Numerical Investigation of Dynamical Response of Parametrically Excited System with Periodic and Chaotic Motions

2018 ◽  
Vol 2 (7) ◽  
Author(s):  
Falade K. I. ◽  
◽  
Ayodele V. I. ◽  
Baoku I. G. ◽  
◽  
...  
Keyword(s):  
Numerical Investigation ◽  
Dynamical Response ◽  
Chaotic Motions ◽  
Parametrically Excited ◽  
Excited System

scholarly journals Time-Delayed Nonlinear Integral Resonant Controller to Eliminate The nonlinear Oscillations of a Parametrically Excited System

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
N. A. Saeed ◽  
Galal M. Moatimid ◽  
Fawzy M. Elsabaa ◽  
Yomna. Y. Ellabban ◽  
S. K. Elagan ◽  
...  
Keyword(s):  
Nonlinear Oscillations ◽  
Parametrically Excited ◽  
Excited System ◽  
Resonant Controller

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

A Parametrically Broadband Nonlinear Energy Harvester

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Tanju Yildirim ◽  
Mergen H. Ghayesh ◽  
Thomas Searle ◽  
Weihua Li ◽  
Gursel Alici
Keyword(s):  
Energy Harvesting ◽  
Cantilever Beam ◽  
Nonlinear Response ◽  
Energy Harvester ◽  
Shaking Table ◽  
Experimental Investigations ◽  
Dynamical Response ◽  
Parametrically Excited ◽  
Nonlinear Dynamical ◽  
Electrodynamic Shaker

In this work, for the first time, an energy harvester based on the nonlinear dynamical response of a parametrically excited cantilever beam in contact with mechanical stoppers has been fabricated and tested; a 145% increase in the bandwidth at which energy can be effectively harvested has been observed. Experimental and theoretical investigations have been performed in order to assess the increased operating bandwidth of the energy harvester fabricated; for the experimental investigations, an electrodynamic shaker connected to a shaking table has been used to parametrically stimulate the energy harvesting device. Results showed that the parametric energy harvester without stoppers displayed a weak softening-type nonlinear response; however, with the addition of mechanical stoppers the energy harvester displayed a strong hardening-type nonlinear response which is ideal for capturing kinetic energy over larger bandwidths. The addition of mechanical stoppers on a parametrically excited cantilever beam has significant qualitative and quantitative effects on the nonlinear parametric energy harvesting; the energy harvesting bandwidth was increased in the range of 35–145% by adjusting the stoppers.

Response Scenario and Nonsmooth Features in the Nonlinear Dynamics of an Impacting Inverted Pendulum

2005 ◽  
Vol 1 (1) ◽  
pp. 56-64 ◽  
Author(s):  
Stefano Lenci ◽  
Lucio Demeio ◽  
Milena Petrini
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Investigation ◽  
Inverted Pendulum ◽  
Numerical Results ◽  
Dynamical Response ◽  
Global Bifurcations ◽  
Bifurcation Diagrams ◽  
Local And Global Bifurcations ◽  
And Behavior

In this work, we perform a systematic numerical investigation of the nonlinear dynamics of an inverted pendulum between lateral rebounding barriers. Three different families of considerably variable attractors—periodic, chaotic, and rest positions with subsequent chattering—are found. All of them are investigated, in detail, and the response scenario is determined by both bifurcation diagrams and behavior charts of single attractors, and overall maps. Attention is focused on local and global bifurcations that lead to the attractor-basin metamorphoses. Numerical results show the extreme richness of the dynamical response of the system, which is deemed to be of interest also in view of prospective mechanical applications.

Chaotic Motions of a Parametrically Excited Pendulum With Non-Exponentially Small Parameters

2005 ◽  
Author(s):  
Chunqing Lu
Keyword(s):  
Poincaré Map ◽  
Poincare Map ◽  
Chaotic Motions ◽  
Parametrically Excited ◽  
Small Parameters ◽  
Exponentially Small

The paper mathematically proves that a pendulum with oscillatory forcing makes chaotic motions for certain parameters. The method is more intuitive than using the Poincare’ map. It provides more information about when the chaos occurs.

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