Bifurcations of periodic motion in a three-degree-of-freedom vibro-impact system with clearance

2017 ◽  
Vol 48 ◽  
pp. 1-17 ◽  
Author(s):  
Yongbao Liu ◽  
Qiang Wang ◽  
Huidong Xu
Keyword(s):  
Periodic Motion ◽  
Degree Of Freedom ◽  
Impact System ◽  
Three Degree Of Freedom

Symmetry Breaking and Symmetry Increasing in a Vibro-Impact with Symmetric Two-Sided Constraints

2011 ◽  
Vol 66-68 ◽  
pp. 229-234
Author(s):  
Yuan Yue ◽  
Jian Huab Xie
Keyword(s):  
Fixed Point ◽  
Symmetry Breaking ◽  
Numerical Simulations ◽  
Poincaré Map ◽  
Jacobi Matrix ◽  
Degree Of Freedom ◽  
Poincare Map ◽  
Impact System ◽  
Existence Conditions ◽  
Three Degree Of Freedom

A three-degree-of-freedom vibro-impact system with symmetric two-sided constraints is considered. Existence conditions of the symmetric period -2 motion are given, and the symmetric period n-2 motion of the system is deduced analytically. The six dimensional Poincaré map is established, and the Jacobi matrix of the symmetrixc fixed point is obtained. By the numerical simulations, we show that symmetry breaking and symmetry increasing exists in the vibro-impact system with symmetric two-sided constraints.

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.

scholarly journals Development of a Compound Speckle Interferometer for Precision Three-Degree-of-Freedom Displacement Measurement

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1828
Author(s):  
Hung-Lin Hsieh ◽  
Bo-Yen Sun
Keyword(s):  
Speckle Interferometry ◽  
Degree Of Freedom ◽  
Heterodyne Interferometry ◽  
Beam Splitting ◽  
Speckle Interferometer ◽  
Real World Applications ◽  
Three Degree Of Freedom ◽  
Contact Displacement ◽  
Displacement Measurements ◽  
Measurement Capabilities

In this study, a compound speckle interferometer for measuring three-degree-of-freedom (3-DOF) displacement is proposed. The system, which combines heterodyne interferometry, speckle interferometry and beam splitting techniques, can perform precision 3-DOF displacement measurements, while still having the advantages of high resolution and a relatively simple configuration. The incorporation of speckle interferometry allows for non-contact displacement measurements by detecting the phase of the speckle interference pattern formed from the convergence of laser beams on the measured rough surface. Experiments were conducted to verify the measurement capabilities of the system, and the results show that the proposed system has excellent measurement capabilities suitable for future real-world applications.

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