Transcript Reed-Resonator Interactions in Reed Organ Pipes

Excitation of Vibrational Eigenstates of Coupled
Microcantilevers Using Ultrasound Radiation Force
ASME 2nd International Conference on
Micro and Nanosystems
Brooklyn, NY August 6, 2008
Thomas M. Huber, Brad Abell, Sam Barthell, Dan Mellema,
Eric Ofstad
Physics Department, Gustavus Adolphus College
Arvind Raman, Matthew Spletzer
Department of Mechanical Engineering, Purdue University
Introduction
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Ultrasound Radiation Force Excitation
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Excitation of microcantilevers using ultrasound radiation force
 Resonance frequency and mode shapes
 Higher order modes
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Selective excitation by phase shift
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Conclusions
Ultrasound Stimulated Radiation Force Excitation
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Vibro-Acoustography
Developed in 1998 at Mayo Clinic
Ultrasound Research Lab by Fatemi &
Greenleaf
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Difference frequency between two
ultrasound sources causes excitation
of object.
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Technique has been used for
imaging in water and tissue, and
mode excitation of objects in air
Modal Excitation Using Ultrasound Radiation Force
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Originally demonstrated in 2004 for Pipe Organ Reeds
 Have since used for ever smaller devices and higher frequencies
Organ Reed
12 mm x 5 mm
100 Hz – 10 kHz
Hard Drive
Suspension
10 mm x 2 mm
Up to 30 kHz
MEMS
Gyroscope
3mm x 0.8mm
18 kHz
Coupled
Microcantilevers
AFM
Microcantilever
0.5 mm x 0.1
0.3 mm x 0.02 mm
Up to 80 kHz
Up to 200 kHz
 The same ultrasound transducer has been used to excite from
100 Hz up to 200 kHz!
Acoustic Radiation Force Excitation
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Consider two sound waves impinging on an object
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Δf =f2 - f1
The dynamic acoustic radiation force on an object is
proportional to the square of the pressure
 P(r,t)=P1(r) sin(2πf1t + φ1) + P2(r) sin(2πf2t + φ2)
 FAcoustic = [ P(r,t)2 / ρc2 ] dr(r) dS
P.J. Westervelt, JASA, 23, 312 (1951)
G. Silva et al, Phys. Rev. E, 71, 056617 (2005)

This radiation force will have component at the
difference frequency Δf
 FDifference = F0 sin [2π Δf t + (φ2 - φ1) ]
Ultrasound Radiation Force Excitation

Suppressed carrier AM signal

Centered at, for example, 450 kHz
Radiation Force Excitation: Advantages
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Non-Contact
Does not have driver resonances and does not excite fixture modes
Wide Bandwidth
 Using our 500 kHz transducer, can excite structures with resonances from
100 Hz to over 200 kHz
Focused
 The transducer used has focal spot of about 2 mm diameter
Capability for selective excitation using multiple transducers
Generation of Excitation Signal

Can also generate a chirp waveform
 For example, fMod=4.5 kHz to 5.5 kHz in 0.6 seconds
 Leads to excitation frequency chirp from 9 kHz to 11 kHz
Radiation Force Excitation: Experimental Setup
Microcantilever Pair using Ultrasound Radiation Force
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Gold Microcantilevers (500 micron by 100 micron, 250 micron separation)
Ultrasound 450 kHz central frequency
 Modulation chirp frequency of 4950 Hz to 5150 Hz
 Difference frequency of 9900 Hz to 10300 Hz
Measure motion using laser Doppler vibrometer
Comparison with scanning probe microsystem (Blue Triangles)
Microcantilever Pair using Ultrasound Radiation Force
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Measure amplitude & phase at
multiple points to determine
operating deflection shapes
2nd Transverse Modes of Au pair (about 60 kHz)
First Torsional Mode of Au Pair (about 87 kHz)
Excitation of AFM Cantilever
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Tipless Silicon AFM Microcantilever (300 micron by 20 micron)
Ultrasound 450 kHz central frequency
 Modulation chirp frequency of 4500 Hz to 6750 Hz
 Difference frequency of 9000 Hz to 13500 Hz
 Smallest structure excited using ultrasound radiation force in air
Excitation using Ultrasound Radiation Force
 Silicon AFM Cantilever (300 micron by 20 micron)
 Vibrometer response using Piezo base excitation (Cyan Triangles)
 Nearly identical frequency response obtained using Ultrasound Excitation
Excitation using Ultrasound Radiation Force
 Silicon AFM Cantilever (300 micron by 20 micron)
 Repeat for 2nd bending mode (72 kHz)
 Ultrasound data taken at single frequencies using lock-in amplifier
Excitation using Ultrasound Radiation Force
 Repeat for 3rd bending mode (204 kHz)
 Highest frequency excited using ultrasound radiation force in air
 Note: Additional peaks in base excitation spectra due to
fixture/piezo resonances
Selective Excitation using Phase-Shifted Pair of Transducers
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Instead of using a single transducer, use a pair of ultrasound transducers to allow
selective excitation
 If radiation force from both transducers are in phase, selectively excites
symmetric mode while suppressing antisymmetric mode
 If radiation force is out of phase, selectively excites antisymmetric mode
while suppressing symmetric mode
 Previously demonstrated for selectively exciting transverse and
torsional modes of cantilevers, and hard drive suspensions
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Phase Shifted Selective Excitation
Adjust amplitudes of two 40 kHz transducers to give roughly equal response
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Phase Shifted Selective Excitation
Adjust amplitudes of two 40 kHz transducers to give roughly equal response
When they are driven together in phase, strong enhancement of the symmetric peak,
while some cancellation of the antisymmetric peak
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Phase Shifted Selective Excitation
Adjust amplitudes of two 40 kHz transducers to give roughly equal response
When they are driven out of phase, strong suppression of the the symmetric peak,
while some enhancement of the antisymmetric peak
Phase Shifted Selective Excitation
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Driving in-phase excites symmetric but suppresses antisymmetric mode
Driving out-of-phase excites antisymmetric while suppressing symmetric mode
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Can differentiate two overlapping modes.
 This capability may be very valuable for coupled cantilevers.
 High mass sensitivity requires weak coupling, but this implies that the symmetric and
antisymmetric would nearly overlap
 By using ultrasound excitation, the symmetric mode can be highly suppressed
Conclusions
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Ultrasound excitation allows non-contact excitation of microcantilever
 Excitation demonstrated up to 200 kHz
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Selective excitation of symmetric versus antisymmetric modes
 Using phase-shifted pair of transducers
 Allows overlapping modes to be individually excited
 May increase sensitivity of mass sensing
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Future possibilities:
 Other MEMS devices
 New transducers should allow about 300 kHz or more of bandwidth
 Excitation of microcantilevers in water
 In-plane excitation
Acknowledgements
Brad Abell, Dan Mellema,
Physics Department, Gustavus Adolphus College
Mostafa Fatemi and James Greenleaf
Ultrasound Research Laboratory, Mayo Clinic and Foundation
This material is based upon work supported by the National Science
Foundation under Grant No. 0509993
Thank You