US3560771A

US3560771A - Acoustically active resonator

Info

Publication number: US3560771A
Application number: US822639A
Authority: US
Inventors: Hugh M Baker Jr
Original assignee: HB ENG CORP
Current assignee: HB ENG CORP; HB ENGINEERING CORP
Priority date: 1966-07-15
Filing date: 1969-05-07
Publication date: 1971-02-02
Anticipated expiration: 1988-02-02

Abstract

An acoustically active resonator is provided having relatively large surface area parts in order to efficiently couple the movement of the oscillating parts to the surrounding atmosphere. In most of the disclosed embodiments, the oscillating parts are disposed about the periphery of the resonator in order to maximize the surface area producing the air compression and rarefaction. A web interconnects the midpoint of the oscillating elements to transmit motion of the web into predictable motion of the oscillating elements. Means are also provided for moving the web at the resonant frequency of the resonator.

Description

llmted States latent 1 1 3,560,771

| 2 Inventor Hugh M. Baker..1r. 1 5 Ref rence Ci d a 2 2 2 3 UNITED STATES PATENTS E l): No Ma; 7 1969 261668] 1 1/1952 Morrow A l 73/505 3.030.606 4/1962 Harris 0 3 l0/9.1X Pmemed 128" 692 11/1966 T 310 83X [73] Assignec HB Engineering Corporation umer Montgomery County Md. 3.311.761 3/1967 Schloss .1 3l0/9.lX a corporation of Maryland 3.360.664 1../1967 Straube l 310/8.2 Continuation-impart of application Ser. No. Prinmry Examiner Milton 0. Hirshfield 714,221, Mar. 19, 1968, now Patent No. Assistant ExaminerMark O. Budd 3,453,462. Attorney-G. Turner Moller ABSTRACT: An acoustically active resonator is provided having relatively large surface area parts in order to efficiently couple the movement of the oscillating parts to the surrounding atmosphere. In most of the disclosed embodiments, the

[54] 3 i3 I L RESONATOR oscillating parts are disposed about the periphery of the alms rawmg resonator in order to maximize the surface area producing the [52] U.S.Cl 310/8.2, air compression and rarefaction. A web interconnects the 310/9.1. 310/9.4 midpoint of the oscillating elements to transmit motion of the [51] Int. Cl H04r 17/00 web into predictable motion of the oscillating elements. Field of Search 310/ Means are also provided for moving the web at the resonant 8.2, 8.3, 8.5, 8.6, 9.1. 9.6; 73/505, (lnquired) frequency ofthe resonator.

PATENTEI] FEB 2 I97! SHEET 2 0F 2 INVENTOR HUGH M. BAKER, JR.

FIG. IO

ACOUSTICALLY ACTIVE RESONATOR CROSS-REFERENCE TO RELATED APPLICATIONS This application is a continuation-in-part of application Ser. No. 7 [4.22] entitled Resonator, filed Mar. I9. I968. now US. Pat. No. 345,462.

BACKGROUND OF THE INVENTION This invention relates to acoustically active resonators and particularly to acoustically active resonators of high mechanical efficiency which may be designed to efficiently couple with the surrounding environment.

It is apparent that any conventional electromechanical resonator can be made acoustically active by making the vibrating element of sufficient size to adequately impart alternate compression and rarefaction to the surrounding atmosphere. Thus, the resonant frequency of a conventional tuning fork can be heard if the tuning fork is relatively large and if it is placed relatively close to the car. It is equally apparent that electronic resonators, such as an LC network, cannot be made acoustically active merely by an increase in size since there is no element in contact with the air that undergoes vibration.

Although conventional mechanical resonators can be acoustically active, e.g. the tuning forks of a piano tuner, such devices are of low mechanical efficiency and are not highly selective.

SUMMARY OF THE INVENTION In accordance with the invention, a relatively compact acoustically active resonator is provided by positioning oscillating elements in a peripheral fashion with a web interconnecting the oscillating elements for transmitting motion of the web into predictable motion of the oscillating parts. Means are provided for moving the web at the resonant frequency of the resonator. Means are also provided for supporting the resonator, preferably at a nodal point.

In several embodiments of the invention, the peripherally disposed oscillating elements have relatively large surface areas to provide an efficient couple with the surrounding environment, e.g. air, water or other fluid, while providing a highly efficient device. In accordance with another embodiment of the invention, the web is used to acoustically couple with the environment, while the peripherally disposed parts are used to assist in mounting of the resonator.

It is accordingly an object of the invention to provide an acoustically active resonator comprising a plurality of peripherally disposed oscillating elements interconnected by a web to produce predictable motion of the elements.

Another object of the invention is to provide an acoustically active resonator comprising a plurality of peripherally disposed oscillating elements acoustically coupled with the surrounding environment.

A further object of the invention is to provide an acoustically active resonator having a plurality of peripherally disposed parts interconnected by a web of relatively large surface area in which the web assumes alternate concave and convex configurations to couple with the environment.

Other objects and advantages of the invention will be apparent from a study of the specification following, taken with the drawing which together describes and discloses preferred embodiments of this invention and what is now believed to be the best mode of practicing the principles thereof. Still other embodiments may be apparent to those having the benefit of the teachings herein, and such other modifications or equivalents are intended to be reserved especially as they fall within the scope and breadth of the subjoined claims.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. I is a side elevational view of one embodiment of the invention;

FIG. 2 is a top plan view of the embodiment of FIG. 1;

FIG. 3 is a vertical cross-sectional view of the embodiment of FIGS. 1 and 2 taken substantially along line 3-3 of FIG. 2;

FIG. 4 is a vertical cross-sectional view of another embodiment ofthe invention:

FIG. 5 is a vertical cross-sectional view of yet another embodiment of the invention;

FIG. 6 is a plan view of still another embodiment of the invention',

FIG. 7 is a side elevational view of the embodiment of FIG. 6, certain parts being broken away for clarity of illustration;

FIG. 8 is a schematic view of the embodiment of FIGS. 6 and 7 illustrating the various parts at rest and at the completion of one-half cycle of operation;

FIG. 9 is another schematic view of the embodiment of FIGS. 6 and 7 illustrating the position of the various components at rest and at the completion of one complete cycle of operation; and

FIG. 10 is a cross-sectional view of still another embodiment of the invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS Reference is made to FIGS. 1-3 wherein there is shown a resonator 10 having as major components support means 12. a plurality of oscillating elements 14, a web 16 and means 18 for moving the web at the resonant frequency of the resonator.

The support means 12 comprises a base 20 which may be placed on or secured to a suitable underlying framework and an upstanding column 22 secured to a nodal point of the web 16 as more fully explained hereinafter.

As shown best in FIG. 2, the oscillating elements 14 are peripherally disposed such that the external surfaces 24 of the elements 14 define the major part of the perimeter of a geometric solid. In the embodiment shown in FIGS. 1-3, the resonator 10 is cylindrical, although polygonal external configurations may also be used.

In the embodiment of FIGS. l3, the coupling between the environment, which for purposes of discussion is assumed to be air, and the resonator is through the oscillating elements 14. If the oscillating elements 14 comprised a single structural unit, such as a tube, exceedingly large forces would be required to expand and contract the tube in order to obtain alternate compression and rarefaction of the atmosphere. In order to make each of the oscillating elements 14 independently movable and thereby decrease the rigidity of the oscillating parts taken as a whole, a gap 26 is provided between the adjacent oscillating elements 14. Since the size of the gaps 26 is small compared to the size of the external surfaces 24, the efficiency of the acoustical coupling of the resonator 10 is only slightly degraded below the acoustical coupling between a geometric solid of the same size. The gaps 26 should accordingly be as small as practicable, although large enough to prevent physical contact between the adjacent oscillating elements 14, as where a thermally expansible material comprises the oscillating elements 14. It will accordingly be seen that the oscillating elements define an annular body, by which is meant a ring-shaped body, independent of the cross-sectional shape thereof.

Most applications using an acoustically active resonator are better performed by a resonator having a thermally independent resonant frequency. Since the therrnal frequency response of a resonator is a rather complex interrelation between the thermal coefficient of expansion, the thermal coefficient of elasticity and the particular design of the resonator, it is not unlikely that a given resonator would include parts which expand upon increase in temperature. It is also possible, of course, to make the oscillating elements 14 from materials having a minimal volume change in response to increasing temperature.

The oscillating elements 14 also include an inner surface 26 to which the web 16 is secured. The junction between the web 16 and the oscillating elements 14 is preferably adjacent the center of mass thereof, which in a symmetrical element, is adacent the midpoint for several reasons. First. if the junction is away from the midpoint of the elements 14. radial expansion of the web 16 will produce complex and perhaps unpredictable reactions in the elements 14. Second. the oscillating elements 14 and the web 16 are preferably machined from a single piece of material and a central junction is convenient for manufacturing reasons.

As shown in FIG. 3. the oscillating elements 14 are illustrated as olsufficient flexibility to flex at the resonant frequency of the resonator 10. A center line 30 illustrates the center of the elements 14 at rest while the solid arcuate line 32 illustrates, in an exaggerated fashion, the center of the oscillating elements 14 at one-half cycle of operation. A dotted line 34 illustrates. again in exaggerated fashion. the centerline of the oscillating elements 14 at the completion of another half cycle of operation. Whether a given element 14 will flex or not is dependent on the rigidity of the element 14 and the force applied by the expanding web 16. The rigidity of the element 14 is. of course, a function of the material used, the distance between the center point of the element 14 and the end thereof, and the thickness of the element 14.

The web 16 is sufficiently thin to be capable of radial expansion and contraction under the influence of the driving means 18 which is preferably a piezoelectric wafer energizable through a pair of wires 36. The connection between the supporting column 22 and the web 16 is preferably at the center of the web 16, and defines the nodal point thereof. Consequently, it is desirable to position the piezoelectric wafer 18 concentrically with respect to the column 22 for optimum functioning. It is preferable that the wafer 18 be larger than the area of connection between the column 22 and the web 16. In this embodiment, the resonant frequency of the elements 14 is substantially less than the resonant frequency of the web 16.

In the operation of the embodiment of FIGS. 13, energization of the piezoelectric wafer 18 with voltage of a predetermined polarity expands the piezoelectric wafer 18 to radially expand the web 16 in the direction shown by the solid arrows in FIG. 3. As the outer periphery of the web 16 moves radially, that portion of the oscillating elements 14 immediately adjacent the web 16 moves in a similar radial fashion. The outer ends of the oscillating elements 14 lag the central part thereof to produce the outwardly concave configuration indicated by the solid centerline 32. Application of a voltage of opposite polarity to the wires 36 contracts the piezoelectric wafer 18 as indicated by the dotted arrows in FIG. 3. The radial contraction of the piezoelectric wafer 18 produces radial contraction of the web 16. The center of the oscillating elements 14 follows the radial contraction of the web 16 while the outer ends of the elements 14 lag the center part thereof to produce the outwardly concave configuration indicated by the dotted centerline 34.

The rapid reversal of polarity applied to the piezoelectric wafer 18 at a frequency substantially equal to the resonant frequency of the oscillating elements 14 produces sufficient air compression and rarefaction adjacent the oscillating elements 14 to produce an acoustically active resonator.

The devices of the invention conveniently operate within the nominal audible range of 20 to 20,000 cycles per second so that more or less conventional microphones may be used to receive emanations from the resonators of the invention. It is within the realm of the invention, however, to provide the resonant frequency of the device above or perhaps below the audible range. It should be noted that the resonator may be energized by a sound wave at its resonant frequency thereby delivering an output from the piezoelectric wafer 18. Consequently, the resonators of the invention can be used as frequency selective microphones. It is immaterial in at least this situation whether the resonant frequency of the device is within the normal audible band.

Referring now to FIG. 4, a resonator 110 is illustrated. For purposes of brevity, analogous reference characters will be used to indicate analogous elements, most of which will not be specifically discussed. As will be apparent. substantially the only difference between the embodiment of FIG. 4 and the embodiment of FIGS. 1-3 lies in the change in cross-sectional shape of the oscillating elements 114 and the resultant change in areal extent of the web 116. The oscillating elements 114 are sufficiently rigid at the resonant frequency of the device so as not 'to flex under motion imparted thereto by the web 116. Upon energization of the piezoelectric wafer 118 to expand the web 116. each of the oscillating elements moves outwardly to a position indicated in an exaggerated fashion by the solid centerline 132. Application of an opposite polarity voltage to the piezoelectric crystal 118 contracts the web 116 and moves the oscillating elements 114 inwardly as exaggeratedly indicated by the dashed centerline 134.

With the exception of the nonflexing oscillating elements 114. the embodiment of FIG. 4 operates in substantially the same manner as the embodiment of FIGS. 1--3 and effectively produces alternate compaction and rarefaction of the atmosphere immediately adjacent the resonator 110.

Referring now to FIG. 5, another resonator 210 having a similar overall construction as the resonators 10, is illustrated. For purposes of brevity, analogous reference characters are used to illustrate analogous components, most of which will not be specifically discussed. In the embodiment of FIG. 5, the oscillating elements 214 are illustrated as substantially rectangular in cross-sectional configuration and are sufficiently rigid not to flex at a first resonant frequency of the oscillating elements 214. In this embodiment, the oscillating elements 214 are designed to have a first resonant frequency without flexing and a second higher resonant frequency wherein the bars 214 resonantly flex at the resonant frequency of the web 216. The piezoelectric wafer 218 is driven in substantially the same manner as previously described.

Attention is now directed to FIGS. 69 wherein resonator 410 is illustrated which constitutes another embodiment of the invention. The resonator 410 comprises as major components an oscillatable structure 412, support means 414 and an energizing means 416.

The oscillatable structure 412 comprises a unitary body divided by a plurality of generally radial slots extending from the periphery of the body and terminating short of the center thereof thereby defining a plurality of peripherally disposed oscillating elements. In the illustrated embodiment, the body is divided by four

slots

418, 420, 422, 424 into a first pair of.

diametrically opposed

rigid members

426, 428 and a second pair of diametrically opposed

rigid members

430, 432. It should be understood that any number of slots may be provided to define any number of rigid members so long as the rigid members on one side of the body are balanced by the rigid members on the other side thereof. In the event that an odd number of slots are provided, it will be apparent that the mass moment of inertia of any given rigid member will be offset by a combination of mass moments of inertia of rigid members on the other side of the body.

For the purpose of ease of manufacture the radial slots are preferably spaced to define rigid members having substantially equal mass moments of inertia. In the event that the slots are spaced to define rigid members of unequal mass moments of inertia, the mass moment of inertia of any given rigid member must be counterbalanced by a combination of the mass moments of inertia of rigid members on the other side of the body.

A first generally longitudinal blind passage 434 extends from one end of the unitary body and terminates short of the center thereof. A second generally longitudinal blind passage 436 extends from the other end of the unitary body and terminates short of the center thereof to define a bodily flexible part or member 438.

It should be noted that the embodiment of FIGS. 6-9 is so constructed as to dispose a substantially greater mass in the rigid members within a given external dimension of the resonating device. The increase of the mass in the

rotating members

426, 428, 430, 432 acts to increase the 0 (quality) or selectivity of the resonator. all other factors remaming the same.

Since the resonator 410 is provided with an oscillatable structure 412 having a relatively large surface area. the resonator 410 is capable of moving substantial quantities of air. The oscillatable structure 412 is illustrated as cylindrical since the same may be conveniently machined from cylindrical stock It will be apparent. however. that other external configurations are practicable. While the passages 434. 436 may be of any suitable cross section such as circular, the same are illustrated as forming generally hom-shaped recesses.

The support means 414 comprises a generally annular resilient collar 440 made of a suitable material, such as sponge rubber or the like. The collar 440 is provided with an internal diameter 442 slightly smaller than the external dimension of the oscillatable structure 412 adjacent the nodal points of the

rigid members

426, 428, 430, 432 only. When the oscillatable structure 412 is inserted into the center of the collar 440, the oscillatable structure 412 is held securely while the

rigid members

426, 428, 430, 432 are free to rotate about the respective centers of gravity thereof. Surrounding the resilient collar 440 is a rigid sleeve 444 held by a suitable bracket 446 from a base or platform 448. An important feature of the collar 440 and sleeve 444 is to operate as an air-directing baffle. Without the collar 440 and sleeve 444, air compressed by an outwardly moving element tends to flow into the adjacent low pressure area at the other end of the moving element. The air directing feature of the collar 440 and sleeve 444 accordingly acts to significantly increase the acoustical efficiency of this device.

The energizing means 416 may be of any suitable type, but is illustrated as comprising a piezoelectric element 450 having a pair of

electrical leads

452, 454 providing access to a source of electrical energy. When an electrical potential of given polarity is applied through the

leads

452, 454 to the piezoelectric element 450, the piezoelectric element expands to move the bodily flexible member 438 into the upwardly convex configuration depicted in FIG. 8. When the bodily flexible element 438 assumes the upwardly convex configuration, the

rigid members

426, 428, 430, 432 are rotated about a

respective axis

456, 458, 460, 462 intersecting the respective center of gravity of the

rigid members

426, 428, 430, 432. When the bodily flexible member 438 is upwardly convex, the upper ends of the

rigid members

426, 428, 430, 432 are moved outwardly as shown in short dash lines in FIG. 8. Since the upper ends of the

members

426, 428, 430, 432 have moved apart, it will be seen that the member 426 has moved counterclockwise about axis 456 while member 428 has moved clockwise about the axis 458 as viewed from the lower left portion of FIG. 8. Similarly, member 430 has moved clockwise about the axis 462 as viewed from the lower right portion of FIG. 8. It will thus be apparent that the member 426 counterrotates with respect to the member 428 and the member 430 counterrotates with respect to the member 432. When an electrical signal of opposite polarity is applied to the piezoelectric element 450, the element 450 contracts so that the bodily flexible member 438 assumes an upwardly concave position as depicted in FIG. 9. In this condition, the upper ends of the bodily

rigid members

426, 428, 430, 432 rotate about the

axes

456, 458, 460, 462 inwardly to assume the short dash line configuration of FIG. 9.

Attention is now directed to FIG. wherein an acoustically active resonator 510 is illustrated which constitutes still another embodiment of the invention. The resonator 510 comprises as major components support means 512, a plurality of oscillating elements 514, a web 516 interconnecting the oscillating elements 514, and driving means 518 for moving the web 516.

The oscillating elements 514 are peripherally disposed about the web 516 in a manner similar to that shown in FIG. 2 with the resonator 510 being supported by a resilient collar 520 and metal band 522 which is connected to a base member in a manner similar to that shown in FIG. 6. The cumulative area of the external surfaces 524 of the oscillating elements 514 is substantially smaller than the areal extent of either side of the web 516. Consequently. the major coupling between the resonator 510 and the surrounding atmosphere is through the web 516 as contrasted with the preceding embodiments wherein the areal extent of either side of the web is substantially less than the cumulative area of the external surfaces of the oscillating elements.

The web 516 may be formed from the same block of material as the oscillating elements 514 in the same manner as discussed with respect to the embodiment of FIGS. l-3. In the alternative, separate oscillating elements 514 may be affixed around the periphery of the web 516.

The driving means 518 is preferably a piezoelectric wafer energized through a pair of wires 526. Application of a voltage or predetermined polarity to the piezoelectric wafer 518 deflects the web 516 from a central position indicated by a centerline 528 to upwardly concave configuration illustrated by another centerline 530. Because of the connection between the web 516 and the oscillating elements 514, the elements 514 will be contracted inwardly from a neutral position indicated by a centerline 532 to an inwardly disposed position indicated by a centerline 534. Application of a voltage of opposite polarity to the piezoelectric wafer 518 bends the web 516 from an upwardly concave position to an upwardly convex position depicted by another centerline 536. The oscillating elements 514 therefore move from the inwardly disposed configuration indicated by the centerline 534 to the neutral position indicated by the centerline 532 as the web 516 approaches the center position. As the web 516 continues to bend into the upwardly convex configuration, the oscillating elements 514 move from the neutral position to the inwardly disposed position as indicated by the centerline 534.

While the invention has been shown and described in terms of embodiments or modifications as presently best known to applicant, the scope of the invention should not be deemed to be limited by the precise embodiments or modifications herein shown or described.

I claim:

1. An acoustically active resonator comprising:

an annular shaped body having a plurality of annular spaced oscillating elements the external surfaces of which define a substantial portion of the external surfaces of a solid, the oscillating elements defining gaps therebetween substantially impairing the rigidly of the annular body;

a generally planar web interconnecting the oscillating elements adjacent the centers of mass thereof for transmitting motion of the web into the predictable motion of the elements;

means for driving the web at a resonant frequency of the resonator; and

means for supporting the resonator.

2. The resonator of claim 1 wherein the driving means comprises means for moving the web radially from a nodal point thereof and the supporting means comprises a column secured to the web at the nodal point thereof.

3. The resonator of claim 2 wherein the oscillating elements are sufficiently rigid so as not to flex under motion imparted by the web at a resonant frequency of the resonator.

4. The resonator of claim 2 wherein the oscillating elements are suffieiently flexible so as to flex under motion imparted by the web at a resonant frequency of the resonator.

5. The resonator of claim 2 wherein the resonant frequency of the oscillating elements is substantially less than the resonant frequency of the web.

6. The resonator of claim 2 wherein the resonant frequency of the oscillating elements is substantially equal to the resonant frequency of the web.

7. The resonator of claim 2 wherein the driving means comprises a piezoelectric member secured to the web, the piezoelectric member being larger than the attachment location of the column to the web and is concentric with respect to the location.

8. The resonator of claim 1 wherein the supporting means comprises a resilient band extending around the oscillating elements adjacent the midpoints thereof.

9. The resonator of claim 8 wherein the moving means comprises means for bending the web into alternately concave and convex configurations.

10. The resonator of claim 14 wherein the gaps extend from each end of the oscillating elements to the other end thereof and the resilient band comprises means mounting the oscillating elements for counterrotary motion about the nodal axes thereof.

H. The resonator of claim 1 wherein the area of either side of the web is substantially greater than the cumulative area of the external surface of the oscillating elements whereby the web comprises the major acoustic coupling with the surrounding atmosphere.

12. A resonator comprising:

a body having:

first and second end surfaces;

a peripheral surface; and

an even number of generally radial slots extending from the peripheral surface toward and terminating short of the center of the body to define diametrically disposed longitudinally extending pairs of bodily rigid members having substantially equal mass moments of inertia;

a first blind passage longitudinally extending from the first end surface and terminating short of the center of the y;

a second blind passage aligned with the first passage and longitudinally extending from the second end surface and terminating short of the center of the body to define a flexible part between the blind passages for inducing counterrotary movement between each one of each pair of rigid members upon flexing ofthe flexible part; means supporting the rigid members to enable the same to rotate about the nodal axes thereof. the nodal axes of the rigid members intersecting the centers of gravity thereof: and means for inducing oscillatory movement of the rigid mem bers. 13. A resonator comprising: at least three radially disposed bodily rigid members. the mass moment of inertia of any of the rigid members being balanced by the mass moment of inertia of at least one of the other rigid members; a bodily flexible member connecting the rigid members into a unitary structure for transmitting rotary movement of one of the rigid members into counterrotary movement of the other rigid members; means supporting the rigid members to enable the same to rotate about the nodal axes thereof, the nodal axes intersecting the centers of gravity ofthe rigid members; and means for inducing oscillatory movement of the rigid members. 14. The resonator of claim 13 wherein there are an even number of rigid members, the mass moments of inertia of the rigid members being substantially equal.

15. The resonator of claim 13 wherein the bodily flexible member joins the rigid members in a plane intersecting the nodal axes of the rigid members.

Claims

1. An acoustically active resonator comprising: an annular shaped bodY having a plurality of annular spaced oscillating elements the external surfaces of which define a substantial portion of the external surfaces of a solid, the oscillating elements defining gaps therebetween substantially impairing the rigidly of the annular body; a generally planar web interconnecting the oscillating elements adjacent the centers of mass thereof for transmitting motion of the web into the predictable motion of the elements; means for driving the web at a resonant frequency of the resonator; and means for supporting the resonator.

4. The resonator of claim 2 wherein the oscillating elements are sufficiently flexible so as to flex under motion imparted by the web at a resonant frequency of the resonator.

11. The resonator of claim 1 wherein the area of either side of the web is substantially greater than the cumulative area of the external surface of the oscillating elements whereby the web comprises the major acoustic coupling with the surrounding atmosphere.

12. A resonator comprising: a body having: first and second end surfaces; a peripheral surface; and an even number of generally radial slots extending from the peripheral surface toward and terminating short of the center of the body to define diametrically disposed longitudinally extending pairs of bodily rigid members having substantially equal mass moments of inertia; a first blind passage longitudinally extending from the first end surface and terminating short of the center of the body; a second blind passage aligned with the first passage and longitudinally extending from the second end surface and terminating short of the center of the body to define a flexible part between the blind passages for inducing counterrotary movement between each one of each pair of rigid members upon flexing of the flexible part; means supporting the rigid members to enable the same to rotate about the nodal axes thereof, the nodal axes of the rigid members intersecting the centers of gravity thereof; and means for inducing oscillatory movement of the rigid members.

13. A resonator comprising: at least three radially disposed bodily rigid members, the mass moment of inertia of any of the rigid members being balanced by the mass moment of inertia of at least one of the other rigid members; a bodily flexible member connecting the rigid members into a unitary structure for transmitting rotary movement of one of the rigid members into counterrotary movement oF the other rigid members; means supporting the rigid members to enable the same to rotate about the nodal axes thereof, the nodal axes intersecting the centers of gravity of the rigid members; and means for inducing oscillatory movement of the rigid members.

14. The resonator of claim 13 wherein there are an even number of rigid members, the mass moments of inertia of the rigid members being substantially equal.