Bifurcations of a High-Frequency Horizontally Excited Double Pendulum

2011 ◽  
Author(s):  
Hiroshi Yabuno ◽  
Kazuya Endo
Keyword(s):  
Bifurcation Point ◽  
High Frequency ◽  
Excitation Frequency ◽  
Pitchfork Bifurcation ◽  
Vertical Position ◽  
Double Pendulum ◽  
Bifurcation Phenomena ◽  
Underactuated Manipulator ◽  
High Frequency Excitation ◽  
Frequency Excitation

The bifurcation phenomena produced in a double pendulum under high-frequency horizontal excitation are theoretically and experimentally examined. It has been well known as dynamic stabilization phenomenon that vertical high-frequency excitation can stabilize inverted pendulum. The phenomenon is produced through a sub-critical pitchfork bifurcation. On the other hand, under horizontal high-frequency excitation, the pendulum undergoes a supercritical pitchfork bifurcation and is swung up from the downward vertical position. There have so far been many researches on such dynamics of a single pendulum under the vertical and horizontal high-frequency excitations, but few investigations on multi-degrees-of-freedom system. Also, the utilization of these bifurcations phenomena under the high-frequency excitation is proposed for motion control of underactuated manipulators, but most researches on application is confined to a single pendulum to which a free of two-link underactuated manipulator corresponds. In this paper, toward the development of a three-link underactuated manipulator, we deal with a double pendulum to which two free links of the three-link underactuated manipulator correspond, and theoretically and experimentally investigate bifurcation phenomena in the two pendulums. First, we theoretically predict two pitchfork bifurcation points while increasing the excitation frequency by linear amplitude equations derived using the method of multiple scales. Furthermore, we experimentally examine the swing-up of the pendulums after the first pitchfork bifurcation point and observe that the system has the four types of stable configurations beyond the second pitchfork bifurcation point.

NONLINEAR LOW FREQUENCY WATER WAVES IN A CYLINDRICAL SHELL

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1615-1618 ◽  
Author(s):  
H. W. PENG ◽  
D. J. WANG ◽  
C. B. LEE
Keyword(s):  
High Frequency ◽  
Water Waves ◽  
Water Wave ◽  
Excitation Frequency ◽  
Low Frequency ◽  
Viscous Effect ◽  
First Approximation ◽  
Quantitative Results ◽  
High Frequency Excitation ◽  
Frequency Excitation

The experiment was carried out to study the low frequency surface waves due to the horizontal high frequency excitation. The feature of the phenomenon was that the big amplitude axisymmetric surface wave frequency was typically about 1/50 of the excitation frequency. The viscous effect of water was neglected as a first approximation in the earlier papers on this subject. In contrast, we found the viscosity was important to achieve the low frequency water wave with the cooperation of hundreds of "finger" waves. Photographs were taken with stroboscopic lighting and thereafter relevant quantitative results were obtained based on the measurements with Polytec Scanning Vibrometer PSV 400.

Stabilization of a Buckled Beam by High-Frequency Excitation: Linear Analysis and Experiments

2005 ◽  
Author(s):  
Koji Tsumoto ◽  
Hiroshi Yabuno ◽  
Nobuharu Aoshima
Keyword(s):  
High Frequency ◽  
Control Method ◽  
Compressive Force ◽  
Pitchfork Bifurcation ◽  
Complex Structures ◽  
Stabilization Control ◽  
Buckled Beam ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
The Stability

Beam is one of the fundamental elements in complex structures. It is very significant to clarify its stability under the various circumstances. In particular, the buckling phenomenon, which is characterized as a pitchfork bifurcation, has accepted much interest by many researchers. In this paper, we propose a stabilization control method for the first-mode buckling phenomenon in the clamped-clamped beam without feedback control. We analyze the stability of a buckled beam under high frequency excitation in linear theory. It is theoretically clarified and experimentally that the high-frequency excitation shifts the bifurcation point (the critical compressive force) and prevents the beam buckling.

Performance Simulation and Analysis of New High-Frequency Valve

2011 ◽  
Vol 219-220 ◽  
pp. 1712-1715
Author(s):  
Yong Zhen Zheng ◽  
Ruan Jian ◽  
Yong He
Keyword(s):  
Mathematical Model ◽  
High Frequency ◽  
Excitation Frequency ◽  
Rotary Motion ◽  
Performance Simulation ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Design Idea ◽  
Spool Valve

This article described the design idea, advantages and operation principle of the new high-frequency valve, designed and analyzed its mathematical model. The rotary motion and axial sliding of valve core are used to realize the independence control of excitation frequency and amplitude. The high-frequency excitation can be achieved by increasing in the number of spool table and selecting the matching relationship between the spool and sleeve valve to improve the spool valve cover window grooves and the communication times per revolution.

Swing-Up Control of a Three-Link Underactuated Manipulator by High-Frequency Horizontal Excitation

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Kazuya Endo ◽  
Hiroshi Yabuno
Keyword(s):  
High Frequency ◽  
Multiple Scales ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Averaged Equations ◽  
Underactuated Manipulator ◽  
High Frequency Excitation ◽  
Pitchfork Bifurcations ◽  
The Stability

In the present paper, we consider a three-link underactuated manipulator, the first joint of which is active and the second and third joints of which exhibit passive motion, on a plane inclined at slight angle from horizontal the plane. We analytically investigate changes in the stability of equilibrium points of the free links connected to the passive joints using high-frequency horizontal excitation of the first link. We derive autonomous averaged equations from the dimensionless equations of motion using the method of multiple scales. We clarify that the two free links can be swung up through pitchfork bifurcations and stabilized at some configurations by producing nontrivial and stable equilibrium points due to the high-frequency excitation. Furthermore, it is experimentally verified that increasing the excitation frequency multiplies stable and nontrivial equilibrium points.

scholarly journals Empirical Expression for AC Magnetization Harmonics of Magnetic Nanoparticles under High-Frequency Excitation Field for Thermometry

Nanomaterials ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 2506
Author(s):  
Zhongzhou Du ◽  
Dandan Wang ◽  
Yi Sun ◽  
Yuki Noguchi ◽  
Shi Bai ◽  
...  
Keyword(s):  
Magnetic Nanoparticles ◽  
High Frequency ◽  
Planck Equation ◽  
Magnetization Dynamics ◽  
Excitation Field ◽  
Fokker Planck Equation ◽  
High Frequency Excitation ◽  
Frequency Excitation ◽  
Ac Magnetization ◽  
Fokker Planck

The Fokker–Planck equation accurately describes AC magnetization dynamics of magnetic nanoparticles (MNPs). However, the model for describing AC magnetization dynamics of MNPs based on Fokker-Planck equation is very complicated and the numerical calculation of Fokker-Planck function is time consuming. In the stable stage of AC magnetization response, there are differences in the harmonic phase and amplitude between the stable magnetization response of MNPs described by Langevin and Fokker–Planck equation. Therefore, we proposed an empirical model for AC magnetization harmonics to compensate the attenuation of harmonics amplitude induced by a high frequency excitation field. Simulation and experimental results show that the proposed model accurately describes the AC M–H curve. Moreover, we propose a harmonic amplitude–temperature model of a magnetic nanoparticle thermometer (MNPT) in a high-frequency excitation field. The simulation results show that the temperature error is less than 0.008 K in the temperature range 310–320 K. The proposed empirical model is expected to help improve MNPT performance.

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