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Publication numberUS3696259 A
Publication typeGrant
Publication dateOct 3, 1972
Filing dateNov 4, 1970
Priority dateDec 25, 1967
Also published asDE1810406A1, DE1810406B2, DE1810406C3
Publication numberUS 3696259 A, US 3696259A, US-A-3696259, US3696259 A, US3696259A
InventorsIto Katsuhiko, Mori Eiji
Original AssigneeIto Katsuhiko, Matsushita Electric Ind Co Ltd, Mori Eiji
Export CitationBiBTeX, EndNote, RefMan
External Links: USPTO, USPTO Assignment, Espacenet
Device for distributing vibratory energy
US 3696259 A
Abstract
A device for distributing vibratory energy comprising a pair of transmission elements joined together in a perpendicular relationship and a transducer positioned such that when the transducer is operable at a vibrational frequency, a displacement node of a standing wave is formed at the junction of the elements and a displacement antinode is formed at an extremity of the second element remote from said junction.
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United States Patent [151 3,696,259 Mori et a1. 5] Oct. 3, 1972 [54] DEVICE FOR DISTRIBUTING [56] References Cited VIBRATORY ENE Y RG UNITED STATES PATENTS [72] Inventors: Eui Mori, 10-35, 2 chome,

Chokayama, Meguro ku; Katsuhiko 2,948,867 8/1960 Mattlat ..310/8.2 X n c/o Matsushita 317 Futako 3,546,498 12/1970 McMaster et a1 ..3 10/ 8.2 Kawasakbshi Kanaawaen both 3,435,250 3/1969 Reggia...' ..333/30 of Japan 3,148,293 9/1964 Jones et a]. ..310/26 2,730,103 1/1956 Mackta ..310/26 X Flledi 1970 2,725,219 11/1955 Firth ..310/26 X 21 A 1.N 86928 I 1 pp 0 Primary Examiner-J. D. Miller Related US. Application Data Assistant ExaminerMark O. Budd [63] Continuation-impart of Ser. No. 777,573, Nov. Atwmey Flynn & Fnshauf 1968- 57 ABSTRACT [30] Foreign Application Priority Data A device for distributing vibratory energy comprising a pair of transmission elements joined together in a D60. 25, Japan perpendicular relationship and a transducer positioned March 25, 1968 Japan ..43/018954 such that when the transducer is operable at a vibra tional frequency, a displacement node of a standing [52] US. Cl. ..310/8, wave is formed at the junction of the elements and a 1 displacement antinode is formed at an extremity of the [51 Int. Cl ..I'I04l' 17/00, I'IOIV 9/00 second element remote from Said junction. [58] Field of Search ..310/8-8.7, 26

13 Claims, 18 Drawing Figures PATENTEDnm 3 I972 SHEET 1 OF 5 FIG./

PATENTEDBBT 3 72 SHEET 2 (IF 5 PATENTED "E 3 I 3 6 96 2 5 9 SHEETHUFSV FIG/4 a 3 ,er L

half amplitude of L- face O I 2 3 4 5 half amplitude of R'- face 9750mm i126mm I 126mm" FIG. /7

FIG. /8

CHARACTERISTIC CURVE (NO LOAD TEST) g 4 FOR FLANGE 30) D 5 (FOR FLANGE 31) l,-

IN PUT POWER (VOLTS) DEVICE FOR DISTRIBUTING VIBRATORY ENERGY This is a continuation-in-partof U.S. Ser. No. 777,573 filed Nov. 21, 1968.

This invention relates to devices for distributing vibratory energy of the type having longitudinal vibrations, and more particularly to a device for distributing vibratory energy from one or more transducers or for combining energy from a plurality of transducers.

7 SUMMARY OF THE INVENTION In accordance with the present invention a device for the distribution of vibratory energy comprises a pair of transmission elements joined together in perpendicular relationship, a transducer for producing longitudinal vibrations connected with the first of the elements, said elements being so dimensioned and the transducer being so positioned that at a vibrational frequency at which the transducer is operable a displacement node of a standing wave is formed at the junction of the elements. At said vibrational frequency a displacement antinode is formed at the boundary or boundaries of the second element remote from the junction.

As will be understood, a longitudinal standing wave has at least one displacement node and at least one displacement antinode at a distance of one quarter wavelength therefrom, the wavelength for any particular frequency being dependent upon'the velocity of Iongitudinal waves in the particular material. .With a device according to the invention, the distance of the transducer from the junction must be an odd number of quarter wavelengths, as also must the distance of the said boundary or boundaries from the junction. In the most compact arrangement, both of these distances are equal to one quarter of a wavelength. For simplicity of description, the possibility of end effects causing distances between certain nodes and antinodes to differ from an exact quarter wavelength will be ignored herein. Such effects are readily recognizable in practice and will be readily allowed for by those skilled in the art once the principles of the invention have been appreciated.

With a device according to the invention, the direction of propagation of the vibrational energy is turned through substantially 90 at the junction. The effect can be applied, not only to change the direction of propagation, but also to distribute the energy from a single transducer, or a number of transducers, to a number of positions (or even uniformly around the circular boundary of a flange-like element), or to combine the energy from a number of transducers and feed it to one or more positions.

It is to be noted that the elements may be connected to intermediate portions of one another. In such a case, any element connected by an intermediate portion thereof should be formed so that the junction is at a displacement node for longitudinal vibrations in the parts of the element separated thereby.

The invention will be further understood from the following description in which reference is made to the accompanying drawings. It will be understood that this description is given for purposes of illustration only and is not intended to limit the scope of the invention. In the drawings:

FIG. 1 is a cross sectional view of an electro-acoustical transducer coupled to a transmission element, the

arrangement being applicable to various devices in accordance with the present invention;

FIG. 2 is an elevation view of a device according to the invention for distributing vibratory energy around the periphery of a circular flange provided as the second of the transmission elements;

FIG. 3 is a plan view of the device of FIG. 2;

FIGS. 4 and 5 show two further devices in perspective;

FIG. 6 is an elevation of a device for combining the energy from a set of transducers;

FIG. 7 is a plan view of the device of FIG. 6;

FIGS. 8 and 9 are perspective views of two further devices for combining the energy from a set of transducers;

FIG. 10 is a perspective view showing the transmission elements of one form of the device according to the invention;

FIG. 11 shows a correlation between the vibratory amplitudes, at an entrance end-face and an exit endface, of the device of FIG. 10;

FIG. 12 is a perspective view of a device similar to the device of FIG. 2;

FIG. 13 shows a correlation between two vibratory displacements at an entrance end-face and an exit endface of the device of FIG. 12;

FIG. 14 is an elevation view of the elements of a device which is a modification of that shown in FIG. 6;

FIG. 15 is an end elevation view of the elements of FIG. 14 with transducers added thereto;

FIG. 16 is a graph illustrating a correlation between two vibratory displacements at one entrance end-face and one exit end-face of the device shown in FIG. 14;

FIG. 17 illustrates a test set-up for the device for FIG. 14; and

FIG. 18 is a graph illustrating the correlation between input power and output vibration.

Many kinds of electro-acoustical transducers, especially magnetostrictive and electro-strictive transducers, may be employed in the device of the present invention. A preferred form of transducer has been developed and is shown in FIG. 1. It gives an adequate level of acoustical energy and is stable in operation.

Referring now to FIG. 1, the transducer 1 consists of metallic supporting members 2 and 3 and a vibrator of the electro-stn'ctive type sandwiched between the two members. The parts are joined together by a threaded bolt 5 which passes through the vibrator and gives the transducer adequate stability and strength. A satisfactory mounting of the transducer upon a transmission element 6 is obtainable by a double-ended bolt 7, as is shown in FIG. 1.

It is necessary, in practice, to provide stable generation and transmission of vibratory energy with a minimum thermal loss and without mechanical disruption of the constructional materials. At the same time, the transducer should be as small as possible for the power handled thereby. For these reasons, it is desirable that an aluminium-base alloy having relatively low density, such as duralumin, is used in the construction of the supporting members 2 and 3, and that lead zirconate titanate is used as the electrostrictive type material in the vibrator, or transducer 4. A multilayer construction is recommended for the transducer 4. The transducer 4 shown in FIG. 1 is composed of four layers of electrostrictive material. The transducer may be activated by a power supply of appropriate frequency (not shown) fed in at the terminals 8 and 9. All of the devices to be described hereinafter may incorporate a transducer or transducers according to FIG. 1. The specification of a convenient transducer is as follows:

Electrostrictive vibrator or transducer Material: lead zirconate titanate Size: diameter 40 mm thickness 5 mm Arrangement: four layers total thickness mm Supporting Members Material: duralumin Diameter: 40 mm Length: resonance length of 20 kHz, viz.,

about 50 mm Detailed structure of transducer assembly is shown in FIG. 1, and has a total overall length of 120 mm.

The power input of this transducer may be up to 300 watts. If the intended frequency of operation is different from 20 kHz the above-mentioned dimensions must, of course, be changed. The re-designing is readily achieved in accordance with known techniques.

The first displacement node of a longitudinal standing wave occurs at a distance of one-quarter v wavelength from the transducer and subsequent nodes wavelength (A)=Velocity/Frequency (f) Operation Conditions resonant frequency: 51 kHz material: AISI- l 045 A-A' element: l8 mm X 12 mm 5l.5 mm 8-8 element: 18 mm X12 mm Sl.5 mm Input power: 20 watts When the driving face A of the body of FIG. 10 is fitted with a transducer (such as is shown in FIG. 1), it has been observed that under no load conditions the amplitudes of vibration of the A, A, B and B'-faces are almost substantially equal. The results of a practical experiment are shown in FIG. 11. The vibration from the transducer is transmitted to the output end-faces by means of resonance. The vibration amplitude at each of the output faces is substantially equal to the input amplitude, and the output energy at each of the output faces is about one third of the input vibrational energy. The input energy is diverged in three directions in the embodiment of FIG. 10. Thus, from this experiment, it is seen that the direction of propagation of the vibratory energy is readily shifted through 90 and also readily diverged (to faces A, B and B) by a device of the present invention.

The device'of FIG. 4 is a modification of that of FIG. 10 and has a third transmission element perpendicular to the other two. Energy from the transducer 1 is distributed in four different directions at right angles to its original direction to pass along transmission elements located at a distance of one-quarter wavelength from the junction between the transducer 1 and transmission element 12. Vibratory energy is received at each of the end-faces 13, 14, 15 and 16 which are one-quarter wavelength from the center of the structure. If the above end-faces are correctly loaded, the vibratory energy from the one simple transducer may be utilized at each of them. The divergent structure is potentially useful in many fields of industry.

The reverse of the above distribution effect is easily realized. FIG. 9 shows transducers l fixed to end-faces corresponding to end'faces 13, l4, l5 and 16 of FIG. 4 and the energy from these transducers is discharged from one end-face of the element 26, while the other end-face of the element 26 is fitted with a reflection plate 22 for the frequency concerned. The total vibratory energy discharged from the end-face of element 26 is about four times that generated by a single transducer. Such a convergence device may be utilized for industrial applications requiring large amounts of vibratory energy to be applied at a single position- In FIG. 12, there is shown another form of divergence structure consisting of a rod-shaped transmission element and a circular flange. This fiangeis located at a distance of one quarter wavelength from one end-face of the rod-shaped element and is at about right angles thereto.

When a transducer, e.g., that of FIG. 1, is fixed to face L, the vibratory energy is discharged radially from the peripheral face R of the flange. The radius of said flange may be calculated from the following equation.

where,

mo fmo 'y radius of flange a standard constant decided by the mode number, m

E Youngs moldulus p specific gravity; and

0'= Poisson s ratio Various examples calculated by the above-mentioned frequency equation are given in the follow table:

Material p E 0' a y,,,,,,

g/cm dyne/em (m=l )(f.,=20 KHZ) Duralumin 2.8 7X l0 0.33 2.07 88 Steel 7.9 2.0Xl0 0.28 2.04 86 Brass 8 9 9.5 l0" 0.36 2.08 58 Note: the above steel" is a kind of AISl-l045 carbon steel The following data show typical dimensions and operating conditions for a structure as shown in FIG. 12:

Resonant Frequency 49 KHz Material AlSl-l045 L-L' length 20 50l 5 mm Flange Thickness l l.5 mm Flange Diameter 68.! mm

Input Power 20 watts The vibratory energy from the transducer, which is fixed to face L or L, is shifted through 90 at the junction of the rod and flange which is one-quarter wavelength long from the transducer, and is then radially diverged from face R. The correlation between the amplitude of vibration of the input face L or L and that of the output face R, as obtained experimentally, under no load conditions, is shown in FIG. 13. The vibration of output face R has less amplitude than that of input face L under these no load conditions. This is a characteristic of this embodiment.

Referring now to FIGS. 2 and 3, vibratory energy transmitted from a transducer 1 to a rod-shaped transmission element is radially diverged from a circular flange l1 placed at a distance of one-quarter wavelength from the transducer. FIG. 5 shows an extension of the principle. The device of FIG. 5 has three flanges 18, 19 and 20 on a transmission rod 17. The flanges are spaced one-half wavelength apart and the distance between each end-face of the rod 17 and the neighboring flange is one-quarter wavelength. The power from the transducer 1 is diverged to the peripheries of the three flanges.

A flange can be used for convergence instead of divergence of the vibratory energy. Thus if the flange of FIG. 12 is given a regular polygonal periphery and the transducer is fixed to one flat peripheral face of the flange, the correlation between the vibration amplitude of the driven face and that of the discharge face is similar to that shown in FIG. 13. If transducers are placed on several flat peripheral sides of the flange, the energy from the transducers converges to the ends-of the rod element. Under no load conditions in an ideal case without losses, energy which is about equal to the total energy from the transducers, is discharged at 90 to its original directions at the output face.

The device of FIGS. 6 and 7 has a flange of regular octagonal shape. A transducer is fixed to every alternate side of the flange shown in FIG. 7. The vibratory energy from the four transducers is converged into the flange and then is discharged from one end-face of transmission element 21 after a change of direction. The discharged energy is about four times that given by a single transducer and is about equal to the combined energy given by the four transducers.

The end-face of said transmission rod 21 is fitted with a reflection plate 22 as is shown in FIG. 9. However, if the above reflection plate is replaced with one more transducer, increased vibratory energy is obtained at the output face.

The device of FIG. 8 is a modification of that of FIGS. 6 and 7. A circular flange is positioned onehalf wavelength from the octagonal flange 24. The vibratory energy converged into the regular octagonal flange 24 is turned through 90 along transmission rod 23, and is then, after being shifted through 90 by circular flange 25, diverged radially. The dimensions of the flange 25 are chosen as hereinbefore described.

In FIG. 14, there is shown a structure suitable for obtaining a high output power for use in heavy industry. This transmission body is made up of a rod-shaped transmission element 33 having a resonant length at the operating frequency. Two supports 32 and 40 are located one-quarter wavelength from each end-face of the rod 33, and two flanges, and 31, of regular l2- sides polygonal periphery are spaced one-half wavelength apart and one-half wavelength from the supporters 40 and 32, respectively. Twelve transducers are fixed to each flange by holes such as the holes 34, 35, 36, 37, 38 and 39. The dimensions and operating conditions are as follows:

Resonant frequency 20 KHz Material AISl-l045 Length of rod m 504 mm Diameter of rod 60 mm Diameter of flange I67 mm Thickness of flange: 40 mm Length of transducer 1 15 mm Input power 200 watts per transducer Each of supporters 32 and 40 is the form of a small circular flange. The dimensions of these flanges are made as small as possible since they lie on the length of a transmission element. Typically they may be about 8 mm in both width and height. It will be observed that they are positioned at displacement nodes in order to minimize disturbance of the operation of the device and that they are deliberately made non-resonant.

In the device of FIG. 14, the correlation between the vibration amplitude at input face R and that of output face L, under no load conditions, is as shown in FIG. 16, it is seen that the ratio of output vibration amplitude to input vibration amplitude is more than 3 to I. This ratio is of particular importance for the purpose of most efficient utilization of the vibration energy. The device of FIG. 14 facilitates synthesis of vibration energy by means of resonance vibration based upon the relation between the transducers and the transmission element. Both in input and output, the following equation applies:

wherein:

v: vibration energy f: frequency g: amplitude 0: sound speed A: wave length f both in input and output is constant. Consequently, when the device shown in FIG. 14 is operated, the following equation applies:

Wherein:

v output vibration energy;

v V input vibration energy for each transducer (i.e., 24 transducers); and

E loss.

Accordingly, the output vibration amplitude grows together with output vibration energy, which inturn, grows together with input vibration energy. As mentioned above, the ratio of output vibration amplitude to input vibration amplitude is about 3 to 1. This has been verified by actual no load tests, the results of which are shown in FIG. 16.

With the device of FIG. 14, an output power of about 4,800 watts can theoretically be obtained with an input power of about 200 watts per transducer. In actual practice, however, the full theoretical output of 4,800 watts will not be obtained due to losses, etc. If the number of the flanges is increased, an even greater output can be obtained.

When the structure of FIG. 14 is increased to 6 stages (72 transducers), output power of approximately 10,000 watts can theoretically be obtained, without taking into account losses, with only a comparatively small input-power of about 150 watts per transducer. With such high power devices some thermal loss is apt to occur. Accordingly, it is desirable to use a special steel such as BS En lll Nickel Chromium Steel in the construction of the device to minimize such losses.

An actual no load test was carried out to show the relationship between input power and output vibration amplitude and the results are shown in FIG. 18. AS shown in FIG. 17, the device of FIG. 14 (shown generally by 30, 31, 33) was connected at its output face L to a long generally rod-shaped plug 41, which in turn was connected to a drawing die 42 used in a pipe forming apparatus. The plug 41 is connected to face L via an intermediary element 43. The output vibration amplitude was measured as the input power to the transducers on flanges 30 and 31 was set at 80, 160, 200 and 240 volts. The amplitudes were measured with a pickup 44 and the results thereof indicated by mV. FIG. 18 shows the output with input energy supplied to transducers on each flange 30 and 31. An actual no load efficiency of about 85 percent was obtained. The

following equations are applicable to such a system:

lR==(21-rfM*)/Q l. wherein:

M equivalent mass in the vibration system IR mechanical resistance Q sharpness of resonance in vibration system f resonance frequency w /2 v 2 2. wherein:

w output energy; v vibration energy Efficiency=w/ W 3. wherein:

W, input energy The devices of the present invention may, of course, utilize tubular transmission elements in place of the solid elements described above.

The electro-strictive material, lead zirconate titanate, has been referred to as a transducer component in the foregoing description. Other materials which can be used, are, for example, magnetrostrictive or piezoelectric materials such as Ferrite, nickel, nickel-iron alloy, crystals, barium titanate and the like.

The forms of the present invention hereinbefore described may be modified without departing from the spirit or essential attributes thereof.

We claim:

1. A device for transmitting virbratory energy comprising:

at least one input transmission element and an output transmission element, said at least one input transmission element being joined to said output transmission element with said at least one input transmission element substantially perpendicular to said output transmission element;

at least two input vibration transducers producing longitudinal vibrations of the same frequency, said input vibration transducers being connected to at least one of said at least one input transmission element;

said transmission elements being dimensioned, and

said transducers being positioned with respect to said at least one input transmission element to which they are connected, such that, at a vibrational frequency at which said transducers are operable a displacement node of a standing wave is formed at a junction of said transmission elements, and such that, said output transmission element has said frequency as a standing wave frequency for which there is a displacement node at said junction and a displacement antinode at an extremity of said output transmission element remote from said junction.

2. A device according to claim 1, wherein the distance of said transducers from said junction and the distance of said extremity from said junction are both one-quarter of the wavelength of the longitudinal vibrations in said transmission elements.

3. A device according to claim 1, wherein said transmission elements are elongate in the direction of the vibrations and have a regular cross section, said atleast one input transmission element being connected to an intermediate position of said output transmission element and said output transmission element being dimensioned to have displacement antinodes at each of its ends.

4. A device according to claim 1, wherein said transmission elements are elongate in the direction of the vibrations and have a regular cross section and said output transmission element is connected to an intermediate position of said at least one input transmission element, thereby dividing said at least one input transmission element into two parts, one on each side of the 5 junction therebetween, at least one of said transducers being connected to one of said two parts and the other of said two parts having a length such that it is resonant at the frequency of said longitudinal vibrations.

5. A device according to claim 4, including at least first and second input transmission elements, said output transmission element being connected to an intermediate portion of said first input transmission element to divide same into said two parts, said second input transmission element being connected to said first input transmission element and to said output transmission element in the vicinity of said junction therebetween, said second input transmission element being of such length that a displacement node is located at said junction and a displacement antinode is located at an extremity of said second input transmission element remote from said junction.

6. A device according to claim 3 wherein said at least two transducers are connected with said input transmission elements at the position of a displacement antinode, said extremity of said output transmission element being located at a displacement antinode and being free to receive vibrational energy from more than one of said transducers.

7. A device according to claim 3, further comprising a reflector, and wherein at least one of said transducers is connected to an input transmission element at a displacement antinode, at least one transmission element is connected to said reflector and has an extremity positioned at a displacement antinode and at least an output transmission element has an extremity positioned at a displacement antinode and which is free to receive vibrational energy from at least two transducers.

8. A device according to claim 1, wherein said at least one input transmission element includes a regularly polygonal flange, one of said at least two transducers being connected to respective peripheral faces of said flange, said flange being dimensioned such that the longitudinal vibrations from each transducer have a common displacement antinode at the center of said flange, said output transmission element being connected with said flange transmission element at said center.

9. A device according to claim 8, wherein said output transmission element is a bar and further comprising a second flange connected at its center to said bar, said second flange being dimensioned such that a displacement antinode is formed around its periphery.

10. A device according to claim 9, wherein said second flange has a regularly polygonal shape, each peripheral face thereof being connected to a respective transducer, all of said transducers on said flanges being operable at the same frequency.

1 l. A device according to claim 9, wherein said barshaped input transmission element extends beyond said flange-shaped output transmission element and further comprising at least a second generally circular flangeshaped output transmission element connected concentrically with said extended portion of said barshaped input transmission element, said second flangeshaped output transmission element being positioned at displacement antinodes of said bar-shaped input transmission element.

12. A device for transmitting vibratory energy comprising:

at least one input transmission element and at least two output transmission faces on at least one output transmission element, said at least one input transmission element being joined to said at least one output transmission element with said at least one input transmission element substantially perpendicular to said at least one output transmission element;

at least one input vibration transducer producing longitudinal vibrations said input vibration transducers being connected to at least one of said at least one input transmission element;

said transmission elements being dimensioned, and

said transducers being positioned with respect to said at least one input transmission element to which they are connected, such that, at a vibrational frequency at which said transducers are operable a displacement node of a standing wave is formed at a junction of said transmission elements, and such that, said at least one output transmission element has said frequency as a standing wave frequency for which there is a displacement node at said junction and a displacement antinode at an extremity of said output transmission element remote from said junction, the input vibrations from said at least one transducer being distributed to said output transmission faces.

13. A device for transmitting vibratory energy comprising:

at least one elongated, generally bar-shaped, input transmission element and a generally circular flange-shaped output transmission element, said at least one input transmission element being 'oined to sald flange-shaped output transmission e ement substantially centrally of said flange-shaped output transmission element with said at least one input transmission element substantially perpendicular to said flange-shaped output transmission element;

at least one input vibration transducer producing longitudinal vibrations said at least one input vibration transducer being connected to at least one of said at least one input transmission element;

said transmission elements being dimensioned, and said at least one transducer being positioned with respect to said at least one input transmission element, such that, at a vibrational frequency at which said transducers are operable a displacement node of a standing wave is formed at a junction of said transmission elements, and such that, said flange-shaped output transmission element has said frequency as a standing wave frequency for which there is a displacement node at said junction and a displacement antinode formed around the periphery of said flange-shaped output transmission element, energy from said at least one vibration transducer being distributed around said periphery.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,69%259 Dated October 3, 1972 It is certified that error appears in the above-identified p atent'. and that said Letters Patent are hereby corrected as shown below:

Column 2, line 26, change "displacement" to amplitudes-;

Column 4, line 21 change "22" to -28-;

Column 4, between lines 37 and 40 rewrite equation as mo mo In the Drawings Figs. 6, 8 and 9, change reference numeral "22" to --28".--.

Signed and sealed this 30th day of April 197M.

(Si-SAL) Attest:

EDWARD TI.FIETCI.ER,JR. h I G. MARSHALL DANE Attesting Officer 'C'onjrriissioner of Patents QRM PO-1050 (10-69) USCOMM-DC 60376-P69 fl' U.Sv GOVERNMENT PRINI'ING OFFICE "09 0 366-334.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3,696,259 Dated October 3, 1972 lnventor(s) Eiji lIOII L, Gt 8.1.

It is certified that error appears in the above-identified ilament: and that said Letters Patent are hereby corrected as shown below:

Column 2, line 26, change "displacement" to -amplitudes-;

Column 4, line 21 change "22" to -28-;

Column 4, between lines 37 and 40 rewrite equation as Column 5, line 49, change "22" to -28--;

In the Drawings Figs. 6, 8 and 9, change "reference numeral 22" to --28'- Signed and sealed this 30th day of April 1971p.

(SEAL) Attest:

mman ILFLETQIIER,JR. a I\IARSHA LL ANE a. Attesting Officer A Commissioner of Patents O R M PO-IOSO (10-69) USCOMM'DC 6O37 6-P69 ILS. GOVERNMENT PRINTING OFFICE 1 Il O -JG-JSL

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Classifications
U.S. Classification310/323.1, 310/26
International ClassificationH04R17/08, H04R17/04, B06B3/00
Cooperative ClassificationB06B3/00, H04R17/08
European ClassificationB06B3/00