Multi-frequency vibration controller using fluid-filled cantilever beam for vibration excitation & absorption

A variable frequency vibration controller includes a cantilever beam supported from the vibration prone structure whose vibrations are to be controlled. The cantilever beam has selectively shaped hollow interior portions into which fluid can be selectively injected or withdrawn to vary the total mass of the cantilever beam. The cantilever beam natural frequency is thus tuned to match or selectively mismatch the frequency at which the vibration prone structure is vibrating. Thereby, the beam is used to optimally absorb or excite the vibrations of the structure.

DESCRIPTION 
1. Technical Field 
This invention relates to vibration controller and more particularly to 
vibration controllers in the form of one or more cantilever beams whose 
natural frequency can be varied by varying the effective mass thereof by 
injection or withdrawal of fluid into the cantilever beam hollow interior 
as a function of the vibrating frequency of the vibration prone structure 
upon which the cantilever beam is mounted. 
2. Background Art 
U.S. Pat. No. 3,540,809 of Paul et al, which teaches bifilar vibration 
absorber mounted on helicopter rotor to absorb the rotor vibrations as a 
function of rotor RPM before they are transmitted to the passenger or 
cargo carrying fuselage, and U.S. patent application Ser. No. 185,070 of 
Mard which utilizes a bifilar absorber fixedly mounted in the helicopter 
fuselage and tuned as a function of rotor RPM to absorb fuselage 
vibrations represent the variable frequency vibration absorber art in its 
present state. These constructions are heavy and mechanically complex. 
Another sector of the prior art is represented by Grivolas U.S. Pat. No. 
991,717 which teaches a clock pendulum having mercury in its hollow 
interior, which mercury expands or contracts to compensate for temperature 
induced variations in the length of the pendulum. However, it will be 
obvious to those skilled in the art that while the Grivolas device can 
only change its mass distribution, my device can change its mass as well 
as its mass distribution. Further, the Grivolas device is only capable of 
compensating for one type of disturbance, namely temperature, to the 
frequency it is attempting to hold. My device will compensate for any 
disturbance to the frequency trying to be held, without respect to how 
that disturbance is felt or from what that disturbance originates. Still 
further, the Grivolas mechanism will compensate for frequency disturbance 
in only one plane, i.e., the plane perpendicular to the clock pendulum 
weight support wire, whereas, my device will correct for disturbances in 
any and all planes. Finally, the Grivolas device is a passive system 
designed to damp out a disturbance, but has no capability for making 
inputs to the system. Contrary to Grivolas, my device can be passive where 
my cantilever beam vibration absorber is mounted on a fixed base, but can 
be an active system when my cantilever device is mounted on a base which 
can be driven, thereby making the system active so as to effect an input 
to the system. 
DISCLOSURE OF INVENTION 
A primary object of the present invention is to provide a lightweight, 
variable frequency vibration absorber in the form of a cantilever beam 
whose effective mass, and hence natural frequency, is varied to match the 
natural frequency of the vibration prone structure to which the cantilever 
beam is mounted to thereby eliminate or reduce the vibrations of the 
vibration prone structure. 
It is a further object of this invention to teach such a vibration absorber 
in which the vibrational frequency of the vibration prone structure being 
controlled is continuously monitored and the effective mass and 
cross-sectional moment of inertia of the cantilever beam absorber which is 
mounted therefrom is varied as required to establish the natural frequency 
of the cantilever beam absorber to match the presently determined 
frequency of the vibration prone structure for optimum vibration 
absorption. 
It is a further object of this invention to accomplish the cantilever beam 
vibration absorber natural frequency variation by injecting or withdrawing 
fluid to the interior of the cantilever beam so as to vary its effective 
mass and cross-sectional moment of inertia to establish its natural 
frequency to be equal to the frequency of vibration of the vibration prone 
structure under control. 
It is still a further object of this invention to teach such a cantilever 
beam vibration absorber in which a plurality of hollow passages are 
provided within the cantilever beam, and in which the effective mass and 
hence the natural frequency of the cantilever beam absorber is varied by 
injecting or withdrawing fluid into one or more of these hollow passages 
in a manner so that each hollow passage is either completely filled with 
fluid or completely empty of fluid at all times. 
It is still a further object of this invention to teach such a cantilever 
beam vibration absorber in which the cantilever beam is of cylindrical 
shape and in which a plurality of small diameter hollow cylindrical tubes, 
of the hyperdermic needle type, are positioned within the cantilever beam 
interior so that the axis of the cantilever beam and the axes of the tubes 
are preferably but not necessarily parallel, and including means to fill 
or empty selective arrays of these hollow tubes to selectively control the 
natural frequency of the cantilever beam as a function of the frequency of 
vibration of the vibration prone structure upon which it is fixedly 
mounted, and so that the tube array to be fluid filled is selected so that 
the cantilever beam effective mass is varied to selectively absorb the 
vibrations of the vibration prone system by establishing cantilever beam 
vibration at its numerically lowest mode of vibration which will effect 
vibration absorption. 
Other objects and advantages of the present invention may be seen by 
referring to the following description and claims, read in conjunction 
with the accompanying drawings.

BEST MODE FOR CARRYING OUT THE INVENTION 
Referring to FIG. 1 we see my cantilever beam vibration absorber 10 fixedly 
mounted from vibration prone structure 12 which may be a fixed structure 
such as a helicopter fuselage, an intermittently movable structure such as 
a helicopter stabilator, or a continuously movable structure such as a 
helicopter rotor. While the geometry of cantilever vibration 10 is 
immaterial, I shall describe it as a cylindrical cantilever beam 
concentric about axis 14, since this is my preferred embodiment, and will 
describe its operation in relation to damping vibrations in the fuselage 
of a helicopter, but it should be borne in mind that this environment is 
chosen purely for descriptive purposes since it represents one practical 
environment in which my vibration absorber may be effectively used. My 
system can also be used to excite vibrations as described hereinafter. 
To best understand the operation of my variable frequency vibration 
absorber, reference will be made to FIG. 2 which shows a schematic diagram 
of its operation. In FIG. 2, the vibration prone structure whose 
vibrations are to be controlled is indicated at 16 and designated as the 
"exciting force". The vibration prone structure 16 could be a helicopter 
fuselage which is caused to vibrate by aerodynamic forces imposed thereon 
by the passage of blades thereover at blade passing frequency. 
Accelerometer 18, or other appropriate mechanism, is fixedly mounted on 
the vibration prone structure, such as fuselage 16, and is subjected to 
the same aerodynamic forces at blade passing frequency. By its nature, 
accelerometer 18 detects and sends a signal to vibration analyzer 20 which 
faithfully represents the vibration characteristics in both frequency and 
amplitude of fuselage 16. Vibration analyzer 20 determines the frequency 
of vibration .omega. of the fuselage and sends a signal of fuselage 
vibration frequency .omega. to the microcomputer 22. Microcomputer 22 is 
programmed, as described hereinafter, to ascertain the cantiliver beam 
vibration absorber spring rate K.sub.effective CB and effective mass 
M.sub.o required to establish the cantilever beam natural vibration 
frequency .omega..sub.nat.CB to be equal to the determined vibrating 
frequency .omega. of the fuselage. Microcomputer 22 sends to 
servomechanism 24 signal of M.sub.o, the cantilever beam total mass 
including beam and fluid, required to establish the centilever beam 
natural frequency to be equal to the present frequency of vibration of the 
fuselage. Servomechanism 24 either injects or withdraws the proper volume 
of fluid V into the cantilever beam hollow interior so as to bring its 
effective mass M.sub.o to that required to establish the desired 
relationship of having the cantilever beam natural frequency 
.omega..sub.nat.CB equal the vibrating frequency of the fuselage .omega.. 
With the cantilever 10 so tuned, it will be caused to vibrate at its 
natural frequency due to the vibration forces and motions imparted thereto 
by the vibrating fuselage on which the cantilever beam is mounted. The 
cantilever beam so vibrating serves to absorb, and therefore either reduce 
cancel, the vibrations of the fuselage 16 at least in the area of 
cantilever beam 10. If fuselage 16 is experiencing vibration problems in 
several areas, several cantilever beam vibration absorbers 10 will be 
selectively positioned in the vibration problem areas of the fuselage, and 
also the size and number of cantilever beam vibration absorbers, and their 
modes of vibration, can be selected as required to produce the force 
necessary to absorb fuselage vibrations. 
In a helicopter, the principal vibration excitation force occurs at blade 
passage frequency. Accordingly, it is desirable to design the cantilever 
beam vibration absorber 10 so that it will absorb the excitation force 
(fuselage vibrations ) at blade passage frequency in the cantilever beam 
absorber's first mode of vibration, although vibration absorption at the 
second and third modes of vibration would also be helpful. To understand 
why vibration absorber 10 is most effective when it is designed to perform 
its vibration absorbing function when vibrating in its first mode of 
vibration, reference will be made to FIGS. 3a, 3b and 3c which show the 
first, second and third modes of vibration of cantilever beam 10, 
respectively. When we consider that the vibration absorbing force F 
generated by the vibrating cantilever beam 10 can be determined by the 
equation F=MA, where M is the mass of the cantilever beam, and A is its 
acceleration, it will be noted by viewing FIG. 3a that when cantilever 
beam 10 vibrates in its first mode of vibration equidistance on opposite 
sides of its static position illustrated at 10, all mass increments along 
the length of the cantilever beam 10 are moving in the same direction at 
all times, and therefore the force being generated at the first mode of 
vibration can be determined by adding the force generated by each of these 
cantilever beam mass increments. By comparison, and noting FIG. 3B which 
shows the vibration absorber space in its second mode of vibration, it 
will be noted by viewing its fixed line of position, or its phantom line 
of position, that there are mass increments moving in opposite directions 
at any given time as illustrated by the arrows and therefore the force 
generated by these oppositely moving mass increments must be subtracted to 
produce the total force F generated by cantilever beam 10 in this second 
mode of vibration. Now viewing FIG. 3c, it will be noted that when 
cantilever beam 10 is operating in its third mode of vibration, that the 
mass increments therealong are travelling in opposite directions at any 
given time and therefore must be subtracted one from the other in 
determining the total force generated by the cantilever beam when 
operating in its third mode of operation. It will therefore be seen that 
maximum vibration absorbing force F can be generated by cantilever beam 10 
when vibrating in its first mode of operation, and it will therefore be 
the objective of my invention to so utilize cantilever beam 10. Further, 
first mode vibrations decay more slowly than do second and third mode 
vibrations. 
To provide a better understanding of the operation of my cantilever beam 
vibration absorber and the significance of the FIG. 2 schematic diagram, 
an explanation of the mathematics involved in the dynamics of absorber 10 
will now be given. 
From Euler's differential equation governing free vibrations of a 
cantilever beam, we can derive the following equations: 
EQU COSH(.beta. l)COS(.beta. l)=-1, Eq. 1 
where COSH .beta. l is the hyperbolic cosine of the international constant 
.beta. and the length of the cantilever beam l, and COS .beta. l is the 
cosine of the product of the international constant .beta. and the length 
of the cantilever beam l, and 
##EQU1## 
where .omega..sub.nat.CB is the natural frequency of the cantilever beam, 
.beta. is an international constant, E is the modulus of elasticity of the 
cantilever beam, I is the cross-sectional area moment of inertia of the 
cantilever beam, m.sub.o is the distributive mass, i.e., mass per unit 
length of the cantilever beam and l is the length of the cantilever beam. 
The total mass of the cantilever beam, M.sub.o, equals the product m.sub.o 
l. 
Equation 2 is the recognized equation for a uniform cantilever beam. 
To best understand the operation of the computer 22 in the FIG. 2 schematic 
and in particular its determination of K.sub.eff.CB, the effective spring 
rate of the cantilever beam, and m.sub.o, the required cantilever beam 
distributive mass to establish the cantilever beam natural frequency 
.omega..sub.nat.CB to be equal to the exciting force frequency .omega., 
the above Equations 1 and 2 will be explored further. 
While a cantilever beam, such as 10, vibrates in its first mode of 
vibration as shown in FIG. 3a, its operation can be likened to the 
conventional spring mounted mass vibration absorber shown in FIG. 4 in 
which mass 26, having an effective mass of m.sub.eff., is suspended from 
spring 28, having an effective spring rate of K.sub.eff., which is in turn 
suspended from the vibration prone structure 16. 
The frequency of vibration of the FIG. 4 spring mounted mass vibration 
absorber can be expressed: 
##EQU2## 
Now reverting to the uniform cantilever beam Equation 2, and bringing the 
.beta..sub.n.sup.2 quantity within the square root sign, we can rewrite 
Equation 2 as: 
##EQU3## 
Comparing Equations 4 and 6, we obtain: 
##EQU4## 
But, since we want m.sub.eff. to equal M.sub.o, our equation becomes 
EQU K.sub.eff. =.beta..sub.n.sup.4 EI l Eq. 10 
Utilizing Equations 6 and 10, computer 22 determines quantities 
K.sub.eff.CB, the effective spring rate of the cantilever beam, and 
M.sub.o, the cantilever beam total mass required to produce the desired 
cantilever beam natural frequency to be equal to the natural frequency of 
the exciting force .omega.. 
Equations 6 or 7 may be used to produce Table I given below: 
______________________________________ 
n (.beta..sub.n l).sup.2 
(.beta..sub.n l) 
W.sub.n /W.sub.1 
______________________________________ 
1 3.52 1.88 1 
2 22.03 4.69 6.26 
3 61.70 7.85 17.53 
4 121.40 11.02 34.49 
5 229.86 15.16 65.30 
6 302.99 17.41 86.08 
7 356.32 18.88 101.23 
8 415.72 20.39 118.10 
9 469.26 21.66 133.31 
10 872.78 29.54 247.95 
11 1084.99 32.94 308.24 
12 1283.10 35.82 364.52 
and so forth... 
______________________________________ 
Wherein n is the cantilever beam natural frequency mode of vibration, 
.beta..sub.n is an international constant, l is the length of the 
cantilever beam, .omega..sub.n is the natural frequency of the cantilever 
beam in mode of vibration n, and .omega..sub.1 is the natural frequency of 
the cantilever beam in the first mode vibration. 
Microcomputer 22 of FIG. 2 can be programmed to solve Equation 2 to 
determine m.sub.o necessary to establish the cantilever beam natural 
frequency to be equal to .omega., the vibrating frequency of the vibration 
prone structure as determined by the vibration analyzer 20. Column 3 of 
Table I can be used to determined .beta..sub.n, since the length l of the 
particular cantilever beam vibration absorber being utilized is known. For 
example, if we wish to have vibration absorber 10 operating at its first 
mode of vibration principally, we extract the first entry "1.88" from the 
third column of Table I headed .beta..sub.n l, and divide that quantity by 
the cantilever beam length l properly dimensioned to determine 
.beta..sub.n required to be entered into Equation 2 to produce first mode 
vibrations in the cantilever beam vibration absorber. Accordingly, Table I 
can be used to determine the .beta..sub.n entry to Equation 2 and Equation 
2 may be solved to determine the mass M.sub.o of the cantilever beam 
required to have the cantilever beam 10 vibrate with its first mode of 
vibration equal to .omega., the output of vibration analyzer 20. M.sub.o 
is the total mass of cantilever beam 10, i.e., the mass of the basic 
cantilever beam plus the mass of fluid which must be added thereto, or 
extracted therefrom, to produce the desired M.sub.o. 
Microcomputer 22 can accordingly be programmed to solve for m.sub.o, based 
upon Equation 2, with the .beta..sub.n input so obtained from Table I, and 
to also solve for M.sub.o. 
A possible construction of my cantilever beam 10, which is preferably 
cylindrical in shape but not necessarily so, may be best understood by 
viewing FIGS. 5 and 6. Cantilever beam 10 may be a solid cylinder, with 
cylindrical, axial passages drilled therein or, as shown in FIGS. 5 and 6, 
may be a hollow cylinder comprising outer cylindrical wall 30, which is 
concentric about axis 14 and carries supported therein by partition 
members 32 and 34 a plurality of hollow, cylindrically shaped tube 
members, five of which are shown and identified as 36. Interior tubes 36 
are hollow in construction and, may or may not be of the same diameter and 
length, but are preferably oriented so that their axes 38 extend parallel 
to axis 14 of cantilever beam 10. While five interior hollow tubes or 
cylinders 36 are shown in FIGS. 5 and 6, it will be evident to those 
skilled in the art that any selected array of interior tubes 36 could be 
chosen. Hollow tubes 36 may be the dimension of a hyperdermic needle, or 
larger. 
It will be evident by viewing FIGS. 5 and 6 that with a five interior tube 
arrangement, the mass M.sub.o of vibration absorber 10 can be varied 
substantially between the maximum mass condition when all tubes 36 are 
filled with the heaviest available fluid, to the minimum mass condition 
when all tubes 36 are emptied of fluid. It is important in the operation 
of this vibration absorber 10 that each tube 36 be either totally filled 
or totally empty of fluid during operation so that a sloshing fluid action 
is not experienced. It will be evident that any number of interior tubes 
36 can be inserted into the interior of vibration absorber 10 thereby 
increasing the number of tube arrays which can be filled or emptied to 
vary the tuning of the vibration absorber 10. Further, depending upon the 
specific problem, an array might be chosen wherein mass is concentrated 
circumferentially around the outside of the vibration absorber 10 by 
filling the outermost tubes only, or more mass may be concentrated on the 
inside of vibration absorber 10 by filling only the tube or tubes at or 
adjacent to its axis 14. 
A possible embodiment of my invention is shown in FIG. 7 in which 
cantilever beam vibration absorber 10 is fixedly mounted from vibration 
prone structure 12, whose vibrations are to be controlled, and 
accelerometer 18 is similarly mounted thereto. As in the FIG. 2 diagram, 
the accelerometer 18 faithfully transmits data on the vibration presently 
being experienced by the vibration prone structure 12, which may be the 
helicopter fuselage, and transmits that data to the vibration analyzer 20, 
which calculates the exciting force frequency .omega.. This .omega. signal 
is transmitted to computer 22, and the required K.sub.effective CB and 
m.sub.o, and hence M.sub.o, are determined by computer 22 so that 
.omega..sub.nat.CB is equal to exciting force frequency .omega., and a 
signal is sent from computer 22 to servomechanisms 40, 42 and 44 as to 
what volume of fluid V must be injected into or withdrawn from cantilever 
beam 10 to produce the desired m.sub.o and hence .omega..sub.nat.CB. 
Servomechanisms 40, 42 and 44 operate to actuate piston mechanisms 46, 48 
and 50 such that they move through fluid reservoirs 52, 54 and 56 so as to 
either inject or withdraw the required volume of fluid V into cantilever 
beam 10 through lines 58, 60 and 62, which are connected to cantilever 
beam interior tubes 36. 
A portion of a second potential embodiment is shown in FIG. 8, and it 
should be borne in mind that the FIG. 8 embodiment is similar to the FIG. 
7 embodiment in that it includes the accelerometer, vibration analyzer, 
computer and servomechanisms illustrated in FIG. 7 but not shown in FIG. 
8. In the FIG. 8 configuration, the range of natural frequencies to which 
cantilever beam vibration absorber 10 may be tuned is increased by 
providing at least two different types of fluid which may be injected into 
or withdrawn from cantilever beam interior tubes 36. As best shown in FIG. 
8, a first fluid is contained in servo operated fluid reservoirs 64 and 66 
and a second fluid is contained in servo operated reservoirs 68 and 70. 
Reservoirs 64 through 70 are joined through appropriate plumbing to 
interior tubes 36 so that all tubes 36 may be empty, may be filled with 
fluid 2, may be filled with fluid 1, or some interior tubes 36 may be 
filled with fluid 1 while the others are selectively filled with fluid 2 
or empty, thereby providing a great variety of cantilever beam total 
masses M.sub.o, and hence a great variety of available cantilever beam 
natural frequencies .omega..sub.nat.CB. 
Computer 22 in any of the above-described configurations may be programmed 
in accordance with the graph shown in FIG. 9 in which the abscissa 
indicates the number of interior tube configurations available, C.sub.n, 
the ordinate represents the cantilever beam natural frequency 
.omega..sub.nat.CB. Using Equation 2, curves 65, 67 and 69, representing 
the first, second and third modes of vibration of cantilever beam 
vibration absorber 10 for each of the configurations C.sub.n, can be 
plotted. In configuration 0, all interior tubes 36 are full of fluid. In 
viewing the FIG. 9 chart, it will be noted that if our objective is to 
have the cantilever beam vibration absorber natural frequency 
.omega..sub.nat.CB to be A, this may be achieved by utilizing either tube 
configurations 5 at the first mode of vibration .omega..sub.1, or tube 
configuration 2 at the second mode of vibration .omega..sub.2. Since, as 
explained earlier, the first mode of vibration is the more durable mode 
and produces the greater vibration absorbing force, the computer 22 will 
be programmed to choose tube configuration number 5. It should be noted 
that while the lowest possible mode is desirable from a force point of 
view, the higher the mode, the less travel the beam actually experiences. 
Thus if there are physical size constraints placed on the cantilever beam 
vibration absorber, it may be necessary to have the beam operate in a 
configuration which produces .omega..sub.m not .omega..sub.n (m&gt;n) to 
avoid damaging adjacent aircraft parts. The computer shall be so 
programmed to provide the lowest vibrational mode provided that the 
ensuing beam travel does not collide with other parts of the system. 
Similarly, if we wanted a cantilever beam natural frequency of vibration 
.omega..sub.nat.CB to be .beta., it will be noted that this can be 
achieved with tube configuration 14 using the second mode of vibration 
.omega..sub.2, or with tube configuration 3 using the third mode of 
vibration .omega..sub.3. Because the second mode of vibration produces 
stronger vibration absorbing forces and does not decay as rapidly as the 
third mode of vibration, the computer will be programmed to select 
configuration 14 to utilize the second mode of vibration. It will be 
evident that computer 22 can be programmed in accordance with the graph 
shown in FIG. 9 to produce the desired interior tube 36 configuration 
C.sub.n which is most desirable to optimally achieve a cantilever beam 
natural frequency .omega..sub.nat.CB equal to the determined present 
frequency .omega. of the vibration prone structure under vibration control 
by absorber 10. 
In practice, after a cantilever beam is designed in accordance with my 
teachings herein, the cantilever beam should be tested using various types 
of fluid in the interior tubes 36 to ascertain which fluid produces 
minimal change in internal damping results in the cantilever beam 
vibration absorber 10, and this fluid would preferably be used. Utilizing 
Equation 2, and knowing the volume of fluid V which has been added to the 
cantilever beam vibration absorber at any particular time, the vibration 
absorber natural frequency .omega..sub.nat.CB can be determined and the 
graph shown in FIG. 10 drawn for each such cantilever beam vibration 
absorber. When a volume V line, such as C, passes through the graph line 
more than once, this represents the first, second and third modes of 
vibration .omega..sub.1, .omega..sub.2, .omega..sub.3, respectively. 
Utilizing the information contained in the FIG. 10 graph, computer 22 can 
be programmed to provide the appropriate volume of fluid V to the interior 
tubes 36 of cantilever beam vibration absorber 10 so as to produce the 
cantilever beam vibration absorber natural frequency .omega..sub.nat.CB 
desired, utilizing the lowest numerical mode of vibration which will 
produce this desired .omega..sub.nat.CB. 
For a more complete explanation of the mathematics discussed herein, 
reference may be made to the texts "Theory of Vibration with Application" 
by William T. Thomson or "Formulas for Stress and Strain" by Raymond J. 
Roark. 
While I have shown my vibration absorber 10 as being fixedly, i.e. 
directly, mounted to the vibration prone structure 12 in my FIG. 1 
embodiment, my preferred embodiment, and while I have described my 
invention in relation to utilizing the vibration absorber 10 to damp 
vibrations, my cantilever beam vibration controller 10 described herein 
also has the capability of being used to excite certain modes of vibration 
when used as shown in my FIG. 11 and 12 embodiments. 
In the FIG. 11 embodiment, my cantilever beam vibration absorber 10 is 
mounted from vibration prone structure 12 through hydraulic 
piston-cylinder arrangement 70 which can be actuated in known fashion by 
servo 72 to impart selected vibrations to support 74 and hence to 
cantilever beam vibration controller 10. 
In FIG. 12, the vibration absorber support 74' is supported from vibration 
prone structure 12 by flexible member 76. Cam 78 is selectively shaped and 
selectively rotated so as to impart selected vibratory motion to support 
74 and hence to vibration controller 10, thereby providing excitation to 
the system, rather than damping. 
FIG. 13 shows another mode of operation of my cantilever beam mechanism 10 
in which it is used either to damp vibrations or excite selected 
vibrations in mechanism 16. It will be noted that FIG. 13 is similar to 
FIG. 2 but with provisions added to permit the cantilever beam 10 to 
excite vibrations rather than damp vibrations. Reference numerals used for 
similar apparatus in FIG. 2 are also used in FIG. 13 and elements 16-24 
operate in the FIG. 13 arrangement precisely as described in connection 
with the FIG. 2 arrangement and are used when the pilot selects to utilize 
cantilever beam 10 as a vibration absorber or damper. When the pilot 
selects to use cantilever beam 10 as a vibration excitation mechanism, he 
energizes switch 80 which causes the signal from element 20 to go to 
microcomputer 22a rather than microcomputer 22. The signal generated by 
microcomputer 22a is as indicated in FIG. 13, namely to establish the 
natural frequency of the cantilever beam to be different from the natural 
frequency of the vibration prone structure 16. This "different from" 
frequency signal from computer 22a is transmitted to servomechanism 24a, 
which functions to inject or withdraw a selected volume of liquid, V, into 
cantilever beam vibration absorber 10 so as to selectively establish the 
natural frequency of the cantilever beam to be dissimilar to the natural 
frequency of the vibration prone structure 16, thereby causing the 
cantilever beam to function to establish a vibration excitation force on 
the vibration prone structure 16 so as to selectively vary its vibration 
characteristics. Those skilled in the art will recognize that the 
excitation of an additional vibrational force within a system can serve to 
reduce vibrations since the vibrations generated by the second vibratory 
exciting force from 10 and the natural frequency of vibration prone 
structure 16 can be made to be cancelling. 
My FIGS. 11 and 12 vibration excitation modifications may be used in 
combination with my FIG. 2 or FIG. 13 embodiment. To best understand the 
cooperation between these embodiments, it is best to consider the 
following equation: 
EQU F.sub.b (t)=M.sub.o y.sub. b Eq. 11 
where F.sub.b =the exciting force 16 and the driving force imposed by 
either the servo operated piston-cylinder mechanism 70 of FIG. 11 or cam 
78 of FIG. 12, where M.sub.o is the total mass of cantilever beam 10 
including the weight of the cantilever beam and the weight of the fluid 
therein, and Y.sub.b is the acceleration of the cantilever beam base 74 or 
74'. 
Considering Equation 11, it will be noted that the acceleration of the 
cantilever beam base 74, 74' can be changed by selectively varying M.sub.o 
or F.sub.b. M.sub.o is changed as shown in the FIGS. 1 and 13 embodiment 
by varying the amount of liquid injected into or withdrawn from cantilever 
beam 10. F.sub.b can be changed through the action of piston-cylinder 
mechanism 70 actuated by servo 72 or by the action of cam 78. 
It will therefore be seen that the frequency generated in cantilever beam 
10 can be varied when the FIG. 11 or 12 embodiments are used in 
combination with the FIG. 2 or 13 embodiments by either using the 
mechanism of FIG. 2 to cause cantilever beam 10 to vibrate so as to reduce 
or eliminate the vibrations of the vibration prone system, by utilizing 
the FIG. 13 construction, and, in particular, the 22a microcomputer and 
24a servo mechanism portion thereof to vary M.sub.o so that the natural 
frequency of the cantilever beam vibrator is different from the natural 
frequency of the vibration prone system to thereby apply vibration 
excitation to the vibration prone system. At the same time, either the 
FIG. 11 or FIG. 12 embodiments can be used with the FIG. 2 or FIG. 13 
embodiments to add a second driving force to exciting force 16 through the 
action of element 70-72 of FIG. 11 or 78 of FIG. 12 to vary the quantity 
F.sub.b in the FIG. 11 equation and hence the mode of vibration of 
cantilever beam 10 by adding an excitation force thereto by means of the 
FIG. 11 or 12 mechanism. 
I wish it to be understood that I do not desire to be limited to the exact 
details of construction shown and described, for obvious modifications 
will occur to a person skilled in the art.