Synchronization behavior of triple-rotor-pendula system in a dual-super-far resonance system

2018 ◽  
Vol 233 (5) ◽  
pp. 1620-1640 ◽  
Author(s):  
Pan Fang ◽  
Yongjun Hou ◽  
Mingjun Du
Keyword(s):  
Average Method ◽  
Lyapunov Equation ◽  
Mass Ratio ◽  
Resonance System ◽  
Transform Method ◽  
Pendula System ◽  
Generalized Lyapunov Equation ◽  
Frequency Ratios ◽  
Novel Design ◽  
Hurwitz Theorem

In this paper, a novel design for vibrating screens, called the triple-rotor-pendula system, is presented in a dual-super-far resonance system, which makes it possible to produce wanted vibrations with self-adjustable of the synchronization state between unbalanced rotors. To grasp the synchronization characteristics of the system, the dynamics equation of the triple-rotor-pendula system is primarily derived by adopting Lagrange’s equations. Next, the displacement responses of the system in steady state are obtained by Laplace’s transform method. Meanwhile, considering the average method with revised small parameter, the synchronization implement of the system is ascertained on condition that the absolute values of residual electromagnetism torques between two arbitrary motors are less than or equal to their load torque differences. Then, according to Routh–Hurwitz theorem and generalized Lyapunov equation, the criterion of synchronization stability of the system is obtained. Finally, the simulation computations confirm the results of analytical investigations, which show that the theoretical analysis for the synchronization behavior of the triple-rotor-pendula system is feasible. It can be known that the synchronization state of the system is influenced by mass ratio coefficients, structure parameters, rotating directions, and frequency ratios.

A dual-band crossover using cross-shaped microstrip line for small and large band ratios

2017 ◽  
Vol 9 (8) ◽  
pp. 1629-1635 ◽  
Author(s):  
Idury Satya Krishna ◽  
Rusan Kumar Barik ◽  
S. S. Karthikeyan
Keyword(s):  
Insertion Loss ◽  
Matrix Method ◽  
Microstrip Line ◽  
Return Loss ◽  
Dual Band ◽  
Band Ratios ◽  
Form Design ◽  
Frequency Ratios ◽  
Novel Design ◽  
Large Frequency

A novel design of planar dual-band microstrip crossover operating at small and large frequency ratios is presented. These features of the proposed dual-band crossover are achieved by a cross-shaped transmission line. To obtain the dual-band characteristics, the required closed form design formulas are computed using the ABCD matrix method. Based on the design formulas, the realizable small and large band ratios are calculated as 1.65–2.14 and 4.1–8.76, respectively. To validate the computed band ratios, three examples of dual-band crossovers are presented. Finally, two prototypes of dual-band crossover working at smaller and larger frequency ratios are fabricated and tested. The fabricated dual-band crossovers exhibit good return loss and isolation of over 20 dB with minimal insertion loss.

On the discrete generalized Lyapunov equation

Automatica ◽  
1995 ◽  
Vol 31 (2) ◽  
pp. 297-301 ◽  
Author(s):  
Vassilis L. Syrmos ◽  
Pradeep Misra ◽  
Ravi Aripirala
Keyword(s):  
Lyapunov Equation ◽  
Generalized Lyapunov Equation

Experimental Comparisons to Assure the Similarity Between VIM (Vortex-Induced Motion) and VIV (Vortex-Induced Vibration) Phenomena

2011 ◽  
Author(s):  
Rodolfo T. Gonc¸alves ◽  
Ce´sar M. Freire ◽  
Guilherme F. Rosetti ◽  
Guilherme R. Franzini ◽  
Andre´ L. C. Fujarra ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Water Channel ◽  
Analytical Models ◽  
Mass Ratio ◽  
Water Displacement ◽  
Transform Method ◽  
Number Range ◽  
Vortex Induced Vibration ◽  
Low Aspect Ratio ◽  
Induced Motion

Vortex-Induced Motion (VIM) is another way to denominate the Vortex-Induced Vibration (VIV) in floating units. The main characteristics of VIM in such structures are the low aspect ratio (L/D < 4.0) and the unity mass ratio (m* = 1.0, i.e. structural mass equal water displacement). The VIM can occur in MPSO (Monocolumn Production, Storage and Offloading System) and spar platforms. These platforms can experience motion amplitudes of around their characteristic diameters. In such cases, the fatigue life of mooring and riser systems can be greatly reduced. Typically, the VIM model testing campaigns are carried out in the Reynolds range between 200,000 and 400,000. VIV model tests with low aspect ratio cylinders (L/D = 1.0, 1.7 and 2.0) and unity mass ratio (m* = 1.0) have been carried out at the Circulating Water Channel facility available at NDF/EPUSP. The Reynolds number range covered in the experiments was between 10,000 and 50,000. The characteristic motions (in the transverse and in-line direction) were obtained using the Hilbert-Huang Transform method (HHT) and then compared with results obtained in experiments found in the literature. The aim of this investigation is to definitely establish the similarity between the VIM and VIV phenomena, making possible to increase the understanding of both and, at same time, allowing some analytical models developed for VIV to be applied to the VIM scenario on spar and monocolumn platforms, logically under some adaption.

scholarly journals On Spectral Decomposition of States and Gramians of Bilinear Dynamical Systems

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3288
Author(s):  
Alexey Iskakov ◽  
Igor Yadykin
Keyword(s):  
Existence Of Solutions ◽  
Bilinear System ◽  
Lyapunov Equation ◽  
Existence Of A Solution ◽  
Bilinear Control ◽  
Spectral Decompositions ◽  
Generalized Lyapunov Equation ◽  
Controllability And Observability ◽  
Bilinear Equations ◽  
Solution Matrix

The article proves that the state of a bilinear control system can be split uniquely into generalized modes corresponding to the eigenvalues of the dynamics matrix. It is also shown that the Gramians of controllability and observability of a bilinear system can be divided into parts (sub-Gramians) that characterize the measure of these generalized modes and their interactions. Furthermore, the properties of sub-Gramians were investigated in relation to modal controllability and observability. We also propose an algorithm for computing the Gramians and sub-Gramians based on the element-wise computation of the solution matrix. Based on the proposed algorithm, a novel criterion for the existence of solutions to the generalized Lyapunov equation is proposed, which allows, in some cases, to expand the domain of guaranteed existence of a solution of bilinear equations. Examples are provided that illustrate the application and practical use of the considered spectral decompositions.

Transverse Vibrations of a Free Circular Plate Carrying Concentrated Mass

1951 ◽  
Vol 18 (3) ◽  
pp. 280-282
Author(s):  
R. E. Roberson
Keyword(s):  
Laplace Transform ◽  
Mode Shape ◽  
Natural Frequencies ◽  
Mass Ratio ◽  
Concentrated Mass ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Transverse Vibrations ◽  
The Laplace Transform ◽  
Plate Face

Abstract The plate under consideration carries a concentrated mass at its center, which is struck impulsively in a direction perpendicular to the undisturbed plate face. Only circularly symmetric vibrations are considered. The solution is carried out by the use of the Laplace transform method, treating the concentrated mass as a plate-density impulse. The first four natural frequencies are displayed as functions of mass ratio, and the first mode shape is displayed for three mass ratios. The natural frequencies, particularly the higher, are shown to be very sensitive to changes in mass ratio at small values of the concentrated mass.

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