Principal parametric resonances of non-linear mechanical system with two-frequency and self-excitations

The dynamical behavior of a non-linear mechanical system with two degrees of freedom (DOFs) during free and forced excitations is studied analytically and numerically. The non-linearity of the system is represented intentionally by a smooth non-linear simple function with periodically varying stiffness around a constant value for the sake of practical investigations. Analysis of the system leads to a method that could be used to design the non-linear energy sink (NES) so that the behavior of the system during relaxation and its strongly modulated response (SMR) could be improved versus the constant stiffness configuration.

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DYNAMICAL BEHAVIOUR OF THE PLANAR NON-LINEAR MECHANICAL SYSTEM — PART II: EXPERIMENT

Journal of Sound and Vibration ◽

10.1006/jsvi.1999.2245 ◽

1999 ◽

Vol 226 (5) ◽

pp. 941-953 ◽

Cited By ~ 7

Author(s):

M. BOLTEŽAR ◽

N. JAKŠIĆ ◽

I. SIMONOVSKI ◽

A. KUHELJ

Keyword(s):

Mechanical System ◽

Dynamical Behaviour ◽

Non Linear ◽

System Part ◽

Linear Mechanical System

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Neural model of the dynamic behaviour of a non-linear mechanical system

Mechanical Systems and Signal Processing ◽

10.1016/j.ymssp.2008.09.004 ◽

2009 ◽

Vol 23 (4) ◽

pp. 1145-1159 ◽

Cited By ~ 10

Author(s):

Vicky Rouss ◽

Willy Charon ◽

Giansalvo Cirrincione

Keyword(s):

Mechanical System ◽

Dynamic Behaviour ◽

Neural Model ◽

Non Linear ◽

Linear Mechanical System

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A Novel 4D Chaotic System Based on Two Degrees of Freedom Nonlinear Mechanical System

Zeitschrift für Naturforschung A ◽

10.1515/zna-2018-0030 ◽

2018 ◽

Vol 73 (7) ◽

pp. 595-607 ◽

Cited By ~ 3

Author(s):

Sezgin Kacar ◽

Zhouchao Wei ◽

Akif Akgul ◽

Burak Aricioglu

Keyword(s):

Mechanical System ◽

Chaotic System ◽

Degrees Of Freedom ◽

Electronic Circuit ◽

Chaotic Behaviour ◽

Two Degrees Of Freedom ◽

Nonlinear Mechanical System ◽

Linear Mechanical System ◽

Low Amplitude ◽

The Mathematical Model

AbstractIn this study, a non-linear mechanical system with two degrees of freedom is considered in terms of chaos phenomena and chaotic behaviour. The mathematical model of the system was moved to the state space and presented as a four dimensional (4D) chaotic system. The system’s chaotic behaviour was investigated by performing dynamic analyses of the system such as equilibria, Lyapunov exponents, bifurcation analyses, etc. Also, the electronic circuit realisation is implemented as a real-time application. This system exhibited vibration along with noise-like behaviour because of its very low amplitude values. Thus, the system is scaled to increase the amplitude values. As a result, the electronic circuit implementation of the 4D chaotic system derived from the model of a physical system is realised.

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