Intermittent transition to chaos in vibroimpact system

Abstract

Chaotic behaviour of dynamical systems, their routes to chaos, and the intermittency in particular are interesting and investigated subjects in nonlinear dynamics. The studying of these phenomena in non-smooth dynamical systems is of the special scientists’ interest. In this paper we study the type-III intermittency route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We apply relatively new mathematical tool – continuous wavelet transform CWT – for investigation this phenomenon. We show that CWT applying allows to detect and determine the chaotic motion and the intermittency with great confidence and reliability, gives the possibility to demonstrate intermittency route to chaos, to distinguish and analyze the laminar and turbulent phases.

Compressible Navier-Stokes Equations in Cylindrical Passages and General Dynamics of Surfaces—(I)-Flow Structures and (II)-Analyzing Biomembranes under Static and Dynamic Conditions

“…It is also assumed δ is small but not zero, so that r * will be large. At the end of the paper for computational simplicity we consider θ i = 0 and look at the one term which is maximum in the series in Equation (12). Also Theorem 1 is true when θ i = 0.…”

“…Replacing Equations (11) and (12) in Reference [29], we use new Equations (4)-(9) above, multiplying scale invariant Equations (1)-(3) by Cartesian unit vectors e r * = (1, 0, 0), 2 e θ * = (0, 2, 0) and k = (0, 0, 1) respectively and adding modified equations for Equations (1)-(3) giving the following equations, for the resulting composite vector…”

“…Boundary layer flow over a moving flat plate with second-order velocity slip, injection and applied magnetic field is presented in Reference [11]. Given the nature and highly nonlinear structure of the Navier-Stokes compressible equations, important work has been presented in nonlinear dynamics for the intermittent transition to chaos in a strong nonlinear non-smooth discontinuous system [12]. Gibbs [13] demonstrated that complex vectors are useful in the formulation of complex harmonic motion and referred to them as bivectors.…”

Tracking Control of a Class of Chaotic Systems

“…In this case, the given chaotic system is stabilized. Although some approaches can track arbitrary desired trajectories, most of them only force one state of a given system to an arbitrary desired trajectory [19][20][21]. As far as we know, there are very few published papers about driving some states of a given chaotic system to arbitrary desired periodic orbits, and the designed controllers are too complicated to be utilized in applications.…”

Direct Sailing Variable Acceleration Dynamics Characteristics of Water-Jet Propulsion with a Screw Mixed-Flow Pump

“…Bazhenov et al studied the strongly nonlinear, nonsmooth, and discontinuous dynamic process of a 2-degree of freedom (DOF) two-body vibration system. Amplitude-frequency 2 of 15 response parameters were obtained by controlling the external loading frequency parameter [8][9][10]. Akkerman [11] used smoothed particle hydrodynamics (SPH) to calculate the drag acting on a hull at different speeds and pitch angles, compared it with the experimental conclusions of [12].…”