Singularities in soft-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.

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

Nonlinear Dynamics ◽

10.1007/s11071-006-9188-8 ◽

2007 ◽

Vol 50 (3) ◽

pp. 409-429 ◽

Cited By ~ 36

Author(s):

R. Alzate ◽

M. di Bernardo ◽

U. Montanaro ◽

S. Santini

Keyword(s):

Numerical Verification ◽

Cam Follower ◽

Impacting Systems

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Vanishing singularity in hard impacting systems

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2011.16.319 ◽

2011 ◽

Vol 16 (1) ◽

pp. 319-332 ◽

Cited By ~ 12

Author(s):

Soumya Kundu ◽

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Soumitro Banerjee ◽

Damian Giaouris ◽

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...

Keyword(s):

Impacting Systems

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Stability of solutions of impacting systems

Lecture Notes in Control and Information Sciences - Nonsmooth Impact Mechanics ◽

10.1007/bfb0027740 ◽

2005 ◽

pp. 223-267

Keyword(s):

Stability Of Solutions ◽

Impacting Systems

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The dynamics of bells as impacting system

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406211413855 ◽

2011 ◽

Vol 225 (10) ◽

pp. 2436-2443 ◽

Cited By ~ 5

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.

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