Research on the Stability Threshold and Subharmonic Oscillation in a Parametric Excitation MEMS Resonator

2021 ◽  
Author(s):  
Kuo Lu ◽  
Kai Wu ◽  
Qingsong Li ◽  
Xin Zhou ◽  
Yongmeng Zhang ◽  
...  
Keyword(s):  
Parametric Excitation ◽  
Stability Threshold ◽  
Mems Resonator ◽  
Subharmonic Oscillation ◽  
The Stability

Oscillations of a moderately underexpanded choked jet impinging upon a flat plate

1996 ◽  
Vol 315 ◽  
pp. 267-291 ◽  
Author(s):  
Chih-Yu Kuo ◽  
Ann P. Dowling
Keyword(s):  
Experimental Data ◽  
Flat Plate ◽  
Pressure Ratio ◽  
Feedback Mechanism ◽  
Pressure Waves ◽  
Stagnation Flow ◽  
Stability Threshold ◽  
Shock Position ◽  
The Stability ◽  
Plate Distance

The oscillation of a moderately underexpanded choked jet impinging upon a flat plate is investigated both analytically and numerically. The feedback mechanism between oscillations of the standoff-shock and the plate is clarified. Pressure waves produced by the motion of the shock are reflected by the plate. In addition, oscillations in the shock position lead to downstream entropy fluctuations, which generate pressure waves as they are convected through the stagnation flow near the plate. A linear stability analysis is used to investigate the stability threshold and frequencies of oscillation, as a function of jet pressure ratio and nozzle-to-plate distance. The analytical predictions are compared to results from a numerical simulation and to the experimental data of Powell (1988) and Mørch (1963, 1964).

scholarly journals The Energy Compensation of the HRG Based on the Double-Frequency Parametric Excitation of the Discrete Electrode

Sensors ◽  
2020 ◽  
Vol 20 (12) ◽  
pp. 3549
Author(s):  
Wanliang Zhao ◽  
Hao Yang ◽  
Fucheng Liu ◽  
Yan Su ◽  
Lijun Song
Keyword(s):  
Parametric Excitation ◽  
Dynamical Equation ◽  
Dynamic Performance ◽  
Free Precession ◽  
Double Frequency ◽  
Energy Compensation ◽  
Hemispherical Resonator ◽  
The Stability ◽  
Resonator Vibration ◽  
Excitation Parameters

In this study, for energy compensation in the whole-angle control of Hemispherical Resonator Gyro (HRG), the dynamical equation of the resonator, which is excited by parametric excitation of the discrete electrode, is established, the stability conditions are analyzed, and the method of the double-frequency parametric excitation by the discrete electrode is derived. To obtain the optimal parametric excitation of the resonator, the total energy stability of the resonator is simulated for the evolution of the resonator vibration with different excitation parameters and the free precession of the standing wave by the parametric excitation. In addition, the whole-angle control of the HRG is designed, and the energy compensation of parametric excitation is proven by the experiments. The results of the experiments show that the energy compensation of the HRG in the whole-angle control can be realized using discrete electrodes with double-frequency parametric excitation, which significantly improves the dynamic performance of the whole-angle control compared to the force-to-rebalance.

Determination of the Fluid-Elastic Stability Threshold in the Presence of Turbulence: A Theoretical Study

1989 ◽  
Vol 111 (4) ◽  
pp. 407-419 ◽  
Author(s):  
J. H. Lever ◽  
G. Rzentkowski
Keyword(s):  
Theoretical Study ◽  
Cross Flow ◽  
Elastic Stability ◽  
Mass Ratio ◽  
Response Curves ◽  
Stability Threshold ◽  
Pitch Ratio ◽  
The Stability ◽  
Experimental Findings

A model has been developed to examine the effect of the superposition of turbulent buffeting and fluid-elastic excitation on the response of a single flexible tube in an array exposed to cross-flow. The modeled response curves for a 1.375-pitch ratio parallel triangular array are compared with corresponding experimental data for the same array; reasonably good qualitative agreement is seen. Turbulence is shown to have a significant effect on the determination of the stability threshold for the array, with increasing turbulent buffeting causing a reduction in the apparent critical velocity. The dependence of turbulence response on mass ratio is also found to yield a slight independence between mass and damping parameters on stability threshold estimates, which may account for similar experimental findings. Different stability criteria are compared, and an attempt is made to provide some guidance in the interpretation of response curves from actual tests.

Simultaneous Resonance and Anti-Resonance in Dynamical Systems Under Asynchronous Parametric Excitation

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Artem Karev ◽  
Peter Hagedorn
Keyword(s):  
Dynamical Systems ◽  
Parametric Excitation ◽  
Analytical Method ◽  
Normal Forms ◽  
High Sensitivity ◽  
Combination Resonance ◽  
Concurrent Study ◽  
The Stability ◽  
Analytical Expressions ◽  
Special Case

Abstract Since the discovery of parametric anti-resonance, parametric excitation has also become more prominent for its stabilizing properties. While resonance and anti-resonance are mostly studied individually, there are systems where both effects appear simultaneously at each combination resonance frequency. With a steep transition between them and a high sensitivity of their relative positions, there is a need for a concurrent study of resonance and anti-resonance. The semi-analytical method of normal forms is used to derive approximate analytical expressions describing the magnitude of the stability impact as well as the precise locations of stabilized and destabilized areas. The results reveal that the separate appearance of resonance and anti-resonance is only a special case occurring for synchronous parametric excitation. In particular, in circulatory systems the simultaneous appearance is expected to be much more common.

scholarly journals Buckling analysis of a non-concentric double-walled carbon nanotube

2020 ◽  
Vol 231 (12) ◽  
pp. 5007-5020 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev ◽  
Hamid M. Sedighi
Keyword(s):  
Carbon Nanotubes ◽  
Theoretical Study ◽  
Static Stability ◽  
Governing Equations ◽  
Stability Threshold ◽  
Lennard Jones ◽  
The Stability ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Nonlocal Approach

Abstract On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs.

Dynamic analysis of a microelectromechanical systems resonant gyroscope excited using combination parametric resonance

2006 ◽  
Vol 220 (9) ◽  
pp. 1463-1479 ◽  
Author(s):  
B J Gallacher ◽  
J S Burdess
Keyword(s):  
Perturbation Analysis ◽  
Parametric Excitation ◽  
Microelectromechanical Systems ◽  
Equations Of Motion ◽  
Multiple Time ◽  
Excitation Scheme ◽  
Electrostatically Actuated ◽  
Modes Of Vibration ◽  
The Stability ◽  
Electrostatic Coupling

This paper investigates the application of parametric excitation to a resonant microelectromechanical systems (MEMS) gyroscope. The modal equations of motion of an electrostatically actuated ring are derived and shown to be coupled via the electrostatic stiffness. Such electrostatic coupling between in-plane modes of vibration permits parametric instabilities that may be exploited in a novel excitation scheme. A multiple time scale perturbation method is used to analyse the response of the ring gyroscope to the combination parametric excitations with the principal objective of separating the drive and response frequencies of the ring gyroscope. As pairs of flexural modes of the perfect ring are degenerate, the combination excitation between distinct modes demand the ring to be analysed as a four degree of freedom system. Slight mis-tuning between the otherwise degenerate modes is incorporated in the perturbation analysis. The results of the perturbation analysis are subsequently used to determine the stability boundaries for a typical ring gyroscope when excited using a sum combination resonance between the flexural modes of order 2 and 5. In this case, the ratio of the drive and response frequencies is approximately 10:1. Drive and sense configurations that enable effective parametric excitation of a desired mode are investigated. Simulation of the oscillator scheme is achieved using MATLAB Simulink and this validates the perturbation analysis. Agreement between the models within 10 per cent is demonstrated.

The Effect of Platen Fins on the Flow-Induced Vibrations of an In-Line Tube Array

2001 ◽  
Vol 123 (4) ◽  
pp. 437-441 ◽  
Author(s):  
D. S. Weaver ◽  
S. Ziada ◽  
Z. Sun ◽  
P. Feenstra
Keyword(s):  
Experimental Study ◽  
Vortex Shedding ◽  
Transverse Flow ◽  
Streamwise Direction ◽  
Stability Threshold ◽  
Fluidelastic Instability ◽  
Flow Induced Vibrations ◽  
The Stability

This paper presents the results of an experimental study of the effect of streamwise “platen” fins on the fluidelastic instability of an in-line tube array. The fins are fixed parallel to the axis of the tubes in the streamwise direction and effectively prevent any transverse flow between streamwise tube rows. A geometrically identical, dynamically scaled bundle of finless tubes were used as a datum case for comparison. The results showed that, while the fins eliminate vortex shedding, they enhance the fluidelastic coupling between adjacent tubes and substantially reduce the stability threshold.

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