Higher order discontinuity mapping for double grazing bifurcations in a slender rigid block confined between side-walls

2022 ◽  
pp. 103915
Author(s):  
Fei Luo ◽  
Zhengdong Du
Keyword(s):  
Higher Order ◽  
Rigid Block ◽  
Discontinuity Mapping ◽  
Side Walls ◽  
Order Discontinuity ◽  
Grazing Bifurcations

scholarly journals Double grazing bifurcations of the non-smooth railway wheelset systems

2021 ◽  
Author(s):  
Pengcheng Miao ◽  
Denghui Li ◽  
Shan Yin ◽  
Jianhua Xie ◽  
Celso Grebogi ◽  
...  
Keyword(s):  
Dynamical Behavior ◽  
Autonomous Systems ◽  
Period Doubling ◽  
Pitchfork Bifurcation ◽  
Railway Vehicle ◽  
Impact Model ◽  
Railway Systems ◽  
Discontinuity Mapping ◽  
Stable Periodic ◽  
Grazing Bifurcations

Abstract There are numerous non-smooth factors in railway vehicle systems, such as flange impact, dry friction, creep force, and so on. Such non-smooth factors heavily affect the dynamical behavior of the railway systems. In this paper, we investigate and mathematically analyze the double grazing bifurcations of the railway wheelset systems with flange contact. Two types of models of flange impact are considered, one is a rigid impact model and the other is a soft impact model. First, we derive Poincaré maps near the grazing trajectory by the Poincaré-section discontinuity mapping (PDM) approach for the two impact models. Then, we analyze and compare the near grazing dynamics of the two models. It is shown that in the rigid impact model the stable periodic motion of the railway wheelset system translates into a chaotic motion after the gazing bifurcation, while in the soft impact model a pitchfork bifurcation occurs and the system tends to the chaotic state through a period doubling bifurcation. Our results also extend the applicability of the PDM of one constraint surface to that of two constraint surfaces for autonomous systems.

Grazing Bifurcations of Initially Quasi-Periodic System Attractors

2001 ◽  
Author(s):  
Harry J. Dankowicz ◽  
Petri T. Piiroinen ◽  
Arne B. Nordmark
Keyword(s):  
Periodic System ◽  
Predictive Power ◽  
Legged Locomotion ◽  
Dimensional Model ◽  
Mapping Approach ◽  
Parameter Variations ◽  
Periodic Attractors ◽  
Discontinuity Mapping ◽  
Low Dimensional ◽  
Grazing Bifurcations

Abstract This paper discusses the dramatic changes in system dynamics that arise as parameter variations lead to the appearance of grazing intersections between periodic and quasi-periodic attractors and state-space discontinuities. In particular, a method based on the discontinuity-mapping approach is employed to predict the effects of near-grazing interactions with the discontinuity surface solely based on information about the discontinuity and the pre-grazing trajectory and requiring no knowledge of the impacting system. An example from the study of legged locomotion is used to illustrate the significance of such grazing bifurcations on the presence of sustained gait in simple anthropomorphic mechanisms. The predictive power of the discontinuity-mapping approach is illustrated on a low-dimensional model example.

Rigid block dynamics confined between side-walls

1994 ◽  
Vol 347 (1683) ◽  
pp. 411-419 ◽  
Keyword(s):  
Nonlinear Equation ◽  
Symmetry Breaking ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Nuclear Industry ◽  
Rigid Block ◽  
Fuel Rods ◽  
Side Walls ◽  
The Stability ◽  
Period Doubling Bifurcations

A rigid block lies on a horizontal surface between two symmetrically placed- walls. Under sinusoidal horizontal excitation, the block can impact both the floor and both side-walls. Periodic orbits are obtained analytically by linking piecewise linear solutions which have as an unknown the time impact difference between the floor and the wall. One nonlinear equation is then obtained in this unknown and solved numerically. The stability of these solutions is also examined. Symmetry-breaking and period-doubling bifurcations are observed. These latter responses can occur with larger than expected impact velocities. This problem has application in the nuclear industry where fuel rods can impact the sides of their containers. The design implication of these results is considered.

scholarly journals Codimension-Two Grazing Bifurcations in Three-Degree-of-Freedom Impact Oscillator with Symmetrical Constraints

2015 ◽  
Vol 2015 ◽  
pp. 1-15
Author(s):  
Qunhong Li ◽  
Pu Chen ◽  
Jieqiong Xu
Keyword(s):  
Periodic Motion ◽  
Mapping Method ◽  
Degree Of Freedom ◽  
Poincaré Mapping ◽  
Impact Oscillator ◽  
Codimension Two ◽  
Poincare Mapping ◽  
Discontinuity Mapping ◽  
Three Degree Of Freedom ◽  
Grazing Bifurcations

This paper investigates the codimension-two grazing bifurcations of a three-degree-of-freedom vibroimpact system with symmetrical rigid stops since little research can be found on this important issue. The criterion for existence of double grazing periodic motion is presented. Using the classical discontinuity mapping method, the Poincaré mapping of double grazing periodic motion is obtained. Based on it, the sufficient condition of codimension-two bifurcation of double grazing periodic motion is formulated, which is simplified further using the Jacobian matrix of smooth Poincaré mapping. At the end, the existence regions of different types of periodic-impact motions in the vicinity of the codimension-two grazing bifurcation point are displayed numerically by unfolding diagram and phase diagrams.

On the motion of a rigid block, tethered at one corner, under harmonic forcing

1992 ◽  
Vol 439 (1905) ◽  
pp. 35-45 ◽  
Keyword(s):  
Period Doubling ◽  
Rigid Block ◽  
Harmonic Forcing ◽  
Wide Range ◽  
Side Walls ◽  
Multiple Impact ◽  
Digital Simulations ◽  
First Time ◽  
Subharmonic Orbits ◽  
Period Doubling Bifurcations

A rigid block, tethered at one corner, is subjected to harmonic forcing. The motion is shown to be equivalent to that of the inverted pendulum impacting one of a pair of asymmetrically placed side-walls. The dynamics of the problem contain subharmonic responses, multiple solutions, period-doubling bifurcations, etc. Stability boundaries are given for a wide range of parameters and orbits are shown to be possible for a large range of forcing amplitudes. Some orbits are possible at forcing amplitudes larger than those in the untethered case. A period- and impact-doubling sequence is shown explicitly for the first time, using digital simulations. Evidence is offered for the existence of more than one type of multiple-impact solution. Large amplitude subharmonic orbits are found.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

Sign in / Sign up

Export Citation Format

Share Document