Frequency Sweeping With Concurrent Parametric Amplification

2008 ◽  
Author(s):  
Nicholas J. Miller ◽  
Steven W. Shaw
Keyword(s):  
Quality Factor ◽  
Parametric Excitation ◽  
Mechanical Systems ◽  
Parametric Amplification ◽  
Stability Conditions ◽  
Mass Sensor ◽  
Modal Interactions ◽  
Numerical Example ◽  
Mems Mass Sensor ◽  
Frequency Sweeping

In this paper we explore parametric amplification of multidegree of freedom mechanical systems. We consider frequency conditions for modal interactions and determine stability conditions for three important cases. We develop conditions under which it is possible to sweep with direct and parametric excitation to produce a sweep response with amplified effective quality factor of resonances encountered during the sweep. With this technique it is possible to improve the measurement of resonance locations in swept devices, such as those that operate on resonance shifting. A numerical example motivated by a MEMS mass sensor is given in support of the analysis.

Frequency Sweeping With Concurrent Parametric Amplification

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Nicholas J. Miller ◽  
Steven W. Shaw
Keyword(s):  
Parametric Excitation ◽  
Mechanical Systems ◽  
Parametric Amplification ◽  
Stability Conditions ◽  
Mass Sensor ◽  
Frequency Range ◽  
Quality Factors ◽  
Modal Interactions ◽  
Electromechanical Systems ◽  
Frequency Sweeping

In this paper, we explore parametric amplification of multiple resonances in multidegree-of-freedom mechanical systems, and the use of frequency sweeping with a parametric pump to amplify several adjacent resonance peaks. We develop conditions under which it is possible to sweep with direct and parametric excitation to produce a sweep response with amplified effective quality factors for all resonances over a given frequency range. We determine gain and stability conditions and include analysis for potential problematic modal interactions. This technique makes it possible to improve the measurements of resonance locations in devices, for example, sensors that rely on tracking shifts in resonance peaks. The results are demonstrated on a model for a multi-analyte micro-electromechanical systems mass sensor.

Applications of the Theory of Impulsive Parametric Excitation and New Treatments of General Parametric Excitation Problems

1973 ◽  
Vol 40 (1) ◽  
pp. 78-86 ◽  
Author(s):  
C. S. Hsu ◽  
W.-H. Cheng
Keyword(s):  
Parametric Excitation ◽  
Stability Theory ◽  
Mechanical Systems ◽  
General Nature ◽  
Periodic Systems ◽  
Stability Conditions ◽  
Approximate Methods ◽  
Step Functions ◽  
The Stability ◽  
New Treatments

In this paper the stability theory of impulsive parametric excitation developed in [1] is first applied to three mechanical systems. Explicit and exact stability conditions are easily found and some typical stability charts are presented. Also presented in the paper is the use of this theory and a parallel theory involving step functions as approximate methods for treating periodic parametric excitations of more general nature. Exploratory studies along this line have led us to believe that these approximate methods have promise to be very powerful and practical tools for dealing with the stability of general high-order periodic systems.

The Application of Parametric Excitation in MEMS Gyroscopes

2013 ◽  
Author(s):  
Barry J. Gallacher ◽  
Zhongxu Hu ◽  
Kiran Mysore Harish ◽  
Stephen Bowles ◽  
Harry Grigg
Keyword(s):  
Angular Velocity ◽  
Parametric Excitation ◽  
Signal To Noise Ratio ◽  
Parametric Amplification ◽  
Signal To Noise ◽  
Primary Mode ◽  
Harmonic Forcing ◽  
Mode Of Operation ◽  
Mems Gyroscopes ◽  
Secondary Mode

Parametric excitation, via electrostatic stiffness modulation, can be exploited in resonant MEMS gyroscopes. In the case of the Rate gyroscope, which is by far the most common type of MEMS gyro, parametric excitation may be used to amplify either the primary mode of the gyro or the response to the angular rate. Both approaches will be discussed. In the more complex mode of operation, known as “Rate Integrating” the output of the gyro is angle directly as opposed to angular velocity in the case of Rate gyro. In this rate integrating mode of operation parametric excitation does offer an effective energy control used to initiate, sustain the vibration and minimise damping perturbations. Parametric amplification of the primary mode of the rate gyroscope is presented and supported with experimental results. In this implementation parametric excitation is combined with external harmonic forcing of the primary mode in order to reduce electrical feedthrough of the driving signal to the sense electrodes. A practical parametric excitation scheme implemented using Digital Signal Processing has been developed to enable either amplification of the primary mode of the gyroscope or amplification of the response to the applied angular velocity. Parametric amplification of the primary mode of the gyroscope is achieved by frequency tracking and regulation of the amplitudes of the harmonic forcing and parametric excitation to maintain a desired parametric gain by closed loop PID control. Stable parametric amplification of the primary mode by a factor of 20 is demonstrated experimentally. This has important benefits regarding the minimisation of electrical feedthrough of the drive signal to the sense electrodes of the secondary mode. By taking advantage of the phase dependence of parametric amplification and the orthogonality of the Coriolis force and quadrature forcing, the response to the applied angular velocity may be parametrically amplified by applying excitation of a particular phase directly to the sensing mode. The major advantage of parametric amplification applied to MEMs gyroscopes is that it can mechanically amplify the Coriolis response before being picked off electrically. This is particularly advantageous for sensors where electronic noise is the major noise contributor. In this case parametric amplification can significantly improve the signal to noise ratio of the secondary mode by an amount approximately equal to the parametric amplification. Preliminary rate table tests performed in open loop demonstrate a magnification of the signal to noise ratio of the secondary mode by a factor of 9.5.

scholarly journals Parametric Excitation Walking of a Biped Robot Using Counter Weight(Mechanical Systems)

2010 ◽  
Vol 76 (768) ◽  
pp. 2117-2126 ◽  
Author(s):  
Takeshi HAYASHI ◽  
Fumihiko ASANO ◽  
Kazuaki KANEKO ◽  
Zhi-Wei LUO ◽  
Atsuo KATO
Keyword(s):  
Parametric Excitation ◽  
Mechanical Systems ◽  
Biped Robot

Mechanical Domain Parametric Amplification

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Jeffrey F. Rhoads ◽  
Nicholas J. Miller ◽  
Steven W. Shaw ◽  
Brian F. Feeny
Keyword(s):  
Communication Systems ◽  
Mechanical Systems ◽  
Harmonic Signal ◽  
Parametric Amplification ◽  
Electrical Systems ◽  
The Past ◽  
Cantilevered Beam ◽  
Representative System ◽  
Micromechanical Systems ◽  
Systematic Formulation

Though utilized for more than 50years in a variety of power and communication systems, parametric amplification, the process of amplifying a harmonic signal with a parametric pump, has received very little attention in the mechanical engineering community. In fact, only within the past 15–20years has the technique been implemented in micromechanical systems as a means of amplifying the output of resonant microtransducers. While the vast potential of parametric amplification has been demonstrated, to date, in a number of micro- and nanomechanical systems (as well as a number electrical systems), few, if any, macroscale mechanical amplifiers have been reported. Given that these amplifiers are easily realizable using larger-scale mechanical systems, the present work seeks to address this void by examining a simple representative example: a cantilevered beam with longitudinal and transverse base excitations. The work begins with the systematic formulation of a representative system model, which is used to derive a number of pertinent metrics. A series of experimental results, which validate the work’s analytical findings, are subsequently examined, and the work concludes with a brief look at some plausible applications of parametric amplification in macroscale mechanical systems.

Mechanical Domain Parametric Amplification

2007 ◽  
Author(s):  
Jeffrey F. Rhoads ◽  
Nicholas J. Miller ◽  
Steven W. Shaw ◽  
Brian F. Feeny
Keyword(s):  
Communication Systems ◽  
Mechanical Systems ◽  
Harmonic Signal ◽  
Parametric Amplification ◽  
Electrical Systems ◽  
The Past ◽  
Cantilevered Beam ◽  
Representative System ◽  
Micromechanical Systems ◽  
Systematic Formulation

Though utilized for more than fifty years in a variety of power and communication systems, parametric amplification, the process of amplifying a harmonic signal with a parametric pump, has received very little attention in the mechanical engineering community. In fact, only within the past fifteen to twenty years has the technique been implemented in micromechanical systems as a means of amplifying the output of resonant micro-transducers. While the vast potential of parametric amplification has been demonstrated, to date, in a number of micro- and nano-mechanical systems (as well as a number electrical systems), few, if any, macroscale mechanical amplifiers have been reported. Given that these amplifiers are easily realizable using larger-scale mechanical systems, the present work seeks to address this void by examining a simple, representative example: a cantilevered beam with longitudinal and transverse base excitations. The work begins with the systematic formulation of a representative system model, which is used to derive a number of pertinent metrics. A series of experimental results, which validate the work’s analytical findings, are subsequently examined, and the work concludes with a brief look at some plausible applications of parametric amplification in macroscale mechanical systems.

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