The Dynamics of Regularized Discontinuous Maps with Applications to Impacting Systems

2010 ◽  
Vol 9 (1) ◽  
pp. 188-219 ◽  
Author(s):  
S. R. Pring ◽  
C. J. Budd
Keyword(s):  
Impacting Systems

Simulation and stability analysis of impacting systems with complete chattering

2009 ◽  
Vol 58 (1-2) ◽  
pp. 85-106 ◽  
Author(s):  
Arne B. Nordmark ◽  
Petri T. Piiroinen
Keyword(s):  
Stability Analysis ◽  
Impacting Systems

Near-Grazing Behaviour of the Harmonic Ocsillator

1999 ◽  
Author(s):  
J. Molenaar ◽  
J. G. de Weger ◽  
W. v. d. Water
Keyword(s):  
Harmonic Oscillator ◽  
Low Speed ◽  
Impact Phenomena ◽  
Grazing Systems ◽  
The Impact ◽  
Grazing Behaviour ◽  
Impacting Systems

Abstract Impacting systems are intrinsically nonlinear. They are found in a great variety of mechanical constructions. The control of the impact phenomena requires a thorough understanding of the dynamics involved. It is discussed that near-grazing systems, i.e. systems in which the impacts take place at low speed, can be described by discrete mappings. The form of this mapping for a harmonic oscillator with a stop is dealt with in detail. It is pointed out how these mappings can be derived and the results are compared to results earlier published. It is indicated how the present results could be checked experimentally.

scholarly journals Experimental and numerical verification of bifurcations and chaos in cam-follower impacting systems

2007 ◽  
Vol 50 (3) ◽  
pp. 409-429 ◽  
Author(s):  
R. Alzate ◽  
M. di Bernardo ◽  
U. Montanaro ◽  
S. Santini
Keyword(s):  
Numerical Verification ◽  
Cam Follower ◽  
Impacting Systems

scholarly journals Vanishing singularity in hard impacting systems

2011 ◽  
Vol 16 (1) ◽  
pp. 319-332 ◽  
Author(s):  
Soumya Kundu ◽  
◽  
Soumitro Banerjee ◽  
Damian Giaouris ◽  
◽  
...  
Keyword(s):  
Impacting Systems

The dynamics of bells as impacting system

2011 ◽  
Vol 225 (10) ◽  
pp. 2436-2443 ◽  
Author(s):  
T Küpper ◽  
H A Hosham ◽  
K Dudtschenko
Keyword(s):  
Research Study ◽  
Double Pendulum ◽  
State Dependent ◽  
Impacting Systems

The dynamics of impacting systems is the topic of this research study. As a familiar example of a simple impacting device, which can be used to demonstrate well-known features, the motion of a bell is analysed. Based on the abstract modelling as a double pendulum with state-dependent impacts given by the strikes of the clapper onto the bell, various forms are derived. In particular, it is shown that the size of the ‘coupling’ between clapper and bell determines the form of the oscillations showing such phenomena as falling or flying clapper, chatter, and the spectacular case of non-ringing which occurred in the case of the famous emperor's bell in the Cathedral of Cologne. Besides the specific results concerning the motion of the bell, the example can serve as a simple illustration of complicated dynamics in the presence of impacts.

Invisible grazings and dangerous bifurcations in impacting systems: The problem of narrow-band chaos

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
Soumitro Banerjee ◽  
James Ing ◽  
Ekaterina Pavlovskaia ◽  
Marian Wiercigroch ◽  
Ramesh K. Reddy
Keyword(s):  
Narrow Band ◽  
Impacting Systems

Singularities in soft-impacting systems

2012 ◽  
Vol 241 (5) ◽  
pp. 553-565 ◽  
Author(s):  
Soumya Kundu ◽  
Soumitro Banerjee ◽  
James Ing ◽  
Ekaterina Pavlovskaia ◽  
Marian Wiercigroch
Keyword(s):  
Impacting Systems
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