US3714475A

US3714475A - Resonator having counter rotating rigid parts

Info

Publication number: US3714475A
Application number: US00071394A
Authority: US
Inventors: H Baker
Original assignee: H ENG CORP
Current assignee: H ENG CORP
Priority date: 1966-07-15
Filing date: 1970-09-11
Publication date: 1973-01-30
Anticipated expiration: 1990-01-30

Abstract

There is disclosed a resonator having rigid oscillating parts interconnected by a resilient web for inducing counterrotary movement of the rigid parts. The rigid parts are mounted to rotate about the nodal axis thereof. The nodal axis of each rigid part intersects the center of gravity of the part.

Description

United States Patent Baker, Jr. 1 1 *Jan. 30, 1973 541 RESONATOR HAVING COUNTER 2,978,597 4 1961 Harris ..310/8 2 ROTATING RIGID PARTS 3,354,413 11/1967 K 3,582,698 6/1971 Baker [75] Inventor: Hugh M. Baker, JL, Washington, 3 3 9 200 2 9 Kunnemunde D.C. 3,091,708 5/1963 Harris .1

. 3,308,313 3/1967 F [73] Assgneei 'f Cmpommm 1,781,513 11 1930 uiil t eck Sliver Spring, 3,389,351 6 1968 Trzeba 3,281,725 /1966 Albsmeier 1 Nome T gztfigg fi f l 3,146,415 8 1964 Albsmeieret a1. 1. y 3,376,522 4/1968 Traub has 3,408,514 10/1968 Adamietz et a1. [22] Filed: Sept. 11, 1970 2,469,951 5/1949 Cooley 2,939,971 6/1960 Holt ..310/ [21] Appl. No.: 71,394

FOREIGN PATENTS OR APPLICATIONS Related U.S. Application Data 43/18352 8/1968 Japan ..333/71 [63] Continuation of Ser. No. 565,430, July 15, 1966.

' Primary Examiner-Herman Karl Saalbach [52] U.S. Cl. ..3l0/8.2, 84/409, 84/457, Attorney-G, Turner Moller 331/116 M, 58/23 TF, 310/25, 333/72 [51] Int. Cl. ..H0lv 7/00 [57] ABSTRACT [58] Fleld of Search .:....333/71, 72; There is disclosed a resonator having rigid Oscillating 331/116 116 parts interconnected by a resilient web for inducing M; 73/505; 58/23 TF; 84/409 counterrotary movement of the rigid parts. The rigid 5 parts are mounted to rotate about the nodal axis [56] References Cited thereof. The nodal axis of each rigid part intersects UNlTED STATES PATENTS the center of gravity of the part.

3,453,464 7/1969 Baker ..310/36 15 Claims, 8 Drawing Figures PATENTEDJAN 30 ms SHEET 10F 2 INVENTOR. HUG/1 M BAKER Jr PATENTEDJAHBO 1915 3,714,475 sum 2 or 2 PW INVENTOR.

HUGH M. BAKER Jr RESONATOR HAVING COUNTER ROTATING RIGID PARTS This application is a continuation of application Ser. No. 565,430, filed July 15, 1961.

This invention relates to resonators, filters, and more particularly to electromechanical type resonators and filters with piezoelectric, magnetostrictive and electromagnetic drive.

At frequencies below KC, electromechanical filters and resonators are generally chosen over capacitance and resistance networks or capacitance and inductance networks since they offer the best temperature stability, frequency selectivity, small size and low cost combination.

While there are many forms of electromechanical resonators and filters, the ones most often selected for frequencies below 20 KC are tuning forks, some form of a simply supported loaded beam, and the cantilevered loaded beam.

Each of these devices has certain design, manufacturing or performance deficiencies. A common objectionable characteristic is reaction felt in the supporting members. Consequently, unless great care is taken to isolate one reasonating device from another, there will be objectionable interaction between them particularly when they are functioning as a frequency selective filter.

Another objectionable characteristic common to all of these devices, especially if they are loaded with high relative mass to obtain low frequency with high selectivity, is that they are affected by the attitude of their mounting or support because of gravitational effects. A tuning fork, for example, resonates at one frequency when mounted horizontally and another frequency when mounted vertically.

When the desired resonant frequency is very low, the physical size of all three forms of resonators becomes a significant factor relative to the frequency selectivity. The flexing members, being very large, are dampened heavily by the surrounding medium such as air, atmosphere or the like. Thus, it is common practice to evacuate the surrounding medium from the container in which the structure is mounted in order to improve its frequency selectivity. The simply supported beam as well as cantilevered beam type of resonator have the further disadvantage of comparatively poor frequency selectivity in part due to damping introduced by a nonrigid base.

It is known by those versed in the art of electromechanical resonators that frequency selectivity is generally improved if the flexible portion of the resonator is made stiffer and a load is added to maintain a given frequency. In general, the frequency selectivity of the resonator is improved by a factor related to the square root of the product of the stiffness and the loading.

In the case of the simply supported beam and the v cantilevered beam type of resonator, this is offset by a to obtain a combination of thermo-elastic properties and compensating thermo-expansion properties.

Because of the physical form of a tuning fork type of resonator, great care must be taken to avoid disturbing the compensating effects of these two properties when bringing the tuning fork to the desired frequency once it is assembled.

In any form of mechanical resonator, the resonant frequency thereof can be adjusted only by changing the physical parameters of the structured the resonator. Because such adjustments are generally awkward and time-consuming, they are permanent or semi-permanent in nature. There are many applications wherein it would be advantageous to produce a controlled temporary shift of the resonant frequency with ease and rapidity. It would be particularly advantageous if this shift could be accomplished by electrical means.

In order to overcome the disadvantages as stated above and to acquire the unforeseen, unobvious and desired results of the instant inventive concept as will be more fully described and disclosed hereinafter, it is an object of my invention to construct a mechanical resonator which may be piezoelectrically electromagnetically and magnetostrictively driven while not being affected by the position or mounting attitude thereof with the resonator having virtually no reaction impressed on the mounting base and therefore having minimal tendency for one resonator to adversely affect an adjacent resonator.

It is also of my invention to provide a mechanical resonator which is simple and inexpensive to design and construct with respect to frequency selectivity and thermal-frequency stability, and to achieve a high degree of frequency selectivity in a small size without need for evacuating the surrounding media from the container in which the resonator may be disposed.

Another object of this invention is to construct an electromechanical resonator which is substantially totally free of the effects of gravity and acceleration on the resonant frequency.

It is a further object of this invention to construct an electromechanical resonator assembly which may be semi-permanently adjusted over some range of resonant frequencies with ease and without cutting away or adding material to the loaded or flexing portions of the assembly.

It is a further object of this invention to provide an assembly by which the resonant frequency of any electromechanical resonator may be temporarily shifted a controlled amount with ease and rapidity via electrical means.

It is also a further object of this invention to provide an electromechanical resonator whose basic configuration is in the general form of the letter I-I.

Other objects and important features of the invention would be apparent from a study of the specification following taken with the drawing, which together show, illustrate, describe and disclose preferred embodiments or modifications of the invention and it is now considered to be the best mode of practicing the principles thereof. Still other embodiments or modifications may be suggested to those having the benefit of the teachings herein, and such other embodiments or modifications are intended to be reserved especially as they fall within the scope and spirit of the subjoined claims.

IN THE DRAWING FIG. 1 shows a perspective view of one embodiment of a mechanical type resonator having the improvements of this invention incorporated therewith;

FIG. 2 is a plan view of the resonator as illustrated in FIG. 1;

FIG. 3 is a diagramatic illustration of the relative position of certain various parts of the resonator illustrated in FIG. 1 taken during a cycle of oscillation;

FIG. 4 is a plan view similar to FIG. 2 of the drawing but showing another embodiment thereof in which a plurality of resonators similar to those illustrated in FIGS. 1 and 2 may be cascaded to improve the frequency selectivity;

FIG. 5 is a perspective view of the resonator shown in FIG. 1 but illustrating a structural arrangement as well as a method of electrically tuning the resonator by employing a plurality of additional transducers;

FIG. 6 is a plan view of the resonator illustrated in FIG. 1 showing another embodiment of the structural arrangement and method of electrically tuning the resonator;

FIG. 7 shows a perspective view of a typical tuning fork illustrating the structural arrangement and the method for electrically tuning same which is similar to that as illustrated in FIG. 5, and

FIG. 8 is a plan view of the tuning fork shown in FIG. 7 but illustrating the embodiment of the structural arrangement and method for electrically tuning same as being similar to that as illustrated in FIG. 6.

Attention is now directed to FIGS. 1 and 2 of the drawing wherein there is illustrated a novel resonator structure 10 which will be described and disclosed herein as being employed as a filter and in such capacity, the resonator 10 will possess certain highly desired, unobvious and unforeseen characteristics and will be explained in more detail hereinafter. It is to be expressly noted that the resonator 10 has a basic configuration which may be considered as being substantially in the form of an H with the resonator 10 being defined by an elongate first part 12 that is relatively bodily rigid having a longitudinal extent D and an elongate second part 14 which is also relatively bodily rigid and which is substantially coextensive with the first part 12 having similar longitudinal extent D.

The first 12 and the second 14 parts of the resonator structure 10 are disposed in parallel relationship relative to each other and are spaced apart a distance d.

The resonator structure 10 is further provided with an elongate third part which extends between and is connected to an intermediate portion 18 of each of the first 12 and the second 14 parts of the resonator structure 10.

For the sake of illustration only, the first l2 and the second 14 parts of the resonator structure 10 have been shown as being of rectangular configuration in cross section with the third part 16 having a relatively large surface area. However, it to be understood that other shapes and configurations may be employed with regard to the first 12, second 14, and third 16 parts of the resonator structure 10 without departing from the spirit of the inventive concept which is being described and disclosed.

There are, however, certain physical characteristics of the parts l2, l4 and 16 which are believed to be of importance, such as: the mass of each of the parts l2 and 14 should be substantially greater than the mass of the third part 16, the longitudinal extent D of the

parts

12 and 14 should be substantially greater than the distance d of the space therebetween, the material from which the first 12 and the second 14 parts are made should have a relatively low coefficient of expansion with the third part being formed of material having an isoelastic property, the intermediate portions 18 of the first 12 and second 14 parts as well as the third part 16 should be located in a plane that is common with the nodal axes 20 of the first 12 and the second 14 parts of the resonator structure 10 being defined respectively by the inner section of a longitudinal plane that is disposed along the one half the width W and a transverse plane which is disposed along the one half longitudinal extent D of the

parts

12 and 14.

The resonator structure 10 is further provided with transducers 22 which in the form as illustrated in FIG. 1 of the drawing is a piezoelectric material. However, other transducers may be employed in the form of electromagnetostrictive or electromagnetic without departing from the instant inventive concept.

The transducers 22 are secured to the third part 16 of the resonator structurelO, in any suitable manner and as illustrated, the pair of transducers 22 is employed with one transducer 22 being disposed on each of the opposed surfaces of the third part 16 of the resonator structure 10. Depending on the type of electrical circuitry to be employed, the number of transducers 22 may vary and the inventive concept as illustrated is an example of a three terminal type filter arrangement. If a two terminal type filter is to be employed, it is only necessary to have a single transducer 22 secured to the third part 16 of the resonator structure 10.

In the three terminal circuitry as illustrated, electrical signals are applied to one of the transducers through a wire 24 and the signals generated on the other transducer 22 disposed on the opposed side of the bodily flexible third part 16 is taken off through another wire 26. By reason of the fact that the flexible third part 16 is disposed between the transducers 22, the flexible third part 16 in effect creates an electrical connection therebetween and the signals created therein are taken off through a wire 28 making the electrical network an effective three terminal device.

If the electrical signal is applied to the flexible third part 16 of the resonator structure 10 through the wire 24 and the transducers 22 associated therewith the flexible third part 16 will assume a position as illustrated in FIG. 3 by the reference character A during one half cycle and by reason of the connection of the third part 16 to each of the first 12 and second 14 parts of the resonator structure 10, the relatively rigid nonflexing first l2 and second 14 parts will assume a position as illustrated by the reference character B. During the second one half cycle of the electrical signal, the flexible third part 16 will assume a position illustrated by the reference character E in FIG. 3 of the drawing which will position the nonflexing bodily rigid first 12 and second 14 parts of the resonator structure 10 in positions as illustrated by the reference character F. In FIG. 3 of the drawing the normal or relaxed positions of the first 12, second 14 and third 16 parts of the resonator structure are illustrated in solid lines with the relative positions thereof during the one half cycle being shown by dotted lines and referred to with the third part 16 being illustrated by the reference character A and the first 12 and second 14 parts being illustrated by the reference character B with the relative positions thereof during the second half cycle of the electrical signal being shown with the third part 16 designated by the reference character E and the first 12 and second 14 parts illustrated by the reference character F. It will thus be apparent that the counterrotation between the parts 12, 14 is substantially coextensive in time in the sense that the parts 12, 14 begin rotation at substantially the same time and end at substantially the same time. Chronocoextensive is used to describe this relationship.

The result of passing the electrical signal to the bodily flexible third part 16 of the resonator structure is that a counter rotational oscillation is created in the first l2 and second 14 parts of the resonator structure 10 occurs about the respective nodal axes 20 and by reason of a rotational or pivotal connection 30, to be described in more detail hereinafter that is provided between the resonator structure 10 and a support structure 32 there is no reaction to the rocking oscillatory motion of the bodily rigid non-flexing first 12 and second 14 parts since the

parts

12 and 14 are, in effect, counterbalancing each other about the pivotal connections along the nodal axes 20.

Having thus balanced all of the various parts or portions of the resonator structure 10 about the rotational or pivotal connections 30 which are common with the respective nodal axes 20 there is no effective gravitational forces or influences operating on the resonator structure 10 against the resonant frequency which may be created thereby. In other words, in dealing with the low frequencies with which we are currently interested, and with the relative properties and characteristics being in existence that relate to the first 12, second 14 and third 16 parts, such as the relative masses etc., and by reason of the non-flexing relatively bodily rigid first 12 and second 14 parts being counterbalanced about the rotational or pivotal connections, there is virtually no effect created by any gravitational forces or influences on the resonant frequency of the resonator structure 10 and further, the characteristics and relative relationship of the parts as disclosed and described creates a condition in which acceleration also has virtually no effect on the resonant frequency of the resonator structure 10.

In the resonator structure 10, as herein described and disclosed, the resultant resonant frequency is determined by the relative stiffness of the bodily flexible third part 16 and the mass as well as the moment of inertia about the pivotal connections 30 of the bodily rigid non-flexing first 12 and second 14 parts and in the preferred embodiment or modification of the resonator structure 10 the bodily flexible third part 16 is preferably formed of a material which has the property of isoelasticity, that is, a material whose elastic properties are least affected by temperature changes such as a material which may be a homogenus steel alloy of 30 percent nickel and 10 percent chromium as described and disclosed in U.S. Pat. No. 1,763,853 with the bodily rigid first l2 and second 14 parts being of a material having a low coefficient of expansion such as Invar or certain glass compounds.

None of the moving parts of the resonator structure 10 are comparatively large for a given resonant frequency and further because the total of distance of travel of any moving part of the resonant structure 10 is similar, the damping effects of the surrounding atmosphere are minimal. If it is desirable to recuce the damping effects of the surrounding atmosphere even further the non-flexing bodily rigid first 12 and second 14 parts may be made of circular cross section wherein the modal axes 20 would extend through the longitudinal center lines thereof at a location which is halfway of the longitudinal extent with the nodal axes being normal to the longitudinal axes thereof.

By reason of the description and disclosure made herein, it is believed obvious on passing the electrical signal through the resonator structure 10 that a resultant resonantfrequency will be created and it is under certain conditions highly desirable to be able to vary the resultant resonant frequency and in order to so vary the resultant frequency there is provided structure 34 which will effectively semi-permanently efficiently and readily enable the resonant frequency of the resonator structure 10 to be varied.

As illustrated in FIG. 1 of the drawing, the structure 34 comprises a generally longitudinally extending bore 36 that passes along the longitudinal axis of each of the first l2 and second 14 parts in which there is longitudinally spaced a plurality of plug-like members 38 with the plug-like members 38 being retained within the respective bore 36 by suitable securements such as a press or friction set as well as screw threads or the like. The relative position of each of the plug-like members 38 from the respective nodal axes 20 will, in effect, vary the resonant frequency of the resonator structure 10 and by reason of the mass of the plug-like members 38 the moment of inertia of the first l2 and second 14 parts may be varied by reason of the disposition of the plug-like members 38 relative to the respective nodal axes 20. It is to be understood that the plug-like members 38 should be of the samemass and position the same distance from the respective nodal axes 20 in order to maintain the balance of the resonator structure 10.

It is to be understood that an arrangement similar to the plug-like members 38 and the bore 36 may be conveniently employed on resonators such as tuning forks, cantilevered beams, some forms of simple supported beams and other similar mechanical resonators to effectively vary the resonant frequency thereof by varying the moment of inertia in a manner similar to that as described and disclosed herein with regard to the first l2 and second 14 parts of the resonator structure 10.

The support structure 32 may comprise as illustrated a base portion 40 from which there projects a plurality of bracket-like members 42 with the bracket like-members 42 being disposed in pairs, one pair being adjacent the first l2 and another pair adjacent the second 14 parts of the resonator structure 10 with the first 12 and second 14 parts thereof being intermediate the respective pair of the bracket-like members 42.

A suitable pivotal pin type connection 44 extends between the associated pair of bracket-like members 42 and passes through the respective nodal axes 20 and the associated first l2 and second 14 parts of the resonator structure 10 and the pivotal pin type connectors 44 divide the rotational or pivotal connection 30 for supporting the resonator structure 10 with the first l2 and the second 14 parts thereof being in the counterbalanced condition.

Attention is now directed to FIG. 4 of the drawing wherein there is illustrated another embodiment or modification of the inventive concept wherein it is desired to obtain a better selection of resonant frequency and in this embodiment or modification there is provided a plurality of resonator structures 10 which are disposed in cascaded relationship relative to each other.

It is to be noted that the pivotal pin type connectors 44 are common to the adjacent resonator structures 10 and thus enable the motion of one of the resonator structures 10 to be coupled to the next adjacent resonator structure 10. It is to'be understood that the disposition of a plurality of resonator structures 10 in cascading relationship relative to each other should not be limited to two and by extending or increasing the number of resonator structures 10 which may be employed there occurs a corresponding improvement in the resonant frequency selectivity. Further, the resonator structures 10 which may be disposed in the cascaded relationship as illustrated may be electrically coupled with no-mechanical coupling, electrically and mechanically coupled or mechanically coupled in order to obtain a specific frequency selectivity characteristic.

Attention is now directed to FIGS. 5 through 8 of the drawing wherein there is illustrated and shown certain embodiments and modifications of an apparatus and method for changing or varying the existing resonant frequency of a resonator and as illustrated in FIG. 5 of the drawing, the resonator 10 is illustrated and like characters of reference are relied upon for the purpose of identification which should correspond to the character references as shown in FIGS. 1 and 2. p

The resonator structure 10, as previously described and disclosed, is driven through the external circuit which is connected by the wire 24 that is attached to the one transducer 22 which is illustrated as a piezoelectric wafer with the resonator structure 10 thus effectively having a resultant resonant frequency which, for reasons previously stated, may be desirable to vary or change.

Apparatus 46 is provided for varying or changing the resultant resonant frequency of the resonator structure 10 and the apparatus 46 comprises at least one and preferably a pair of additional transducers 48 which, as illustrated, are in the form of piezoelectric wafers with the additional transducers 48 being secured to bodily flexible third part 16 of the resonator structure 10 and suitable wiring 50 is provided to create a circuit that comprises a potentiometer 52 that is in series with a battery or source of electrical energy 54 so that a DC voltage which may be varied is applied to the additional transducers 48.

As illustrated in FIG. 7, a similar apparatus 46 is employed to a conventional type of tuning fork 56 having a plurality of tines 58 to which there is secured the additional transducers 48 which are provided with wiring 50 that creates a circuit that includes the potentiometer 52 and the source of electrical energy 54, all in a manner similar to the circuitry of FIG. 5.

Since in any mechanical resonating device there is a relationship between the resultant resonant frequency and the stiffness of the flexible portion of the resonant structure the resultant resonant frequency may be shifted, changed, varied or altered by the relative stiffness of the flexible member or members as the case may be. ln the

resonant structure

10 and 56, as illustrated in FIGS. 5 and 7 of the drawing, the additional transducers 48 employed in the apparatus 46 form part of the respective bodily flexible portions or members, that is the third part 16 and the tines 58 and contribute to shifting, changing varying or altering the relative stiffness thereof. As the voltage of the circuitry of the apparatus 46 which is supplied from the source of electrical energy 54 through the potentiometer 52 and the wiring 50 is applied across the additional transducers 48, the additional transducers 48 will stretch or contract according to the polarity and magnitude of the applied voltage as varied by the potentiometer 52.

By attaching or securing the additional transducers 48 to the bodily flexible portions or

members

16 and 58 of the

resonator structures

10 or 46, as the case may be, so that the additional transducers 48 are disposed on opposite surfaces of the associated bodily flexible part or member the additional transducers 48 will tend to stretch or contract, in the same direction in response to a given applied voltage and accordingly, increase or decrease, as the case may be the relative stiffness of the part 16 or member 58 in response to the variance of the voltage from the source of electrical energy 54 as opposite polarities thereof is applied.

The result of employing the apparatus 46 as a method for altering, shifting, varying or changing the resultant resonant frequency of a resonator structure is that the resultant resonant frequency may be altered, shifted, varied to correspond to the magnitude or polarity of the voltage which may be applied from the source of electrical energy 54 which passes through the additional transducers 48.

While the apparatus 46 has been illustrated in FIGS. 5 and 7 of the drawing as having a component part thereof piezoelectric wafers which define the transducers 48, it may be desired that the additional transducers 48 take the form of an electromagnet 60 which, as illustrated in FIGS. 6 and 8 of the drawing may be employed with the apparatus 46 to alter, vary, change, shift or modify the resultant resonant frequency of resonator structures 10 and tuning forks 56.

As illustrated in FIG. 6 of the drawing, the electromagnet 60 is disposed between the first l2 and the second 14 bodily rigid part of the resonator structure 10 with the electromagnetic field thereof being controlled by a coil 62 which is connected through the wiring 50 to a source of electrical energy 54 and a potentiometer 52.

As current from the source electrical energy 54 is increased by the potentiometer 52 to the coil 62, such an increase in the current will thus increase the influence of the magnetic field which will in turn bring a strain or bias to the end portions of the first 12 and the second 14 parts of the resonator structure 10 and such strain or bias will influence and thus vary, change, modify and effectively control the relatively flexibility of the third part 16 and thus alter the stiffness thereof. Accordingly, the resultant resonant frequency of the resonator structure 10 may be altered, influenced, varied and changed in accordance with the current flow to the electromagnetic 60.

Similarly and as illustrated in FIG. 8 of the drawing, the electromagnetic 60 may be placed between the tine members 58 of a resonator structure which may be in the form of a tuning fork 56 and as the current flow to the coil 62 of the apparatus 46 will influence the flexibility of the tine members 58 and thus vary, change, modify and control the resultant resonant frequency thereof.

The variation of the electromagnetic field of the apparatus 46 as illustrated in FIG. 8 through varying the current from the source of electrical energy 54 by the potentiometer 52 is reflected as a change in the stress on the tine members 58 which thus changes the relative stiffness thereof and as the stiffness is altered, there is a corresponding change in the resonant frequency of the tuning fork 56. While the invention has been shown, illustrated, described and disclosed in terms of certain embodiment or modifications which it has assumed in practice, the scope of the invention should not be deemed to be limited by the precise embodiment or modification has herein shown, illustrated, described or disclosed and such other embodiments or modifications intended to be reserved especially as they fall within the scope of the claims here appended.

I claim:

1. A resonator comprising first and second parts rigid at a resonant frequency of the resonator;

means supporting the first part to enable the same to rotate about the nodal axis thereof, means supporting the second part to enable the same to rotate about the nodal axis thereof, the nodal axes substantially intersecting the centers of gravity of the respective first and second parts;

means for providing a resilient connection between the first and second parts for inducing counter rotary movement of the first and second parts upon a movement of one of the parts, the resilient means comprising a third part connected to the first and second parts and flexible at a resonant frequency of the resonator; and v means for moving at least one of the parts.

2. The resonator of claim 1 wherein the nodal axes define a plane.

3. The resonator of claim 2 wherein the first and second parts are substantially parallel.

4. The resonator of claim 1 wherein the third part is independent of the supporting means.

5. The resonator of claim 1 wherein the resilient means comprises means for transmitting rotary movement of the first part into counterrotary movement of the second part.

6. The resonator of claim 1 wherein the resilient means comprises means for transmitting rotary movement of the first part into substantially simultaneous counter rotation of the second part.

7. The resonator of claim 1 wherein the moving means comprises an electromechanical transducer disposed on the third part.

8. The resonator of claim 1 wherein the third part comprises a planer section and the moving means comprises an electromechanical transducer on surfaces of he planar section which are in opposed relation to each other.

9. The resonator as set forth in claim 1 wherein the first and second parts are formed of material having a relatively low coefficient of expansion, and the third part is formed of material having isoelastic properties.

10. The resonator as set forth in claim 1 wherein the mass of the first and second parts are each substantially greater than the mass of the third part.

11. The resonator as set forth in claim 1 wherein the length of the first and second parts are each substantially greater than the space therebetween.

12. The resonator as set forth in claim 1 wherein the mass moment of inertia of the first part is substantially equal to the mass moment of inertia of the second part.

13. The resonator of claim 12 wherein the connection between the third part and each of the first and second parts produces equal momentson the first and second parts upon rotation thereof.

14. The resonator of claim 1 wherein the nodal axes are spaced apart.

15. The resonator of claim 1 further comprising means for adjusting the resonant frequency of the resonator including means for changing the relative stiffness of the third part.

Claims

1. A resonator comprising first and second parts rigid at a resonant frequency of the resonator; means supporting the first part to enable the same to rotate about the nodal axis thereof, means supporting the second part to enable the same to rotate about the nodal axis thereof, the nodal axes substantially intersecting the centers of gravity of the respective first and second parts; means for providing a resilient connection between the first and second parts for inducing counter rotary movement of the first and second parts upon a movement of one of the parts, the resilient means comprising a third part connected to the first and second parts and flexible at a resonant frequency of the resonator; and means for moving at least one of the parts.

2. The resonator of claim 1 wherein the nodal axes define a plane.

8. The resonator of claim 1 wherein the third part comprises a planer section and the moving means comprises an electromechanical transducer on surfaces of the planar section which are in opposed relation to each other.

13. The resonator of claim 12 wherein the connection between the third part and each of the first and second parts produces equal moments on the first and second parts upon rotation thereof.

14. The resonator of claim 1 wherein the nodal axes are spaced apart.