Abstract:
The present invention relates to a vibration absorber in which an absorber end mass is coupled to a primary mass by means of a cantilevered beam, wherein at least a portion of the beam comprises a shape memory alloy (SMA). Preferably, the end mass is coupled to the primary mass with several discrete SMA wires which may be individually heated. When each of the SMA wires is heated above a predetermined temperature, the SMA material undergoes a phase change which results in a change in the stiffness of the SMA wire. Heating of the various wires in various combinations allows the operational frequency of the absorber to be actively tuned. The frequency of the absorber may therefore be tuned to closely match the current vibrational frequency of the primary mass, thereby allowing the absorber to be adaptively tuned to the frequency of the primary mass in a simple and straightforward manner.

Description:
TECHNICAL FIELD OF THE INVENTION 
     The present invention generally relates to vibration control devices and, more particularly, to a vibration absorber using shape memory material. 
     BACKGROUND OF THE INVENTION 
     Vibration control has been and remains an important field of study in engineering. Most commonly, the goal is the attenuation of the vibration of a primary system. Motivations include the reduction of dynamic stresses on machinery, the isolation of precision devices from shock and vibration, and the reduction of vibration-induced sound. Vibration absorbers are a well-known technique for achieving vibration attenuation in the presence of harmonic disturbances to a system. The greatest merit of vibration absorbers is that they are passive mechanisms that do not require external power or complex control algorithms. The greatest drawback to vibration absorbers is that they are generally effective only within a narrow band of frequencies and may cause large resonances in the frequency response at frequencies just above and below that narrow band. Adaptive absorbers have been designed that address this limitation by moving the effective operating band to match the input frequencies. The difficulty is in finding an adaptive design that is both simple to control and easily manufactured. The ideal absorber is one that incorporates a technology to eliminate moving parts and produce a design with a control logic that is easily implemented. 
     Vibration control techniques generally fall into one of three areas. These are passive, active, and adaptive-passive. Passive control techniques include the use of tuned-vibration absorbers (TVAs) and isolation mounts. As their name implies, passive techniques do not involve the addition of energy to a system, but rely on the inherent passive characteristics of the system to achieve a specified response. In its simplest form, as shown in FIG. 1, the TVA consists of a secondary mass  10  and spring  12  assembly attached to a primary mass  14  being driven by an external forcing function. Tuning the resonance of the secondary system  10 / 12  to the driving frequency will result in attenuation of the vibration of the primary mass  14 . This effect is shown in FIG. 2, where the dashed line represents the frequency response of an undamped single degree of freedom (sdof) system to an external sinusoidal forcing input. The solid line shows the response with the addition of a vibration absorber with 0.1% of damping (c abs /m abs =2*ζabs*ωabs). Also shown is a smaller dashed line that describes the response of the system when fitted with an absorber with 2% damping. For the data shown in FIG. 2, the natural frequency of the primary system is ωn=sqrt(2) and the absorber&#39;s undamped natural frequency is ωabs=1.0. The absorber&#39;s mass was chosen to be 10% of the primary system&#39;s mass. Many similar prior art plots show the case of the absorber  10 / 12  tuned to the natural frequency of the primary system  14 . This is not believed to be a fair representation of the use of an absorber  10 / 12  in practice, as a primary system  14  with a resonance at an operating frequency is an obviously bad design. Rather, the expectation is that the primary system  14  will have been designed without a resonance at the driving frequency and that the absorber  10 / 12  will be used to attenuate the primary system&#39;s response below already non-resonant conditions. 
     Two significant observations are the addition of the second resonant peak below the absorber&#39;s tuned frequency and the effect that the addition of damping has on the resonant peaks and attenuation “notch.” The increased damping of the 2% damped absorber  10 / 12  has the effect of smoothing out the response of the system, such that the resonant peaks are not so large, however it also reduces the depth of the notch where the attenuation of the primary system  14  is significant. The beneficial effect of the absorber  10 / 12  on the primary system  14  is defined as the reduction in the vibration of the primary system  14 . If this reduction is defined as any response below the 0 dB line, then the region where the absorber  10 / 12  is effective is shown in FIG.  3 . 
     Regarding the history of vibration absorbers, Frahm is credited as the inventor of the vibration absorber, with his 1911 patent. Ormondroyd and Den Hartog later gave a comprehensive treatment of the theory of vibration absorbers, including the effect of damping on absorber performance, in their 1928 paper (Ormondroyd, J. and Den Hartog, J. P., “Theory of the Dynamic Vibration Absorber.” Transactions of the ASME, Applied Mechanics Division, APM-50-7, 1928, p. 9-22). Sun et al. provide a more recent study and examples of the application of passive TVAs in industry (Sun, J. Q., Jolly, M. R., and Norris, M. A., “Passive, Adaptive, and Active Tuned Vibration Absorbers—A Survey.” Journal of Mechanical Design. Vol. 117B, June 1995, p. 234-242). The authors also describe the draw-back of passive TVAs in the limitation of their effectiveness to fixed bands of frequencies, as shown in FIG.  3 . In the presence of uncertainties, which may include time-varying driving frequencies, the effectiveness of the TVAs is substantially reduced and may prove to have negative effects on the vibration of the primary structure. 
     The two main differences between active and passive control are the need for an external actuator and measurements for implementation of active control, while passive control needs neither. In vibration control, the active control techniques often involve driving the primary system in opposition to the external forcing function, such that the two forcing inputs cancel to produce no net motion of the primary mass. In general, active control techniques suffer from the requirement of input power equal to the disturbance signal. Additionally, active control schemes may require complicated matching of sensors and actuators and have the potential for adding instabilities to the system. 
     In contrasting passive and adaptive techniques, the passive techniques have the advantage of simplicity of design, reduced complexity, and guaranteed stability. Active techniques have the advantage of being able to control vibration across wider bands of operating frequencies. 
     Passive-adaptive control methods attempt to combine the positive aspects of the passive and active schemes into a single package. In general, active techniques are used to modify the passive characteristics of the primary system. In recent years, increasing research has been performed concerning the use of adaptable TVAs (ATVAs). Active modification of the absorber stiffness provides for a device that is on-line tunable for operation at different frequencies. The bandwidth of operation varies with the technique used for the active stiffness modification. A good example of a passive adaptive absorber is the design detailed in Franchek et al. (Franchek, M. A., Ryan, M. W., and Bernhard, R. J., “Adaptive Passive Vibration Control.” Journal of Sound and Vibration, vol. 189, no. 5, 1995, p. 565-585). In this design, the stiffness of the absorber&#39;s spring is “dialed-in” by means of screwing the helical spring through a hole in a fixed plate. The spring stiffness is inversely dependent on the number of coils, so a softer spring may be achieved through screwing greater lengths of spring through the plate. A softer spring lowers the frequency of operation of the absorber, thereby allowing a tunable vibration absorber to be implemented. 
     Many adaptive passive absorber designs may suffer reliability limitations due to the complexity of their design and operation. There is therefore a need for an adaptive-passive absorber design that avoids the use of mechanisms that are unreliable and/or costly. The present invention is directed toward meeting this need. 
     SUMMARY OF THE INVENTION 
     The present invention relates to a vibration absorber in which an absorber end mass is coupled to a primary mass by means of a cantilevered beam, wherein at least a portion of the beam comprises a shape memory alloy (SMA). Preferably, the end mass is coupled to the primary mass with several discrete SMA wires which may be individually heated. When each of the SMA wires is heated above a predetermined temperature, the SMA material undergoes a phase change which results in a change in the stiffness of the SMA wire. Heating of the various wires in various combinations allows the operational frequency of the absorber to be actively tuned. The frequency of the absorber may therefore be tuned to closely match the current vibrational frequency of the primary mass, thereby allowing the absorber to be adaptively tuned to the frequency of the primary mass in a simple and straightforward manner. 
     In one form of the invention, a vibration absorber coupled to a primary mass for absorbing a vibration of the primary mass is disclosed, the vibration absorber comprising a tuning mass; and at least one shape memory element coupled between the primary mass and the tuning mass; wherein a frequency band of vibration absorbed from the primary mass by the vibration absorber may be tuned by heating the shape memory element. In another form of the invention, a vibration absorber coupled to a primary mass for absorbing a vibration of the primary mass is disclosed, the vibration absorber comprising a tuning mass; a first shape memory element coupled between the primary mass and the tuning mass; and a second shape memory element coupled between the primary mass and the tuning mass; wherein a frequency band of vibration absorbed from the primary mass by the vibration absorber may be tuned by heating only the first element, only the second element, or both the first and second elements. 
     In yet another form of the invention, a vibration absorber coupled to a primary mass for absorbing a vibration of the primary mass is disclosed, the vibration absorber comprising an tuning mass; a first pair of shape memory wires coupled between the primary mass and the tuning mass; a second pair of shape memory wires coupled between the primary mass and the tuning mass; a pair of non-shape memory wires coupled between the primary mass and then tuning mass; a sensor coupled to the primary mass and operative to sense a frequency of vibration of the primary mass; a first current source coupled to the first pair of shape memory wires; a second current source coupled to the second pair of shape memory wires; and a processor coupled to the sensor and to the first and second current sources, the processor operative to control the first and second current sources in response to an output received from the sensor; wherein a frequency band of vibration absorbed from the primary mass by the vibration absorber may be tuned by heating only the first pair of shape memory wires by passing a first current therethrough, by heating only the second pair of shape memory wires by passing a second current therethrough, or by heating both the first and second pair of shape memory wires by passing the first and second currents therethrough, respectively. 
     In another form of the invention, a method for controlling a vibration absorber incorporating a shape memory element therein is disclosed, comprising the steps of: a) sensing a vibration of the absorber; b) heating the shape memory element to a first temperature in order to stiffen the vibration absorber relatively quickly; c) determining when the vibration of the absorber has been attenuated by at least a predetermined amount; d) reducing the heating of the shape memory alloy element to a second temperature; e) wherein the first temperature is greater than the second temperature; and f) wherein the second temperature is great enough to cause the shape memory element to continue to exhibit a shape memory effect. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic diagram of a tuned-vibration absorber. 
     FIG. 2 is a graph of the response versus frequency of a vibration absorber including damping. 
     FIG. 3 is a close-up of a portion of the graph of FIG. 2, showing the effective region of the absorber of FIG.  1 . 
     FIG. 4 is a schematic diagram of a mass-ended cantilevered beam absorber. 
     FIG. 5 is a schematic diagram of the system of FIG. 4 treated as a simple lumped-mass single degree of freedom system. 
     FIG. 6 is a schematic diagram of a preferred embodiment absorber design of the present invention coupled to a primary mass. 
     FIG. 7 is a perspective view of a preferred embodiment absorber of the present invention. 
     FIG. 8 is a schematic side-elevational view of the absorber of FIG.  7 . 
     FIG. 9 is a schematic side-elevational view of the absorber of FIG. 7 coupled to an electromagnetic shaker. 
     FIG. 10 is a graph of the response of the absorber of FIG. 7 versus frequency for various levels of heating of the SMA wires. 
     FIG. 11 is a graph of the response of the absorber of FIG. 7 versus time illustrating a speed of the absorber with differing levels of current to actuate heating of the SMA wires. 
     FIG. 12 is a schematic side-elevational view of the absorber of the present invention attached to a primary mass in an experimental setup. 
     FIG. 13 is a graph of the response of the system of FIG. 12 versus frequency. 
     FIG. 14 is a close-up of a portion of the graph of FIG.  13 . 
     FIG. 15 is a graph of the response of the system of FIG. 12 versus frequency while the absorber is being actively tuned. 
     FIG. 16 is a close-up of the graph of FIG.  15 . 
     FIG. 17 is a schematic diagram and table of a digital tuning method of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     For the purposes of promoting an understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, and alterations and modifications in the illustrated device, and further applications of the principles of the invention as illustrated therein are herein contemplated as would normally occur to one skilled in the art to which the invention relates. 
     Shape memory alloys (SMA) are a class of alloys exhibiting the shape memory effect (SME). SMA is an alloy that undergoes a reversible phase change. The present description discusses only the SMA Nitinol, an alloy of nickel and titanium, discovered at the U.S. Naval Ordinance Laboratories; however, those having ordinary skill in the art will recognize that any shape memory material (alloy or non-alloy, metallic or non-metallic) may be employed in the present invention, and the appended claims are intended to cover such alternate materials. For example, shape memory polymers, which respond to temperature in a manner opposite to shape memory alloys, are also comprehended for use with the present invention. 
     The state of a shape memory alloy is dependent on its temperature. The two phases are martensite and austenite, which generally correspond to the “cold” and “hot” states of the material. In the martensitic state, the metal exhibits a relatively low elastic modulus and yield strength, beyond which the material may be plastically deformed. Subsequent heating of the material induces the phase change to austenite, with a correspondingly higher elastic modulus and yield strength. In its “hot” state, SMA exhibits an elastic modulus that is as much as three times that of the “cold” state. The net effect is that when unrestrained, the heated material will “remember” its original zero-stress condition, and revert to that shape. Restraining the metal during heating will induce stresses in the material, the magnitude of the stresses dependent upon the initial plastic strain. Values of the elastic modulus of Nitinol are shown in Table 1, along with the elastic modulus for structural steel. 
     
       
         
               
             
               
               
             
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Elastic Moduli of Nitinol and Steel 
               
             
          
           
               
                   
                 Elastic Modulus (ksi) 
               
               
                   
                   
               
             
          
           
               
                   
                 Nitinol: 
                   
               
               
                   
                 Martensite: 
                 4000-6000 
               
               
                   
                 Austenite: 
                 12000 
               
               
                   
                 Structural Steel: 
                 29000 
               
               
                   
                   
               
             
          
         
       
     
     It should be noted that the shape memory alloy Nitinol displays a hysteresis effect during heating and cooling in the transition between the martensite state and the austenite state. For example, when Nitinol is heated, it is necessary to elevate the Nitinol above a first temperature threshold in order to induce the phase change to austenite. When cooling the Nitinol in order to induce a phase change back to martensite, the threshold temperature at which this phase change occurs is lower than the first temperature at which the phase change occurred in the opposite heating direction. When using such a shape memory element in the present invention, it is necessary to account for this hysteresis effect in order to achieve proper operation of the vibration absorber. 
     The prior art generally defines two classifications for the use of SMA in vibration control. The first is active properties tuning (APT), where the change in the elastic modulus of SMA with heating is used. The construction of composite plates and beams, with embedded SMA has been described. Resistive heating of the SMA is accomplished through application of an electrical potential across the SMA wires. This heating changes the elastic modulus of the SMA elements, with a corresponding stiffening of the plate and a change in the plate&#39;s natural frequencies and mode shapes. The other classification used in the prior art is active strain energy tuning (ASET). In this application, the SMA is given an initial plastic strain before being embedded in the composite material. Heating of the SMA then results in in-plane forces within the composite, with subsequent changes in the structure&#39;s natural frequency and mode shapes. 
     Both the ASP and the ASET techniques, as described above, are implemented on the primary system. The necessity to modify the primary system represents several drawbacks. Among these is the fact that embedding the vibration control within the system requires that vibration control be provided from the beginning of the design phase of the primary system, which is not always possible. Furthermore, modification of the primary system to the extent necessary for such embedded systems is normally not practical for retrofit solutions. 
     There is therefore a need for a vibration absorber that may be easily attached to the primary system without substantial modification to the design of the primary system. 
     The present inventors have determined that the properties of SMA may be used to create a tunable vibration absorber with a variable tuning frequency. This represents a passive-adaptive approach to the issue of vibration control, as the absorber is acting as a passive element in influencing the vibration of the primary system. The use of the SMA would provide an absorber that could adapt to attenuate harmonic excitation of a primary system across a band of frequencies. To realize this adaptively tunable design, SMA was chosen as a spring material for the absorber. 
     Many spring designs have been proposed and studied for use in vibration absorbers. In particular, the mass-ended cantilevered beam offers a very simple realization of the spring-mass system for use as a vibration absorber. Such a mass-ended cantilevered beam is illustrated schematically in FIG.  4  and indicated generally at  20 . The system  20  includes an end mass  22  having a mass M and a cantilevered beam  24 . The first natural frequency of a mass-ended cantilevered beam is given by:                  ω   2     =       3      EI         L   3          (     M   +     0.24                   M   b         )                                   Where                 E     =     elastic                 modulus                 I   =     cross        -        sectional                 inertia                 M   =     mass                 of                 the                 end                 mass                 22                   M   b     =     mass                 of                 the                 beam                 24                     (   1   )                                
     Using this equation, and assuming that only the first mode is of interest, the mass-ended cantilevered beam  20  may be treated as a simple lumped-mass sdof system as shown in FIG. 5, where:              ω   =         K   *       M   *                 (   2   )                                
     To create an adaptively tuned absorber, a variable spring is needed. Considering the equation from FIG. 5 for the spring stiffness K* in a mass-ended cantilevered beam, the variable elastic modulus of SMA provides a direct modification of the spring stiffness, through the heating and cooling of SMA beam elements. As noted above, the elastic modulus of SMA varies by a factor as high as three, when the SMA is heated above the threshold temperature. In turn, this results in a change in the effective stiffness of a beam composed of SMA. Considering the extreme cases of a beam composed entirely of SMA, heating the beam through the temperature threshold would result in a stiffness change by a factor as high as three. Further, as the natural frequency of such a system varies as the square root of the stiffness, such a beam would theoretically experience a change in natural frequency of approximately 73%. 
     Two limitations exist here. The first is the large change in the natural frequency with actuation. Rather than such a large shift in the natural frequency, which would result in two distinct, widely separated notches in the frequency response of the primary system, the goal is to widen the single notch created by the absorber, such that attenuation is possible across a continuous band of frequencies. The present inventors have developed a solution to this problem by using multiple SMA elements and actuating them incrementally. For example, a beam composed of three separate SMA elements, that can be actuated independently, would then have the same overall change in natural frequency, between the “all-cold” and “all-hot” states of the SMA. Between those extremes, however, there will be an additional two states, corresponding to the actuation of one and then two of the elements. Assuming comparable authority for each of the beam elements, the four stiffnesses and the corresponding natural frequencies are shown in Table 2, below. 
     
       
         
               
             
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Natural Frequency with Various Levels of SMA Actuation 
               
             
          
           
               
                 Stiffness: 
                 Equivalent Stiffness: 
                 Natural Frequency: 
               
               
                   
               
             
          
           
               
                 3 K cold   
                 3 K cold  = 
                 K1 
                   
                 ω 1   
               
             
          
           
               
                 2 K cold  + 
                 K hot   
                 5 K cold  = 
                 5/3 K1 
                 1.29 
                 ω 1   
               
               
                 K cold  + 
                 2 K hot   
                 7 K cold  = 
                 7/3 K1 
                 1.53 
                 ω 1   
               
             
          
           
               
                 3 K hot    
                 9 K cold  = 
                 3 K1 
                 1.73 
                 ω 1   
               
               
                   
               
             
          
         
       
     
     The second limitation is that, as noted above, SMA has a relatively low yield strength (10000-20000 psi, as compared with 36000 psi for structural steel). For use as a spring material, where displacements may be significant, this represents a strain/displacement limitation. For large-stroke applications, plastic yielding will add hysteretic losses to the system, which may be seen as increased damping in the absorber. As seen in FIG. 3, increased damping severely limits the benefits of adding an absorber to a system. The present inventors have determined that one method of dealing with this limitation is to increase the overall stiffness of the beam system through the use of additional, non-SMA material, in parallel with the SMA. In a preferred embodiment, using steel in parallel with SMA creates an absorber with a higher overall stiffness, resulting in a greater force output for a given displacement. It should be understood, however, that the present invention comprehends the use of other non-SMA materials, both metallic and non-metallic. The non-SMA beam elements also have the effect of limiting the authority of the SMA beam elements in dictating the natural frequency of the absorber. This effectively constricts the tuning band of the absorber. In light of the first limitation, listed above, this has the benefit of increasing the tuning resolution about a higher base frequency. The location of the base frequency is determined by the “cold-state” of the absorber, where the stiffness is the sum of the stiffnesses of the steel and the cold SMA elements. 
     Thus, a preferred embodiment design for an adaptive tunable vibration absorber  30  with solid-state tuning is a mass-ended cantilevered beam constructed of multiple SMA elements  32  and steel elements  34  in parallel. Such a design, attached to a primary mass  36 , is schematically illustrated in FIG.  6 . 
     In order to test the preferred embodiment design, an absorber  40  was constructed, according to the design of FIG. 6, using SMA wires for tuning elements. As shown in FIG. 7, to investigate the tuning of the absorber across a band, three pairs of SMA wires  42 ,  44 ,  46  were used, in parallel with three individual steel wires  48 ,  50 ,  52 . The wires were embedded into a 4.65 gram end mass 54 used as the tuning mass. The addition of a 2.37 gram accelerometer  56  created an effective end mass, not including the mass of the embedded wire, of approximately 7 grams. 
     Actuation of the SMA wires was accomplished through the use of a current-controlled power supply (not shown). Analysis of the heat transfer between the SMA wires  42 - 46  and the ambient temperature laboratory air predicted a required current of approximately 1 amp to maintain SMA temperature above the phase-change threshold of 50 degrees C. Testing showed this to be an adequate current, although during tests of the absorber  40 , higher currents were used to ensure actuation of the SMA wires  42 - 46 . The SMA wires  42 - 46  were actuated in pairs for two reasons. First, with the panel-like geometry shown in FIG. 7, actuation of an off-center SMA would result in an skewed distribution of stiffness about the vertical axis of the absorber  40 . It was believed that this would have effects of exciting undesired torsional modes of vibration. The other reason for the use of the SMA wires  42 - 46  in pairs was the reduction of wiring harness that was achieved by conductively coupling the SMA wire pairs together at their ends adjacent the end mass  54 , thereby creating a current-carrying loop for resistive heating. Using the SMA beam elements  42 - 46  as the conductors of current through the absorber  40  eliminated the need for additional current-carrying wires in the design. 
     The length of the absorber wires  42 - 46  between the fixture  58  and the inside edge of the end-mass  54  was 1.87 cm. The width of the end-mass  54  was 0.64 cm. The length of the absorber  40  was measured to the centroid of the end-mass  54 , resulting in an absorber  40  beam-length of 2.18 cm. As shown in FIG. 8, the absorber fixture  58  consisted of two brass plates  60 , separated by two phenolic plates  62  that served as electrical insulation, to keep the current from short-circuiting through the brass plates  60 . Grooves were milled into the phenolic plates  62  that served to align the absorber wires. Screws were used between each of the grooves, to clamp the absorber in the fixture 58. 
     As shown in FIG. 9, testing of the absorber  40  was performed on an electromagnetic shaker  64 . The absorber fixture  58  was clamped to the top of the shaker  64 , as shown. Actuation of the absorber  40  was accomplished through resistive heating of the wires  42 - 46  via a current-regulating power supply (not shown). The supply voltage was put through a switch-box (not shown) that ran an identical current through one, two, or three pairs of the SMA wires  42 - 46 , depending on the switch positions. For cold tests, the power supply was not turned on. 
     Excitation of the absorber  40  was accomplished through a stepped-sine signal fed to the shaker  64  from a signal analyzer (not shown) and was at a level of 0.5 g, from 59 to 131 Hz, in 0.125 Hz increments. The transfer functions for the absorber  40  at the various levels of heating were calculated by the DSP based on measurements taken from accelerometers  56 ,  57  on the absorber end-mass  54  and the shaker  64  base. These transfer functions are shown in FIG.  10 . 
     FIG. 10 shows the absorber  40  frequency responses at the various levels of actuation. The natural frequencies vary from approximately 83.55 Hz in the all-cold (non-actuated) state, to 98.0 Hz when totally actuated (all wires  42 - 46  heated). This represents an increase in the natural frequency form the cold state of approximately 17.4%. It is interesting to note the general shapes of the curves in FIG.  10 . With no actuation, the frequency response shows the characteristic shape of the nonlinear response of a “softening spring.” With greater actuation, the response peaks grow in magnitude and the general shape appear more like the typical frequency response of a linear system. Heating the wires  42 - 46  implies increasing the overall stiffness of the system. At the same time, the effective damping is reduced. This may have some effect on the growth of the magnitude peaks with actuation. A more likely reason, however, is the nonlinear response of the SMA  42 - 46  in its cold state, where the plastic yield strength creates a nonlinear spring effect. For small strains about the zero-yield state, the material  42 - 46  will act as a linear spring. With larger displacements, however, the restoring force will peak as the material experiences plastic yielding. 
     To calculate the expected natural frequencies of the absorber  40 , Equation (1) was used, but with one modification. FIG. 4 shows the length of the beam measured to the outer edge of the lumped mass  22 , as is typical in the prior art. It was not felt that this was an appropriate measure of the length of the beam, in this case, as the lumped mass&#39; thickness is approximately {fraction (1/3+L )} the length of the absorber  40  wires from the fixture  58  to the lumped mass  54 . Instead, the length of the wires was calculated to the center of the lumped mass  54 , as shown in FIG.  8 . The measured and predicted results are shown below in Table 3. 
     
       
         
               
             
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Predicted and Measured Absorber Natural Frequencies 
               
             
          
           
               
                   
                 Actuation Level: 
                 Predicted ωn (Hz) 
                 Measured ωn (Hz) 
               
               
                   
                   
               
             
          
           
               
                   
                 None 
                 88.8 
                 83.5 
               
               
                   
                 One pair 
                 95 
                 88.9 
               
               
                   
                 Two pairs 
                 100.8 
                 93.5 
               
               
                   
                 All three pairs 
                 106.3 
                 98.0 
               
               
                   
                   
               
             
          
         
       
     
     In FIG. 10 comparison of the two extreme states, the “all-cold” and the “all-hot” states, shows a difference of almost 18 dB between the two responses at 83.5 Hz. This frequency corresponds to the resonant frequency of the all-cold absorber  40 . To investigate the time-domain response of the absorber  40 , the absorber  40  was driven at this frequency when in the all-cold state. The power supply was then switched on, such that all three pairs of SMA wires  42 - 46  were actuated. This corresponded to a switch from the all-cold to that all-hot state of the absorber  40 . Three current levels were used to perform this test, 1.5, 3.0, and 4.5 amps. The actuation occurred one second after the signal analyzer began recording the response of the system. The time-domain responses to these three actuations are shown in FIG.  11 . 
     Following actuation of the SMA wires  42 - 46 , the magnitude of the response of the absorber  40  was approximately 10% of the magnitude of the response before actuation. This is somewhat better than the 12.6% predicted by the frequency response plots. Another interesting point to note about FIG. 11 is the different responses with the different actuation levels. Actuation for all three levels occurred at the same point in the tests, one second into the record. The 4.5 amp response was relatively rapid, with the response achieving its new state in less than on-half second. The 3.0 amp response was somewhat slower, requiring almost a full second to achieve the actuated state, while the 1.5 amp level as much slower and did not achieve the fully actuated state within the five seconds of actuation shown in the record. These different responses indicate a desirable tuning strategy for the absorber  40  that uses high current levels for a relatively short duration, in order to achieve the actuated state. Once that state is achieved, the current level may be scaled back to that required to maintain the temperature of the SMA wires  42 - 46  above the threshold temperature of the material. 
     With the absorber  40  characterized, the next step is to implement the absorber  40  on a primary system to see what influence the absorber  40  has in reducing the vibration of that system. To approximate a sdof system to which the absorber  40  could be applied, a second mass-ended cantilevered beam system was used. In this case, the brass absorber fixture  58  represented the lumped mass. The spring element was approximated by an aluminum beam  66  to which the absorber fixture  58  was mounted. The schematic of this setup is shown in FIG.  12 . 
     Accelerometers were mounted to the absorber fixture  58  and to the shaker  64 , which was driven with a stepped-sine input, from 60 to 190 Hz., from the signal analyzer. The spacing of the measurements was every 0.25 Hz, from 60 to 75 Hz, every 0.125 Hz from 75 to 110 Hz, and every 0.25 Hz from 110 to 190 Hz. The reason for the varied spacing of the sampling was the desire for increased resolution in the absorber&#39;s operating range. The accelerometer outputs were fed into the DSP which calculated the resulting transfer function between the acceleration of the shaker  64  and the acceleration of the fixture  58 . The natural frequency for the mass-ended beam alone (no absorber attached) was approximately 142.5 Hz. To tune the absorber  40  to the natural frequency of the primary system was not seen as an appropriate test of the absorber&#39;s effectiveness. It is expected that the design of a primary system will not include vibration-sensitive elements driven at resonance. The transfer functions for the system at various levels of actuation of the absorber  40  are shown in FIG.  13 . FIG. 14 is a close-up of FIG. 13, showing the primary system&#39;s response over the operating range of the absorber  40 . 
     The various levels of actuation achieve attenuation of the vibration of the primary mass from −7 to almost −20 dB, across an approximately 13 Hz band of frequencies. Also, with increasing actuation of the SMA wires  42 - 46 , the responses show increasingly sharp “peaks” and “notches.” This is attributed to the reduced effective damping of the absorber  40  with the stiffening of the SMA wires  42 - 46 . Close examination of FIG. 14 shows that with increasing actuation, the frequency bands between the notches are reduced, from almost 6 Hz between the “All Cold” and “One Pair Actuated” states, to approximately 2 Hz between the “Two Pair Actuated” and “All Hot” states. One possible reason for this may be fraternal heating of the SMA wires  42 - 46  during the course of the tests. For example, if the epoxy end-mass  54  is acting to conduct heat between actuated and non-actuated wires  42 - 46 , a temperature profile may exist that includes a certain amount of unintended actuation of SMA wires  42 - 46 . This fraternal heating may not have been significant during the absorber  40  characterization tests, due to the shorter duration of those tests. This still does not explain the location of the notch in the “All Hot” frequency response at a frequency below the natural frequency of the absorber  40  in this state. 
     FIG. 14 does show the distinct notches in the frequency response of the primary system due to the absorber  40 . Additionally, the resonant frequency of the primary system is shifted to higher frequencies than the original no-attached-absorber  40  resonant frequency. The figure suggests a simple approach to tuning the absorber  40  in response to a harmonic excitation of increasing frequency. This is to actuate the absorber  40  to higher levels of stiffness as the response at those levels becomes more advantageous. For example, the “All Cold” state is the most appropriate state for frequencies up to approximately 88 Hz. FIG. 14 shows that for higher frequencies, the “One Pair Actuated” state of the absorber  40  will result in greater attenuation than the unactuated state. There are similar cross-over frequencies describing advantageous transitions between the “One Pair Actuated” and “Two Pairs Actuated” and the “Two Pairs Actuated” and “All Hot” states. So, actuation of increasing pairs of absorber wires  42 - 46  at known cross-over frequencies provides a convenient method of intelligently tuning the absorber  40  to provide the minimal response of the primary system. 
     To test this, the stepped-sine input was again applied to the system of FIG.  12 . The absorber  40  was not actuated until a frequency of 88 Hz, at which time the first pair of SMA wires  42 - 46  was heated. The second and third pairs of wires  42 - 46  were actuated at 92.625 and 95.625 Hz, respectively. The resulting performance plot of the system is shown in FIG.  15  and is labeled “Manual Tuning,” in reference to the method of manual tuning of the absorber  40 . Manual tuning involved the operator manually switching the current supply to actuate additional pairs of wires  42 - 46  at the appropriate frequencies. Two additional performance plots are also shown, for comparison with the manually-tuned absorber  40 . These are the “Fixed Tuning” and “Baseline” plots. The fixed tuning plot shows the absorber  40  left in its “All Hot” state, with no actuation of the SMA wires  42 - 46  during the frequency sweep. The absorber  40  was removed from its fixture  58  for the baseline plot. As such, this plot represents the transfer function of the untreated mass-ended cantilevered beam  66  alone. FIG. 16 is a close-up of FIG. 15, showing the primary system&#39;s response over the operating-range of the absorber  40 . 
     A distinction should be made between these “performance plots” and the frequency response plots discussed above. The frequency response plots are indications of the response of the system to excitation at the different frequencies. This excitation may occur across a band of frequencies, or may be random noise. In contrast, the performance plots show the response of the system to a harmonic input of a single, fixed frequency. They do not represent the response of the system to broadband excitation. 
     Examination of FIG. 16 shows that the manually tuned absorber  40  represents a substantial improvement in performance over the case of the absorber  40  with fixed tuning. Attenuation of the primary system&#39;s response is achieved over a much wider frequency band. The result is that the absorber  40  is more effective across a wider window of frequencies than is possible with a fixed absorber. An unanticipated benefit is the reduction of the first peak in the magnitude of the response, due to initial operation with no actuation. A similar effect may be achieved through the use of active dampers that increase the damping of a system through resonance. 
     Use of the preferred embodiment absorber  40  described hereinabove was by manual activation of the current source used to resistively heat the SMA wires  42 - 46 . It will be appreciated by those having ordinary skill in the art that a more preferred method for use of the absorber  40  is an automated system imploying a processing device such as a microprocessor and associated memory. An accelerometer placed upon the primary mass may provide an input to the microprocessor of the vibrational frequency being exhibited by the primary mass. Based upon this frequency input, the processor may execute an internally stored software program which will determine which of the SMA wires  42 - 46  should be actuated (heated) in order to tune the frequency of the absorber  40  to most closely match the frequency of vibration of the primary mass. In this way, the absorber  40  may be made automatically responsive to varying vibrational modes of the primary mass, with the microprocessor affecting control of the absorber  40  in order to tune the absorption response to the vibrational frequencies of the primary mass. The design and programming of such a processor-based system will be readily apparent to those having ordinary skill in the art in view of the present disclosure. 
     Useful variations of the above-described concepts have also been developed by the present inventors. One such variation is the concept of continuous tuning, in which the vibration absorber may be operated in such a way that the SMA wires do not have to be considered as digital entities (i.e. either cold or hot). The concept of continuous tuning recognizes the fact that between the low elastic modulus state (martensite) and the high elastic modulus state (austenite), there lies an intermediate temperature band of approximately 5-10° C. in which the SMA material transitions between these two states according to a predetermined continuous function. By precisely controlling the temperature of the SMA element, it is possible to continuously tune the elastic modulus of the element between its low and high extremes and therefore continuously tune the frequency at which the vibration absorber operates. 
     A second variation developed by the present inventors involves the concept of digital tuning of a vibration absorber. In this design, the SMA wires may be constructed of differing diameters, such that each wire exhibits different values for its low elastic modulus state and high elastic modulus state. The system controlling the vibration absorber may then choose to heat or cool wires of differing diameters in order to more precisely tune the frequency of the vibration absorber. For example, FIG. 17 illustrates what is possible with a vibration absorber according to the general principles of the preferred embodiment, however utilizing SMA wires having different diameters. In the example of FIG. 17, wires having three different diameters are illustrated; however, the present invention comprehends the use of wires having any number of diameters. Furthermore, as discussed above, it may be desirable to implement wires of different diameters in pairs in order to eliminate torsional vibration concerns. The matrix of ones and zeros below the wire diameters represent a chart specifying whether each of the individual wires is heated or cooled in order to place the wire into one of its two states. A one represents that the wire is heated to its austenite state, while a zero indicates that the wire is cooled to its martensite state. As can be seen from the chart, the wires may be activated and deactivated in various combinations similar to a binary counting sequence that will allow the vibration absorber to transition from a low overall elastic modulus to a high overall elastic modulus in very small, discrete (digital) steps. With such tuning available to the processor controlling the system, it will be possible to more precisely tune the vibration absorber to the desired frequency. 
     Other modifications of the present invention should be apparent to one having ordinary skill in the art in view of the present disclosure. For example, heating of the SMA wires in the preferred embodiment was accomplished by passing a current through these wires, allowing them to heat up due to the natural resistance of these wires. The present invention also comprehends the use of other heating methods. For example, independent resistive heaters may be placed in close proximity to the SMA elements in order to more rapidly heat those elements. In one embodiment, a resistive wire may be wrapped around each of the SMA elements and current flowed through the resistive wire in order to provide more rapid heating of the SMA element. Other heating methods, such as forced-air heating are also comprehended. 
     Additionally, the preferred embodiment relies on convective losses to the ambient air to achieve cooling of the absorber  40 . As such, while the absorber  40  will eventually achieve effective steady-state operation in the case of a reduction in excitation frequency, a much longer period of mistuning must be tolerated than in the case of heating the absorber to match an increasing excitation frequency. Geometries other than the solid wire SMA are available that may allow for increased cooling rates. Such an example is the hollow SMA currently available that may allow for forced-air cooling of the absorber  40 . Active cooling technologies may also be used with the present invention. 
     An alternate technique to deal with the slower cooling rate may be the use of active stiffness reduction. Materials (such as shape memory polymers, for example) are available that, when heated, experience substantial reductions in their elastic modulus. Judicious use of elements constructed of such materials will result in a design that incorporates active stiffness reduction. The strategy would then be to utilize the active stiffness reduction to drop the stiffness of the system, at the same time as power is removed from some or all of the SMA wires. As the SMA wires cool to the point where this active stiffness reduction is no longer needed, that system may also be phased out. 
     The question of fraternal heating among the SMA elements also points out the desirability of a feedback temperature controller. In the test described above, temperature feedback consists of an operator monitoring thermocouples attached to the SMA. The operator then increases or reduces the electrical current input to the SMA. Implementation into an autonomous control system should include transfer functions or other similar control models that describe the response of the SMA. 
     While the invention has been illustrated and described in detail in the drawings and foregoing description, the same is to be considered as illustrative and not restrictive in character, it being understood that only the preferred embodiment has been shown and described and that all changes and modifications that come within the spirit of the invention are desired to be protected.