U -sequence in electrostatic microelectromechanical systems (MEMS)

2006 ◽  
Vol 462 (2075) ◽  
pp. 3435-3464 ◽  
Author(s):  
Sudipto K De ◽  
N.R Aluru
Keyword(s):  
Microelectromechanical Systems ◽  
Dynamic Properties ◽  
Electrostatic Force ◽  
Period Doubling ◽  
Chaotic State ◽  
Electrostatic Mems ◽  
Nonlinear Dynamic Properties ◽  
Mass Spring ◽  
Intermittent Chaos ◽  
Period Doubling Bifurcations

In this paper, the presence of U (Universal)-sequence (a sequence of periodic windows that appear beyond the period doubling (PD) route to chaos) in electrostatic microelectromechanical systems (MEMS) is reported. The MEM system is first brought to a nonlinear steady state by the application of a large dc bias close to the dynamic pull-in voltage of the device. An ac voltage (the bifurcation parameter) is next applied to the system and increased gradually. A sequence of PD bifurcations leading to chaos is observed for resonant and superharmonic excitations (frequency of the ac voltage). On further increase in the ac voltage (beyond where chaos sets in), U -sequence is observed in the system. Under superharmonic excitation, the sequence is found to be a modified form of the U -sequence referred to as the ‘ UM -sequence’ in this paper. The appearance of a periodic window with K oscillations per period or K -cycles in the normal U -sequence is replaced by a corresponding periodic window with KM -cycles in the UM -sequence. M stands for the M th superharmonic frequency of excitation. The formation of the periodic windows from a chaotic state in the UM -sequence takes place through intermittent chaos as the ac voltage is gradually increased. On the other hand, the periodic states/cycles formed through intermittent chaos transform back into a chaotic state through the period doubling route. A sequence of period doubling bifurcations of the UM -sequence cycles result in the formation of -cycles in electrostatic MEMS. n corresponds to the n th period doubling bifurcation in the sequence. A simplified mass–spring–damper (MSD) model for MEMS is used to understand the physical mechanism that gives rise to these nonlinear dynamic properties in MEMS. The nonlinear nature of the electrostatic force acting on the MEM device is found to be responsible for the reported observations.

The Characteristic Parameter Estimation of Low Temperature Target Weak Signal Based on VanderPol-Duffing System

2013 ◽  
Vol 347-350 ◽  
pp. 706-710
Author(s):  
Yan Chun Xu ◽  
Dan Feng Zhao ◽  
Mi Lu
Keyword(s):  
Turning Point ◽  
Dynamic Properties ◽  
Dynamic Performance ◽  
Period Doubling ◽  
Characteristic Parameter ◽  
System Dynamic ◽  
Weak Signal ◽  
Chaotic State ◽  
Duffing System ◽  
Periodic Signals

The weak signal, which is usually submerged in strong noise, is very difficult to detecte for its amplitude and frequency. The dynamic properties of VanderPol-Duffing are studied in this paper. Such system can go into the chaos under certain parameters. In chaotic state the disturbance of weak periodic signals can make the system dynamic behavior change dramatically. Our research results show that the system is from period doubling state to chaotic state when the amplitude of input signal is changed. And it has a remarkable impact influence on the system dynamic performance when the input frequency is varied. The unknown frequency can be detected through counting the numbers of turning point in phase diagram. The simulation results verified that the presented method is feasible and there are a lot of theory values in the research.

Dynamic Analysis of MEMS Resonators Under Primary-Resonance Excitation

2005 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Mohammad I. Younis ◽  
Eihab M. Abdel-Rahman
Keyword(s):  
Dynamic Analysis ◽  
Microelectromechanical Systems ◽  
Initial Conditions ◽  
Electrostatic Force ◽  
Primary Resonance ◽  
Period Doubling ◽  
Resonance Excitation ◽  
Global Dynamics ◽  
Mems Resonators ◽  
Primary Resonance Excitation

We present a dynamic analysis and simulation of electrically actuated microelectromechanical systems (MEMS) resonators under primary-resonance excitation. We use a shooting technique, perturbation techniques, and long-time integration of the equation of motion to investigate the global dynamics of the resonators. We study the dynamic pull-in instability and show various scenarios and mechanisms for its occurrence. Our results show that dynamic pull-in can occur through a saddle-node bifurcation, a period-doubling bifurcation, or homoclinic tangling, depending on factors such as the initial conditions of the device and the level of the electrostatic force.

scholarly journals Identification of Dynamic Parameters of Pedestrian Walking Model Based on a Coupled Pedestrian–Structure System

2021 ◽  
Vol 11 (14) ◽  
pp. 6407
Author(s):  
Huiqi Liang ◽  
Wenbo Xie ◽  
Peizi Wei ◽  
Dehao Ai ◽  
Zhiqiang Zhang
Keyword(s):  
Negative Correlation ◽  
Dynamic Properties ◽  
Damping Ratio ◽  
Field Testing ◽  
The Body ◽  
Structural Vibration ◽  
Pedestrian Dynamics ◽  
Structure Interaction ◽  
Mass Spring ◽  
Stiffness And Damping

As human occupancy has an enormous effect on the dynamics of light, flexible, large-span, low-damping structures, which are sensitive to human-induced vibrations, it is essential to investigate the effects of pedestrian–structure interaction. The single-degree-of-freedom (SDOF) mass–spring–damping (MSD) model, the simplest dynamical model that considers how pedestrian mass, stiffness and damping impact the dynamic properties of structures, is widely used in civil engineering. With field testing methods and the SDOF MSD model, this study obtained pedestrian dynamics parameters from measured data of the properties of both empty structures and structures with pedestrian occupancy. The parameters identification procedure involved individuals at four walking frequencies. Body frequency is positively correlated to the walking frequency, while a negative correlation is observed between the body damping ratio and the walking frequency. The test results further show a negative correlation between the pedestrian’s frequency and his/her weight, but no significant correlation exists between one’s damping ratio and weight. The findings provide a reference for structural vibration serviceability assessments that would consider pedestrian–structure interaction effects.

scholarly journals Can short time delays influence the variability of the solar cycle?

2010 ◽  
Vol 6 (S271) ◽  
pp. 288-296
Author(s):  
Laurène Jouve ◽  
Michael R. E. Proctor ◽  
Geoffroy Lesur
Keyword(s):  
Solar Cycle ◽  
Convection Zone ◽  
Mean Field ◽  
Period Doubling ◽  
Temporal Modulation ◽  
Solar Convection Zone ◽  
Flux Tubes ◽  
Solar Convection ◽  
Short Time ◽  
Period Doubling Bifurcations

AbstractWe present the effects of introducing results of 3D MHD simulations of buoyant magnetic fields in the solar convection zone in 2D mean-field Babcock-Leighton models. In particular, we take into account the time delay introduced by the rise time of the toroidal structures from the base of the convection zone to the solar surface. We find that the delays produce large temporal modulation of the cycle amplitude even when strong and thus rapidly rising flux tubes are considered. The study of a reduced model reveals that aperiodic modulations of the solar cycle appear after a sequence of period doubling bifurcations typical of non-linear systems. We also discuss the memory of such systems and the conclusions which may be drawn concerning the actual solar cycle variability.

Bifurcations and Chaos in a Minimal Neural Network: Forced Coupled Neurons

2021 ◽  
Vol 31 (10) ◽  
pp. 2150147
Author(s):  
Yo Horikawa
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Period Doubling ◽  
Output Function ◽  
Piecewise Constant ◽  
Border Collision Bifurcations ◽  
Saddle Node ◽  
Periodic Input ◽  
Symmetric Periodic Solution ◽  
Period Doubling Bifurcations

The bifurcations and chaos in a system of two coupled sigmoidal neurons with periodic input are revisited. The system has no self-coupling and no inherent limit cycles in contrast to the previous studies and shows simple bifurcations qualitatively different from the previous results. A symmetric periodic solution generated by the periodic input underdoes a pitchfork bifurcation so that a pair of asymmetric periodic solutions is generated. A chaotic attractor is generated through a cascade of period-doubling bifurcations of the asymmetric periodic solutions. However, a symmetric periodic solution repeats saddle-node bifurcations many times and the bifurcations of periodic solutions become complicated as the output gain of neurons is increasing. Then, the analysis of border collision bifurcations is carried out by using a piecewise constant output function of neurons and a rectangular wave as periodic input. The saddle-node, the pitchfork and the period-doubling bifurcations in the coupled sigmoidal neurons are replaced by various kinds of border collision bifurcations in the coupled piecewise constant neurons. Qualitatively the same structure of the bifurcations of periodic solutions in the coupled sigmoidal neurons is derived analytically. Further, it is shown that another period-doubling route to chaos exists when the output function of neurons is asymmetric.

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

scholarly journals Chaotic dynamics of a pulse modulated control system for a heating unit

2018 ◽  
Vol 224 ◽  
pp. 02055
Author(s):  
Yuriy A. Gol’tsov ◽  
Alexander S. Kizhuk ◽  
Vasiliy G. Rubanov
Keyword(s):  
Control System ◽  
Differential Equations ◽  
Chaotic Dynamics ◽  
Period Doubling ◽  
Classical Period ◽  
Nonlinear Phenomena ◽  
Pulse Control ◽  
Heating Unit ◽  
Border Collision Bifurcation ◽  
Period Doubling Bifurcations

The dynamic modes and bifurcations in a pulse control system of a heating unit, the condition of which is described through differential equations with discontinuous right–hand sides, have been studied. It has been shown that the system under research can demonstrate a great variety of nonlinear phenomena and bifurcation transitions, such as quasiperiodicity, multistable behaviour, chaotization of oscillations through a classical period–doubling bifurcations cascade and border–collision bifurcation.

Nonlinear Dynamic Properties of the Pancreas and Liver

1973 ◽  
Vol 6 (4) ◽  
pp. 503-508
Author(s):  
Richard N. Bergman ◽  
Richard J. Bucolo
Keyword(s):  
Nonlinear Dynamic ◽  
Dynamic Properties ◽  
Nonlinear Dynamic Properties
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