US1860529A - Electromechanical system - Google Patents
Electromechanical system Download PDFInfo
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- US1860529A US1860529A US443685A US44368530A US1860529A US 1860529 A US1860529 A US 1860529A US 443685 A US443685 A US 443685A US 44368530 A US44368530 A US 44368530A US 1860529 A US1860529 A US 1860529A
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- 230000005684 electric field Effects 0.000 description 11
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- RTZKZFJDLAIYFH-UHFFFAOYSA-N Diethyl ether Chemical compound CCOCC RTZKZFJDLAIYFH-UHFFFAOYSA-N 0.000 description 2
- 239000004020 conductor Substances 0.000 description 2
- 238000013016 damping Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 238000006584 Barton reaction Methods 0.000 description 1
- 229920001800 Shellac Polymers 0.000 description 1
- 229910000831 Steel Inorganic materials 0.000 description 1
- 239000004568 cement Substances 0.000 description 1
- 239000011248 coating agent Substances 0.000 description 1
- 239000002131 composite material Substances 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 239000011888 foil Substances 0.000 description 1
- 239000002184 metal Substances 0.000 description 1
- 238000000034 method Methods 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 238000007747 plating Methods 0.000 description 1
- 239000010453 quartz Substances 0.000 description 1
- ZLGIYFNHBLSMPS-ATJNOEHPSA-N shellac Chemical compound OCCCCCC(O)C(O)CCCCCCCC(O)=O.C1C23[C@H](C(O)=O)CCC2[C@](C)(CO)[C@@H]1C(C(O)=O)=C[C@@H]3O ZLGIYFNHBLSMPS-ATJNOEHPSA-N 0.000 description 1
- 229940113147 shellac Drugs 0.000 description 1
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- VYPSYNLAJGMNEJ-UHFFFAOYSA-N silicon dioxide Inorganic materials O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 239000010959 steel Substances 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
Images
Classifications
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
- H03H9/00—Networks comprising electromechanical or electro-acoustic devices; Electromechanical resonators
- H03H9/15—Constructional features of resonators consisting of piezoelectric or electrostrictive material
- H03H9/17—Constructional features of resonators consisting of piezoelectric or electrostrictive material having a single resonator
Definitions
- the present invention relates to electromechanical systems, and more particularly to alternating-current systems comprising piezo-electric bodies.
- an alternating-current system the frequency of which is substantially the same as the natural frequency of mechanical vibration of the piezo-electric body.
- the piezo-electric body at such frequencies, is set into vibration, and by virtue of its vibrations, it reacts upon the alternating current thus constituting a piezo-electric resonator.
- Fig. l is a diagrammatic view of apparatus constructed according to a preferred embodiment of the present invention.
- Figs. 2, 3 and 4 are similar views of modifications.
- the preferred form of the flexural piezoelectric resonator of the present invention comprises two narrow, flat piezo-electrie plates 1 and 2, preferably out parallel from the same crystal in the manner described in the aforesaid Letters Patent, one of the plates then'being turned side for side and firmly secured to the other plate in such turned position, in face-to-face relation, as by the use of hard wax or cement, like solid brown shellac.
- the piezo-electric plates should preferably be capable of vibrating by the transverse effect; that is, they should tend to become elongated or shortened in a direction perpendicular to the electric field and parallel to their length.
- one of the plates under the action of an electric field, will lengthen while the other Will shorten; when the field is reversed, the one plate shortens, the other lengthens.
- the plates are thus caused to curve slightly, as shown exaggerated, in dotted lines, in Fig. 1.
- the plate will curve first in one direction and then in the other, producing flexural vibrations, whose amplitude will be a maximum when in resonance.
- the frequency of mechanical vibration will be the same as the frequency of the applied alternating voltage.
- the vibrator is thus a fiexural piezo-electric resonator.
- the same efl'ect, though less pronounced, will be obtained if one only of the plates is piezo-electric.
- the other plate may be of a piezo-electrically inactive substance, like steel.
- the crystal be not too difficult to procure, free from flaws and twinning, mechanically strong and durable, of small damping, and that it shall be fairly strongly piezo-electric.
- These qualities are well combined in quartz, but other piezo-electric crystals may be used, or indeed any electro-mechanical system that is capable of being excited into flexural vibrations when stimulated electrically and which shows the converse efi'ect, particularly if elastic.
- the word plate In the following description of the device, wherever the word plate is used, it should be understood that other geometric forms may be employed, so long as the finished structure is capable of becoming bent or flexed in an electric field, and of vibrating flexurally when in an alternating electric field.
- the word flexed will, for brevity, be understood to mean bent in such a manner as to convert a plane surface into a cylindrical surface.
- Conductive coatings 3, 4 are fixed close to the outer surfaces of the resonator, as illustrated more particularly in Fig. 1, separated therefrom by a small air gap. This is preferable to cementing or plating thin conductive coatings directly on to the said outer surfaces, because producing less damping, but cemented or plated coatings may be employed.
- the plates 3, 4 are connected with a source of alternating current by conductors 5, 6, thus causing the coatings to become charged oppositely.
- the frequency of the source is tuned close to that of the natural frequency of fiexural vibration of the resonator, the latter will be flexed back and forth between the dotted-line position shown in Fig. 1, and its opposite.
- the plates will thus be placed under a periodic mechanical strain, causing an alternating electric field to be produced, the direction of which at any instant is the same as that which it would be necessary to apply from without in order to flex the plates in the given direction.
- the electric field thus produced reacts upon the current in the manner described in the aforesaid Letters Patent.
- the fiexural vibrations are of considerable amplitude and their frequency is much lower than that of the longitudinal vibration of a corresponding single crystal plate 1 or 2.
- the frequency of the single plate may, for example, be in the neighborhood of 70,000; and that of the composite vibrator only onetenth as high.
- the frequency may be varied with the length and thickness of the plates, their breadth being without effect, if not too large, except that the electric response is greater, the greater this breadth.
- a wide range 'of frequencies may be obtained by proper choice of the length and thickness of the plates. If frequencies other than the resonant frequency are used, vibrations of smaller amplitude will,of course,be produced.
- the piezoelectric plates 1, 2 are cemented firmly on opposite sides of a thin leaf of conducting material 7, for example, a strip of metal foil.
- the conducting coatlngs 3, 4 are placed close to the outer surfaces of the plates and electrically connected together, for instance by the short wire 8.
- Leads 9 and are attached to the coating7 and the wire 8 in order to connect the resonator to the electric circuit.
- the crystal plates 1, 2 must be so cut and oriented that when an electric field is established between the conducting leaf'7 and the coatings 3, 4, in parallel, one of the plates tends to lengthen while the other tends to become shorter. Then when an alternating field is applied of a uenc approximating the natural frequency of exural vibration, the combination 1, 2, 7 will be set into resonant vibration.
- a fiexural resonator is shown mounted between three pa rs of coatings, 11, 12, 3, 4 and 13, 14, each pair occupying somewhat less than onethird the length of the crystal. Only the coatings 3, 4 are represented in the figure as connected to the source of alternating current, though vibrations could be excited by the use of either of the other two airs or by all three pairs connected in parai l'or series. If all are in parallel, coatin s 11, 4, 13 should be connected together, an' likewise 12, 3, 14, in order to bend the plate as indicated by the dotted line. This mode of vibration is the one whose frequency is (7 /3) or 5.4 times that of the fundamental.
- one end In order to make the fiexural resonator respond at a frequency lower than the fundamental frequency with both ends free, one end ma be ri dly clamped, or otherwise rigidly eld, as lietween massive jaws 15, 16, Fig. 4. In this case, only one end of the resonator is free and the fundamental frequency of fiexural vibration is, according to the well known theory of narrow plates, less than one-sixth of the fundamental frequency of the same resonator when vibrating flexurally with both ends free.
- a musica tone of sufficiently low pitch for the ear to detect, and of very constant frequency may be thus piezo-electrically generated.
- the fiexure resonators described above may be used in the same manner and for the same purposes as the piezo-electric resonators described in the said Letters Patent and in Letters Patent No. 1,472,583, granted October 30, 1923, including those applications in which more than two coatin s are employed.
- An advantage of the flexural form lies in its inherently low frequency in comparison with the frequency of the resonators in which compressional waves are employed.
- An electro-mechanical vibrator comprising two vibrator elements secured together to vibrate as a unit, the elements being adapted to become deformed oppositely under the action of an electric field, and a plurality of pairs of coatings applied to the vibrator and adapted to be energized with alternating current.
- An electro-mechanical vibrator comprising two vibrator elements secured together to vibrate as a unit, the elements being adapted to become deformed oppositely under the action of an alternating electric field, a plurality of pairs of coatings applied to the vibrator, and a source of alternating current connected with each pair of the coat ings.
- a piezo-electric resonator comprising a piezo-electric element composed of a pair of piezo-electric crystal slabs joined to ether in face to face relation, both ends 0 said element bein free to vibrate, and means to impress a. p urality of alternating current fields upon said element whereby to cause the same to vibrate.
- a piezo-electric resonator comprising a body made up of two piezo-electric crystal sections attached together in face to face relation, both ends of said body being free to vibrate, electrodes connected toopposite faces of said body whereby to impress a plurality of alternating current fields upon the same, and alternating current circuit leads connected to said electrodes.
- a piezo-electric resonator comprising a body made up of two piezo-electric crystal sections attached together in face to face relation, a plurality of coatings connected to opposite faces of said body, each of said coatings being of a length less than said body, and means for energizing said pairs of coating so as to impress a plurality of alternating current fields upon said piezo electric crystal sections.
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- Physics & Mathematics (AREA)
- Acoustics & Sound (AREA)
- Piezo-Electric Or Mechanical Vibrators, Or Delay Or Filter Circuits (AREA)
Description
May 31, 1932. w CADY 1,860,529
ELECTROMECHANICAL SYSTEM Original Filed Aug. 1, 1925 INVENTOR WALTER c1 0m BY W44 ATTORNEY Patented,wy 31, 1932 UNITED STATES PATENT OFFICE WALTER G. CADY, OF KIDDLETOWN, CONNECTICUT, ASSIGNOR TO RADIO CORPORATION OF AMERICA, A CORPORATION OF DELAWARE ELECTROIECHANIOAL SYSTEM Original application fled August 1, 1925, Serial No. 47,483. Divided and this application filed April 12, 1930. Serial No. 443,685.
The present invention relates to electromechanical systems, and more particularly to alternating-current systems comprising piezo-electric bodies.
5 This application is a division of an application Serial No. 47,483, filed August 1, 1925,
for electro-mechanical systems, whichhas matured into Patent #1,? 81,680.
In United States Letters Patent No. 1,450,-
246, granted April 3, 1923, there is disclosed an alternating-current system the frequency of which is substantially the same as the natural frequency of mechanical vibration of the piezo-electric body. The piezo-electric body, at such frequencies, is set into vibration, and by virtue of its vibrations, it reacts upon the alternating current thus constituting a piezo-electric resonator. Ordinary piezo-electrie plates or rods, suitably cut from the native crystal, however, have comparatively high natural periods of vibration.
It is therefore an object of the present invention to provide an improved method and s stem of the above-described character that shall operate at comparatively low frequencies.
Other and further objects will be explained hereinafter and will be particularly pointed out in the appended claims.
In the accompanyin drawings, Fig. l is a diagrammatic view of apparatus constructed according to a preferred embodiment of the present invention; and Figs. 2, 3 and 4 are similar views of modifications.
The preferred form of the flexural piezoelectric resonator of the present invention comprises two narrow, flat piezo-electrie plates 1 and 2, preferably out parallel from the same crystal in the manner described in the aforesaid Letters Patent, one of the plates then'being turned side for side and firmly secured to the other plate in such turned position, in face-to-face relation, as by the use of hard wax or cement, like solid brown shellac. The piezo-electric plates should preferably be capable of vibrating by the transverse effect; that is, they should tend to become elongated or shortened in a direction perpendicular to the electric field and parallel to their length. Secured together and oriented in the manner above-described, one of the plates, under the action of an electric field, will lengthen while the other Will shorten; when the field is reversed, the one plate shortens, the other lengthens. The plates are thus caused to curve slightly, as shown exaggerated, in dotted lines, in Fig. 1. In an alternating electric field, therefore, the plate will curve first in one direction and then in the other, producing flexural vibrations, whose amplitude will be a maximum when in resonance. The frequency of mechanical vibration will be the same as the frequency of the applied alternating voltage. The vibrator is thus a fiexural piezo-electric resonator. The same efl'ect, though less pronounced, will be obtained if one only of the plates is piezo-electric. The other plate may be of a piezo-electrically inactive substance, like steel.
For most practical applications, it is naturally of importance that the crystal be not too difficult to procure, free from flaws and twinning, mechanically strong and durable, of small damping, and that it shall be fairly strongly piezo-electric. These qualities are well combined in quartz, but other piezo-electric crystals may be used, or indeed any electro-mechanical system that is capable of being excited into flexural vibrations when stimulated electrically and which shows the converse efi'ect, particularly if elastic.
In the following description of the device, wherever the word plate is used, it should be understood that other geometric forms may be employed, so long as the finished structure is capable of becoming bent or flexed in an electric field, and of vibrating flexurally when in an alternating electric field. The word flexed will, for brevity, be understood to mean bent in such a manner as to convert a plane surface into a cylindrical surface.
If the frequency of the source is tuned close to that of the natural frequency of fiexural vibration of the resonator, the latter will be flexed back and forth between the dotted-line position shown in Fig. 1, and its opposite. The plates will thus be placed under a periodic mechanical strain, causing an alternating electric field to be produced, the direction of which at any instant is the same as that which it would be necessary to apply from without in order to flex the plates in the given direction. The electric field thus produced reacts upon the current in the manner described in the aforesaid Letters Patent.
The fiexural vibrations are of considerable amplitude and their frequency is much lower than that of the longitudinal vibration of a corresponding single crystal plate 1 or 2. The frequency of the single plate may, for example, be in the neighborhood of 70,000; and that of the composite vibrator only onetenth as high. The frequency may be varied with the length and thickness of the plates, their breadth being without effect, if not too large, except that the electric response is greater, the greater this breadth. A wide range 'of frequencies may be obtained by proper choice of the length and thickness of the plates. If frequencies other than the resonant frequency are used, vibrations of smaller amplitude will,of course,be produced.
In the modification of Fig. 2, the piezoelectric plates 1, 2 are cemented firmly on opposite sides of a thin leaf of conducting material 7, for example, a strip of metal foil. The conducting coatlngs 3, 4 are placed close to the outer surfaces of the plates and electrically connected together, for instance by the short wire 8. Leads 9 and are attached to the coating7 and the wire 8 in order to connect the resonator to the electric circuit. The crystal plates 1, 2 must be so cut and oriented that when an electric field is established between the conducting leaf'7 and the coatings 3, 4, in parallel, one of the plates tends to lengthen while the other tends to become shorter. Then when an alternating field is applied of a uenc approximating the natural frequency of exural vibration, the combination 1, 2, 7 will be set into resonant vibration.
While the devices pictured in Figs. 1 and 2 are suitable for an excitation of the fundamental mode of fiexural vibration of the plates, it is possible by using coatings of proper size and located in the right position, to excite various other modes of fiexural vibration whose frequencies, according to the theory of narrow vibrating plates, will be approximately ual to 5 3 z 7 3 2 }9/3) ctc.,times tl1e fundamian tal rcundyi n this connection see Winkelmann, Handbuch der Physik, 1908, Vol. 1, Part 1, page 735; Bartons Textbook on Sound, London 1919, page 281, page 286; Raylei hs Theory of Sound, 2nd Edition, 1894, ol. 1, Figure 28, page 282, Fi ure 29, page 284, Figure 30, page 284. In ig. 3, for example, a fiexural resonator is shown mounted between three pa rs of coatings, 11, 12, 3, 4 and 13, 14, each pair occupying somewhat less than onethird the length of the crystal. Only the coatings 3, 4 are represented in the figure as connected to the source of alternating current, though vibrations could be excited by the use of either of the other two airs or by all three pairs connected in parai l'or series. If all are in parallel, coatin s 11, 4, 13 should be connected together, an' likewise 12, 3, 14, in order to bend the plate as indicated by the dotted line. This mode of vibration is the one whose frequency is (7 /3) or 5.4 times that of the fundamental. In order to cause the crystal to vibrate at a mode having a frequency equal to (5/3) 2 times the fundamental it is merely necessary to properly position a series of plates adjacent to the crystal in ac-' cordance with the principles of the arrangement shown in Fi 3. Thus, for a frequency of (5/3) times t e fundamental, two pairs of coatings are used, and for a frequency of (9/3) times the fundamental, four pairs are used. By using one pair of end coatings alone, it would be possible to excite either the fundamental vibration or a vibration of frequencies either ap roximately (5/3) or (7/3) times the fund iimental frequency, by ap lying an alternating electric field of the rig t frequency.
In the above description, both ends of the resonator have been assumed to be free.
In order to make the fiexural resonator respond at a frequency lower than the fundamental frequency with both ends free, one end ma be ri dly clamped, or otherwise rigidly eld, as lietween massive jaws 15, 16, Fig. 4. In this case, only one end of the resonator is free and the fundamental frequency of fiexural vibration is, according to the well known theory of narrow plates, less than one-sixth of the fundamental frequency of the same resonator when vibrating flexurally with both ends free. By usin sufficiently long and thin plates, a musica tone of sufficiently low pitch for the ear to detect, and of very constant frequency, may be thus piezo-electrically generated.
The fiexure resonators described above may be used in the same manner and for the same purposes as the piezo-electric resonators described in the said Letters Patent and in Letters Patent No. 1,472,583, granted October 30, 1923, including those applications in which more than two coatin s are employed.
An advantage of the flexural form, as stated, lies in its inherently low frequency in comparison with the frequency of the resonators in which compressional waves are employed.
Other modifications will occur to persons skilled in the art, and all such are considered to fall within the spirit and scope of the invention, as defined in the appended claims.
Having thus described my invention, I claim:
1. An electro-mechanical vibrator comprising two vibrator elements secured together to vibrate as a unit, the elements being adapted to become deformed oppositely under the action of an electric field, and a plurality of pairs of coatings applied to the vibrator and adapted to be energized with alternating current.
2. An electro-mechanical vibrator comprising two vibrator elements secured together to vibrate as a unit, the elements being adapted to become deformed oppositely under the action of an alternating electric field, a plurality of pairs of coatings applied to the vibrator, and a source of alternating current connected with each pair of the coat ings.
3. A piezo-electric resonator comprising a piezo-electric element composed of a pair of piezo-electric crystal slabs joined to ether in face to face relation, both ends 0 said element bein free to vibrate, and means to impress a. p urality of alternating current fields upon said element whereby to cause the same to vibrate.
4. A piezo-electric resonator compris ing a body made up of two piezo-electric crystal sections attached together in face to face relation, both ends of said body being free to vibrate, electrodes connected toopposite faces of said body whereby to impress a plurality of alternating current fields upon the same, and alternating current circuit leads connected to said electrodes.
5. A piezo-electric resonator comprising a body made up of two piezo-electric crystal sections attached together in face to face relation, a plurality of coatings connected to opposite faces of said body, each of said coatings being of a length less than said body, and means for energizing said pairs of coating so as to impress a plurality of alternating current fields upon said piezo electric crystal sections.
WALTER G. CADY.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
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US443685A US1860529A (en) | 1925-08-01 | 1930-04-12 | Electromechanical system |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
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US47483A US1781680A (en) | 1925-08-01 | 1925-08-01 | Electromechanical system |
US443685A US1860529A (en) | 1925-08-01 | 1930-04-12 | Electromechanical system |
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US1860529A true US1860529A (en) | 1932-05-31 |
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US443685A Expired - Lifetime US1860529A (en) | 1925-08-01 | 1930-04-12 | Electromechanical system |
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Cited By (14)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US2452571A (en) * | 1933-06-14 | 1948-11-02 | Submarine Signal Co | Sound signaling apparatus |
US2795648A (en) * | 1952-10-17 | 1957-06-11 | Bell Telephone Labor Inc | Dielectric amplifier employing ferroelectric materials |
US3107630A (en) * | 1955-01-31 | 1963-10-22 | Textron Inc | Non-magnetic electro-hydraulic pump |
US3437850A (en) * | 1963-08-19 | 1969-04-08 | Baldwin Co D H | Composite tuning fork filters |
US3474268A (en) * | 1966-04-21 | 1969-10-21 | Gulton Ind Inc | Piezoelectric ceramic transducer |
US3614483A (en) * | 1970-06-24 | 1971-10-19 | Clevite Corp | Width flexural resonator and coupled mode filter |
US3930982A (en) * | 1973-04-06 | 1976-01-06 | The Carborundum Company | Ferroelectric apparatus for dielectrophoresis particle extraction |
US4533186A (en) * | 1983-02-28 | 1985-08-06 | International Business Machines Corporation | Cylindrical type squeeze bearing systems with bearing and driving elements attached in areas of maximum deflection |
US4545625A (en) * | 1983-02-28 | 1985-10-08 | International Business Machines Corporation | Prestressed cylindrical squeeze bearing member |
US4666315A (en) * | 1981-06-12 | 1987-05-19 | International Business Machines Corporation | Planar and cylindrical oscillating pneumatodynamic bearings |
US4685767A (en) * | 1984-02-27 | 1987-08-11 | Matsushita Electric Industrial Co., Ltd. | Fine adjustment apparatus for optical system lens |
US5235238A (en) * | 1989-08-10 | 1993-08-10 | Dainabot Company, Limited | Electrode-separated piezoelectric crystal oscillator and method for measurement using the electrode-separated piezoelectric crystal oscillator |
US5552655A (en) * | 1994-05-04 | 1996-09-03 | Trw Inc. | Low frequency mechanical resonator |
US6563400B2 (en) * | 2000-10-30 | 2003-05-13 | Murata Manufacturing Co., Ltd. | Piezoelectric resonator utilizing bending vibrations and ladder-type filter including the same |
-
1930
- 1930-04-12 US US443685A patent/US1860529A/en not_active Expired - Lifetime
Cited By (14)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US2452571A (en) * | 1933-06-14 | 1948-11-02 | Submarine Signal Co | Sound signaling apparatus |
US2795648A (en) * | 1952-10-17 | 1957-06-11 | Bell Telephone Labor Inc | Dielectric amplifier employing ferroelectric materials |
US3107630A (en) * | 1955-01-31 | 1963-10-22 | Textron Inc | Non-magnetic electro-hydraulic pump |
US3437850A (en) * | 1963-08-19 | 1969-04-08 | Baldwin Co D H | Composite tuning fork filters |
US3474268A (en) * | 1966-04-21 | 1969-10-21 | Gulton Ind Inc | Piezoelectric ceramic transducer |
US3614483A (en) * | 1970-06-24 | 1971-10-19 | Clevite Corp | Width flexural resonator and coupled mode filter |
US3930982A (en) * | 1973-04-06 | 1976-01-06 | The Carborundum Company | Ferroelectric apparatus for dielectrophoresis particle extraction |
US4666315A (en) * | 1981-06-12 | 1987-05-19 | International Business Machines Corporation | Planar and cylindrical oscillating pneumatodynamic bearings |
US4533186A (en) * | 1983-02-28 | 1985-08-06 | International Business Machines Corporation | Cylindrical type squeeze bearing systems with bearing and driving elements attached in areas of maximum deflection |
US4545625A (en) * | 1983-02-28 | 1985-10-08 | International Business Machines Corporation | Prestressed cylindrical squeeze bearing member |
US4685767A (en) * | 1984-02-27 | 1987-08-11 | Matsushita Electric Industrial Co., Ltd. | Fine adjustment apparatus for optical system lens |
US5235238A (en) * | 1989-08-10 | 1993-08-10 | Dainabot Company, Limited | Electrode-separated piezoelectric crystal oscillator and method for measurement using the electrode-separated piezoelectric crystal oscillator |
US5552655A (en) * | 1994-05-04 | 1996-09-03 | Trw Inc. | Low frequency mechanical resonator |
US6563400B2 (en) * | 2000-10-30 | 2003-05-13 | Murata Manufacturing Co., Ltd. | Piezoelectric resonator utilizing bending vibrations and ladder-type filter including the same |
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