Bifurcations in Twinkling Oscillators

2012 ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
High Frequency ◽  
Energy Levels ◽  
Low Frequency ◽  
Degree Of Freedom ◽  
Nonlinear Structure ◽  
High Frequency Oscillations ◽  
Mass Chain ◽  
New Type ◽  
The Masses ◽  
Two Degree Of Freedom

We present the underlying dynamics of snap-through structures that exhibit twinkling. Twinkling occurs when the nonlinear structure is loaded slowly and the masses snap-through, converting the low frequency input to high frequency oscillations. We have studied a nonlinear spring-mass chain loaded by a quasistatic pull. The spring forces are assumed to be cubic with intervals of negative stiffness. Depending on the parameters, the system has equilibria at multiple energy levels. The normal form and the bifurcation behaviors for the single and two degree of freedom systems are studied in detail. A new type of bifurcation, which we refer to as a star bifurcation, has been observed for the symmetric two degree of freedom system, which is of codimension four for the undamped case, and codimension three or two for the damped case, depending on the form of the damping.

“Eclipse” Bifurcation in a Twinkling Oscillator

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Bifurcation Point ◽  
High Frequency ◽  
Low Frequency ◽  
Negative Stiffness ◽  
Symmetric System ◽  
Ambient Vibrations ◽  
High Frequency Oscillations ◽  
Mass Chain

This work regards the use of cubic springs with intervals of negative stiffness, in other words, “snap-through” elements, in order to convert low-frequency ambient vibrations into high-frequency oscillations, referred to as “twinkling.” The focus of this paper is on the bifurcation of a two-mass chain that, in the symmetric system, involves infinitely many equilibria at the bifurcation point. The structure of this “eclipse bifurcation” is uncovered, and perturbations of the bifurcation are studied. The energies associated with the equilibria are examined.

Global “Eclipse” Bifurcation in a Twinkling Oscillator

2013 ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Bifurcation Point ◽  
High Frequency ◽  
Global Bifurcation ◽  
Low Frequency ◽  
Negative Stiffness ◽  
Symmetric System ◽  
Ambient Vibrations ◽  
High Frequency Oscillations ◽  
Mass Chain

This work regards the use of cubic springs with intervals of negative stiffness, in other words “snap-through” elements, in order to convert low-frequency ambient vibrations into high-frequency oscillations, referred to as “twinkling”. The focus of this paper is on a global bifurcation of a two-mass chain which, in the symmetric system, involves infinitely many equilibria at the bifurcation point. The structure of this “eclipse” bifurcation is uncovered, and perturbations of the bifurcation are studied. The energies associated with the equilibria are examined.

Degenerate “Star” Bifurcations in a Twinkling Oscillator

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Normal Form ◽  
Multiple Equilibria ◽  
Degree Of Freedom ◽  
Negative Stiffness ◽  
Nonlinear Spring ◽  
Mass Chain ◽  
New Type ◽  
Two Degree Of Freedom

We have studied a nonlinear spring-mass chain loaded by a quasistatic pull. The spring forces are assumed to be cubic with intervals of negative stiffness. Depending on the parameters, the system has multiple equilibria. The normal form and the bifurcation behaviors for the single- and two-degree-of-freedom systems are studied in detail. A new type of bifurcation, which we refer to as a star bifurcation, has been observed for the symmetric two-degree-of-freedom system. This bifurcation is of codimension-four for the undamped case and codimension-three or two for the damped case, depending on the form of the damping.

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

scholarly journals A Two-Degree-of-Freedom Cantilever-Based Vibration Triboelectric Nanogenerator for Low-Frequency and Broadband Operation

Electronics ◽  
2019 ◽  
Vol 8 (12) ◽  
pp. 1526 ◽  
Author(s):  
Gang Tang ◽  
Fang Cheng ◽  
Xin Hu ◽  
Bo Huang ◽  
Bin Xu ◽  
...  
Keyword(s):  
Output Voltage ◽  
Low Frequency ◽  
Degree Of Freedom ◽  
Triboelectric Nanogenerator ◽  
Energy Harvesters ◽  
Harvesting Technique ◽  
Wide Range ◽  
Operating Bandwidth ◽  
Self Powered ◽  
Two Degree Of Freedom

With the continual increasing application requirements of broadband vibration energy harvesters (VEHs), many attempts have been made to broaden the bandwidth. As compared to adopted only a single approach, integration of multi-approaches can further widen the operating bandwidth. Here, a novel two-degree-of-freedom cantilever-based vibration triboelectric nanogenerator is proposed to obtain high operating bandwidth by integrating multimodal harvesting technique and inherent nonlinearity broadening behavior due to vibration contact between triboelectric surfaces. A wide operating bandwidth of 32.9 Hz is observed even at a low acceleration of 0.6 g. Meanwhile, the peak output voltage is 18.8 V at the primary resonant frequency of 23 Hz and 1 g, while the output voltage is 14.9 V at the secondary frequency of 75 Hz and 2.5 g. Under the frequencies of these two modes at 1 g, maximum peak power of 43.08 μW and 12.5 μW are achieved, respectively. Additionally, the fabricated device shows good stability, reaching and maintaining its voltage at 8 V when tested on a vacuum compression pump. The experimental results demonstrate the device has the ability to harvest energy from a wide range of low-frequency (<100 Hz) vibrations and has broad application prospects in self-powered electronic devices and systems.

A two-degree-of-freedom string-driven rotor for efficient energy harvesting from ultra-low frequency excitations

Energy ◽  
2020 ◽  
Vol 196 ◽  
pp. 117107
Author(s):  
Qinxue Tan ◽  
Kangqi Fan ◽  
Kai Tao ◽  
Liya Zhao ◽  
Meiling Cai
Keyword(s):  
Energy Harvesting ◽  
Low Frequency ◽  
Degree Of Freedom ◽  
Efficient Energy ◽  
Two Degree Of Freedom

Experimental Forced Response Analysis of Two-Degree-of-Freedom Piecewise-Linear Systems With a Gap

2020 ◽  
Author(s):  
Akira Saito ◽  
Junta Umemoto ◽  
Kohei Noguchi ◽  
Meng-Hsuan Tien ◽  
Kiran D’Souza
Keyword(s):  
Piecewise Linear ◽  
Excitation Frequency ◽  
Forced Response ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Phase Portraits ◽  
Response Analysis ◽  
Experimental Setup ◽  
The Masses ◽  
Two Degree Of Freedom

Abstract In this paper, an experimental forced response analysis for a two degree of freedom piecewise-linear oscillator is discussed. First, a mathematical model of the piecewise linear oscillator is presented. Second, the experimental setup developed for the forced response study is presented. The experimental setup is capable of investigating a two degree of freedom piecewise linear oscillator model. The piecewise linearity is achieved by attaching mechanical stops between two masses that move along common shafts. Forced response tests have been conducted, and the results are presented. Discussion of characteristics of the oscillators are provided based on frequency response, spectrogram, time histories, phase portraits, and Poincaré sections. Period doubling bifurcation has been observed when the excitation frequency changes from a frequency with multiple contacts between the masses to a frequency with single contact between the masses occurs.

scholarly journals Recognition of Emotional States using Multiscale Information Analysis of High Frequency EEG Oscillations

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 609 ◽  
Author(s):  
Gao ◽  
Cui ◽  
Wan ◽  
Gu
Keyword(s):  
Emotion Recognition ◽  
High Frequency ◽  
Low Frequency ◽  
Support Vector ◽  
Discrete Wavelet ◽  
Emotional States ◽  
Circumplex Model ◽  
Information Analysis ◽  
Eeg Signals ◽  
High Frequency Oscillations

Exploring the manifestation of emotion in electroencephalogram (EEG) signals is helpful for improving the accuracy of emotion recognition. This paper introduced the novel features based on the multiscale information analysis (MIA) of EEG signals for distinguishing emotional states in four dimensions based on Russell's circumplex model. The algorithms were applied to extract features on the DEAP database, which included multiscale EEG complexity index in the time domain, and ensemble empirical mode decomposition enhanced energy and fuzzy entropy in the frequency domain. The support vector machine and cross validation method were applied to assess classification accuracy. The classification performance of MIA methods (accuracy = 62.01%, precision = 62.03%, recall/sensitivity = 60.51%, and specificity = 82.80%) was much higher than classical methods (accuracy = 43.98%, precision = 43.81%, recall/sensitivity = 41.86%, and specificity = 70.50%), which extracted features contain similar energy based on a discrete wavelet transform, fractal dimension, and sample entropy. In this study, we found that emotion recognition is more associated with high frequency oscillations (51–100Hz) of EEG signals rather than low frequency oscillations (0.3–49Hz), and the significance of the frontal and temporal regions are higher than other regions. Such information has predictive power and may provide more insights into analyzing the multiscale information of high frequency oscillations in EEG signals.

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