Jtam.dvi JOURNAL OF THEORETICAL AND APPLIED MECHANICS 48, 1, pp. 135-153, Warsaw 2010 A SHAPE MEMORY ALLOYS BASED TUNEABLE DYNAMIC VIBRATION ABSORBER FOR VIBRATION TONAL CONTROL Barbara Tiseo Antonio Concilio Salvatore Ameduri Antonio Gianvito C.I.R.A, The Italian Aerospace Research Centre, Capua (CE), Italia e-mail: b.tiseo@cira.it; a.concilio@cira.it; s.ameduri@cira.it; a.gianvito@cira.it This paper examines a novel model of an Adaptive Tuneable Dynamic VibrationAbsorber (ATDVA), based on the use of ShapeMemoryAlloy materials (SMA). Being adaptive, the absorber is able to track variation of the structural dynamic response. The absorber architecture is extremely simple: it consists of a clamped SMA wire and a concentrated mass. Two reference structures have be- en considered: a typical aeronautical aluminium panel and a fibreglass panel. In the first part, the investigated concept is introduced with a short presentation about the SMAmain properties. The realisation and experimental characterisationof the device are thenpresented. Its imple- mentation, a report on the experimental campaign and the presentation of the attained results conclude the work, together with a discussion on the achieved results and the next investigation steps. Key words: ATDVA, SMA, vibration control 1. Introduction Vibrating environments are a common experience in the all-day life. When a structure is undergoing some form of vibration, there are a number of ways in which this vibration can be controlled. Passive control involves some form of structural interventions, often including the use of springs and dampers, that leads to reduction of the vibration levels, while active control uses sen- sors, actuators and electronic control systems, aimed at reducing themeasured response. 136 B. Tiseo et al. This study investigates the use of ATDVA, based on shape memory alloy materials, to control structural vibration. A Dynamic Vibration Absorber (DVA) is essentially a secondary mass, attached to the main system generally via a spring and a damper. The na- tural frequency of the DVA may be tuned to the eigenfrequency of unwanted vibration. In this case, its action produces a split of the response peak. If it matcheswith the disturbance frequency, a specific absorption of the structural vibration occurs, extracting energy from the primary system. The application of DVA’s has been investigated bymany authors (Hartog, 1956). Among themost significant examples, the work of Dayou andBrennan (2002) can be recalled. They investigated how to use vibration neutralizers to control global vibration of structures and the influence of certain parameters in the control of kinetic energy. Huang and Fuller (1997) examined the effect of DVA on the forced vibration of a cylindrical shell and its coupled interior sound field. Traditional vibration absorbers have limited applications for its narrow frequency bandwidth; in fact, the DVA must be tuned very accurately to a specific frequency value, in order to obtain substantial vibration reduction. The use of a tuneable device instead of a classical one, allows changing the frequency atwhich it can operate. A significant example of implemented tune- ableDVA is the one at theArsenal Football Club (Texas), where the structure is particularly excited by the crowd jumps that happenat a rhythmnear to its resonances (TDVA..., 2008). The device was chosen to be tuneable, to satisfy the structure in case the initial experimental test campaign characterisation was not correct. ”Adaptively tuned” refers to the capabilities of the DVA to change its internal properties to take into account changes or follow variations of the vibrating structure. Mechanical components are however hard to be adapted. Dealing with systems that may be intrinsically adaptive is fashionable and may lead to simplified control architectures. SMA’s are a kind of smart materials whose physical properties change as a function of temperature. This effect can be exploited to build tuneable and adaptive devices. One of the first studies carried out on the subject is due toBaz (1990) who demonstrated the feasibility of using SMA in controlling flexural vibrations of a beam. Rustighi, Brennan and Mace first designed an SMA-based vibration absorber and implemented a control algorithm for its real time adaptation (Rustighi et al., 2005b), Williams et al. (2002) investigated the use of SMA A shape memory alloys... 137 to build an adaptive-passive absorber. Elahainia (2005) presented a tuned vibration absorber, based onSMAwiresworking as adaptive stiffness elements and taking advantage of the elastic modulus variation. This paper presents anATDVA, based on the use of SMAwires that explo- its its capabilities through a proper architecture. Its arrangement is extremely simple: it consists of an SMA clamped wire and a concentrated mass placed in its middle. It works as a tensioned spring whose stiffness is controlled by varying the electrical current through the wire. Two effects are taken advan- tage of: the change of the material phase from martensite to austenite that induces an increase of the Young modulus and the adopted wire constraint that causes an increase of the internal tension as the transformation occurs. In this way, the natural frequency of the absorber may be adjusted in a wide range to match one of the targeted frequencies. Further the traditional DVA’s advantages, the proposed device presents benefits as extremely low cost, simplicity of implementation and integration, with its architecture being very simple and compact. For instance, it could be easily embedded in the core of a honeycombpanel. Itwould result in a comple- tely self-standing active vibration insulating element that could be integrated within existing aircraft, replacing the already installed panels. Because of the thermal nature of activation, these SMA-based devicesmay be used to follow slow structural-related variations like turboprop rotation regimes, different stationary conditions (i.e. electrical machinery working at different rpm). This research builds upon past works (Tiseo et al., 2005), where the fe- asibility of the concept and preliminary experimental studies were performed, aimed at verifying the functionality of the proposed device to control noise and vibrations. In the first part of the paper, the investigated concept is introduced, with a short presentation of the SMAmaterials. Then, details about the two herein considered reference structures, the realisation and experimental characterisa- tion of the device are presented. The experimental campaign and the presen- tation of the attained results conclude thework, together with a discussion on the achieved results and the next investigation steps. 2. One-DOF system controlled by tuned vibration absorber Vibration absorbers are a valuable tool used to suppress vibrations due to harmonic excitation in structural systems. 138 B. Tiseo et al. Fig. 1. Schematic of Dynamic Vibration Absorber attached to a host structure The concept of the dynamic vibration absorber is fairly old and consists in a simply mass-spring system attached to a vibrating host structure, which can be modelled as in Fig.1. The inertia of the absorber mass reduces the net force and hence the response of the host structure. According to Estéve (2004), the analytical model of a dynamic vibration absorber attached to a single-degree-of-freedom host structure is described by the following equations of motion m s ẍ s +(k s +k a )x s −k a x a +(c s + c a )ẋ s − c a ẋ a = f(t) (2.1) m a ẍ a +k a (x a −x s )+ c a (ẋ a − ẋ s )= 0 The impedance of the host structure without the dynamic vibration absorber is given by Z s (ω)= m s (ω2 s −ω2−2iωω s ξ s ) −iω (2.2) The impedance of the dynamic vibration absorber is defined as the reacting force through the spring and damper exerted on the primary system due to unit velocity of its attachment point.UsingEqs. (2.1), the absorber impedance is given by Z a (ω)=m a iωω2 a +2ξ a ω2ω a ω2 a −ω2−2iξ a ωω a (2.3) Therefore, the effect of the dynamic vibration absorber on the host structure vibration is a functionof the ratio of the absorber impedance to the impedance of the structure at its attachment point since ẋ s = ẋ0 ( 1− Z a Z s ) −1 (2.4) A shape memory alloys... 139 The bigger the impedancemismatch between the dynamic vibration absorber and the structure, themore the absorber affects the response of the structure. Dynamic vibration absorbers are used in two different ways. When tuned to a specific vibration of the hosting structure, usually driven by a broadband excitation, they act as tuned dampers. When they are not tuned to a mode but toa specificexcitation frequencyusually encountered in rotatingmachines, dynamicvibrationabsorbers aredesigned topresent a large impedanceat their attachment points in a very narrowband around the excitation frequency, and therefore the absorber damping is kept as small as possible. The idea herein presented deals with using SMA as adaptive spring ele- ments. The architecture is made of an SMAwire, clamped at the edges, with a concentrated mass placed at its geometric centre. Because the SMA mate- rial have variable properties, the device may present different configurations in terms of themechanical response. In detail, the absorber design consists of a trained NiTi wire. To let it modify its dynamic behaviour, it was heated by an electrical current (Joule effect), forcing the internal tension to change, and then attaining a controlled frequency shift. 3. SMA background general overview SMA’s show a reversible change in the crystalline structure depending on tem- perature or internal stress variations. At low temperatures, the SMAmaterial structure is in a martensite phase, characterised by low stiffness and high damping values. When the alloy is heated up, the phase changes into auste- nite, stiffer (around three times higher) and slightly damped; it also recovers eventual residual strain the alloy underwentwhenmartensite. If the SMA is a one-way type, by reversing the process, thematerial transforms into a pseudo martensite phase, called ”twinned” with no further strain recovery. If a load is applied, thematerial transforms into de-twinnedmartensite andmay resto- re the original shape, depending on the load combination and other factors. Generally speaking, under a pre-load, a cycle may be aroused. If the SMA is a two-way type, the strain is recovered in both directions, austenite to mar- tensite and vice versa. This last phenomenon, however, does not demonstrate symmetry in the two directions in terms of strength. Another interesting property is the so-called super-elastic (or, after certa- in authors, pseudo-elastic) effect. If the environmental temperature is higher than the one that allows complete transformation into austenite, thematerial will fully recover spontaneously, when unloaded, large strain fields (magnitude 140 B. Tiseo et al. 105 strain) that led its internal structure from austenite to martensite phase (Fig.2). Fig. 2. Stress-strain curve for a generic SMA; (a) – shape memory effect, (b) – superelastic effect Summarising, the SMAmaterial, deformedbyan external load, changes its internal structure from austenite into martensite displaying very high strain (around 10%), that is fully recovered when thematerial itself is heated (shape memory effect) or simply unloaded (super-elastic effect). SMA’s showagoodpotential for vibration control, linked to their property of changing their elastic modulus, showing different levels of damping and recovering large strains (Otsuka andWaymann, 2002). Because the transition from martensite to austenite is continuous and because it can be represented through a well-sketched relationship with respect to its intrinsic composition (see themodels of Tanaka et al.(1986) or the one of Liang andRogers (1990), for instance), SMAwires can be easily used as continuously adaptive tensioned spring elements. A DVA that incorporates such devices could continuously control the vibration field of a structure in a large band around a specific frequency (tonal control). Another possibility is to switch from a frequency to another if the reference system is characterised by the possibility or the necessity to work at different frequencies. 4. SMA-based ATDVA Standing on the characteristic properties of the SMA, a novel concept of DVA is introduced, able to be tuned to a prescribed frequency, inside a determi- ned band, without any external mechanical device. This device is therefore an Adaptive Tuneable DVA and is referred to as an ATDVA. The architecture is extremely simple. The absorber consists of a pre-stressed Ni-Ti wire, clamped at the edges, with a concentrated mass placed in its geometric centre. It is A shape memory alloys... 141 heated by an electrical current (Joule effect), so that the internal stress field is forced to change (strain is inhibited), attaining a large controlled eigenfrequ- ency shift. The design is completed by a sustaining frame that hosts the wire (Fig.3). Fig. 3. ATDVA basic architecture Such a kind of a device is able to track slow variations of the structural vibration response andprovide tonal vibration attenuation. It does not require tight tolerances and may be easily applied when the characteristic external forces vary into a definite range or assume finite different values (different working regime). Thedesign frequency range is computed throughanapproximated relation- ship that can be derived from the formula valid in the case of a non-massive string with a concentrated mass at its centre, and the formula which refers to the case of a massive vibrating string (Blevins, 1979; Imman, 1989) f = √ T (π2M c +4M w )L (4.1) In (4.1), f is the resonance frequency, M c – concentrated, M w – total wire mass, L – wire length and T the force per unit of area acting on the SMA wire (internal stress). 5. Referred applications In order to preliminarily evaluate its capabilities, the proposed ATDVA has been tested on two reference structures that are both of certain interest for aeronautical applications. 142 B. Tiseo et al. In the first case, a thin aluminium plate (480× 760× 1.5mm) has been selected, representing a classical fuselage panel. A 1.2mmdiameter SMA (Ni- Ti) wire, 100mm long has been adopted. Thewire has been clamped at both the extremities to a circular steel frame. The complete device has been then bonded to the plate. In the second case, an advanced adaptive-stiffness panel was referred to, in order to evaluate the investigated device (SMA-based ATDVA) capabilities to further affect the dynamic response of such a next generation structural element (Ameduri et al., 2005). More in detail, the adaptive panel is made of four, 0.3mm thick fibreglass plies; on the middle plane, 17 SMA wires are embedded, oriented along the panel widest dimension and 1cm spaced. By driven variations of the SMA properties (by heating, for instance), the dynamic response of the panel may be affected. The ATDVA architecture is basically the same as the previous one. However, a ligther solution was tested: a rectangular aluminium framewas used anda 0.76mmdiameter SMA(NiTi) wire, 80mm long was adopted (Fig.4). Fig. 4. ATDVA lighter architecture Tocheck different control strategies, in thefirst case, the current, travelling through the SMA wire, measured through an amperometer, has been chosen as the control parameter; in the second case, the wire temperature, measu- red through a thermocouple. A feedback controller has been implemented to stabilise the selected parameters. In particular, temperature appeared to be strongly dependent on both environmental conditions and the current. The objective of thework has been the assessment of a single-DOF system aimed at reducing the dynamic structural response at certain resonances. This can be seen as a first step beforemoving towards to the control of generic tone excitations (e.g. sinusoidal periodic excitation). A shape memory alloys... 143 6. ATDVA architecture and characterisation The design phase of the SMA-based absorber has needed some previous ope- rations aimed at characterising the structural element to be controlled. Having fixed the SMA length and diameter, the absorber mass has to be varied to match a proper range around the chosen structure eigenvalue. Firstly, an experimental campaign has been addressed to characterise an isolated SMAwire. It has been pre-strained, using a dedicated stretching de- vice that has also provided the desired constraining conditions. Pre-strain ensures a starting eigenfrequency different from zero. Then, the wire has been heated to pass from the initial martensite to the austenite phase. The wire vibration has beenmeasured by using a laser vibrometer. Theworking temperatures rangehasbeen set to: 25◦C(roomtemperature) – 38◦C. Seventy-five temperature cycles havebeen enforced.A large eigenfrequency shift has beenmeasured, resulting in about 140Hz as shown in (Fig.5) where only some of the cycle results are reported, for the sake of clarity. Fig. 5. Thermal test on a constrained SMAwire; first modal frequency vs. wire temperature The graph also shows a drastic variation of the SMA behaviour between the first and the next cycles afterwhich clear behaviour stabilisation occurred. At this point, awirewitha concentratedmass andhosted in the abovemen- tioned frames has been experimentally characterised. This device represents the studied ATDVA. Two values of themass have been set, respectively equal to 1 and 1.5% of themain systemmass. Thewire has been connected into an electrical circuit, with the aim of heating it up. The global system (made of the wire, mass 144 B. Tiseo et al. and the ring frame) has been bonded on a heavy steel block. It has been excited through impulsive forces by an instrumented hammer, as the internal excitation current was varying between 0 and 2.5A. Different wire internal stress levels have then been obtained and consequent different values of the absorber vibration frequency have been measured. The laser vibrometer, the other sensors (thermocouples), the actuator and the excitation devices have been connected to a 36-channel acquisition system (LMS SCADAS III). In the 1% concentrated mass configuration, the absorber natural frequen- cy proved to vary between 50 and 80Hz from the cold (0A) to the hot state (2.5A), roughly corresponding to a 60% frequency shift. When the mass is increased (1.5%mass configuration), the natural frequency varies from 34Hz (0A) to 42Hz (2.5A), roughly corresponding to a 25% frequency shift. The results are reported in (Fig.6). Of course, the larger the mass, the larger the expected capability of the device in attenuating the vibration in the selec- ted range. However, rising the mass value, a narrower frequency variation is expected, also according to simplified expression (4.1). Fig. 6. Experimental characterization of isolated ATDVA: eigenfrequency [Hz] vs. current [A] 7. ATDVA: implementation results 7.1. Aluminium panel A preliminary numerical simulation has been performed, aimed at esti- mating panel mode shapes and frequencies for the configurations with and without the ring frame. All the panel edges were not constrained. The ring mass implied a significant panel response modification in terms of eigenfre- quencies, while the eigenvectors modifications were negligible. This is easily A shape memory alloys... 145 understood by considering that the frame acts as a concentrated mass loca- ted at the centre of the plate. In the low frequency range, it then affects the modalmass for the oddmodes without varying their shape, while it is simply non-effective for the even modes. The selected placement came up from the necessity of having large displacement for the considered frequency and then, a large potential energy dissipation. Experimental modal analysis has been then carried out on the set-up illu- strated in (Fig.7a), confirming the early numerical predictions. The ATDVA working frequency range has been set to the one around the first eigenmode at 66Hz, (umbrellamode, Fig.7b). Table 1 reports a comparison of the natu- ral frequencies for the numerical (with and without frame) and experimental results (installed frame). Fig. 7. (a) ATDVA on the aluminium panel: experimental setup and block diagram; (b) mode shape comparison (66Hz): numerical vs. experimental results The experimental setup has beenmade of the following main equipment: • shaker (Gearing andWatson) as the excitation device, with the associa- ted electronics (amplifier); • laser vibrometer (Polytec) as the velocity sensor; • power supply (Delta) to drive the SMAwire; • acquisition and generation system (LMS SCADAS III). The block diagram is reported in Fig.7a. The exciter has been driven by a chirp signal having a frequency content between 0and 500Hz; theplateFrequencyResponseFunction (FRF)hasbeen 146 B. Tiseo et al. Table 1. Modal analysis – numerical-experimental eigenfrequencies compari- son Natural frequencies [Hz] Numerical Numerical Experimental plate plate + ring plate + ring 13.1 12.3 9.5 29.1 29.5 25.1 34.8 31.6 30.1 36.3 35.7 38.4 44.7 43.4 47.3 54.6 54.9 50.3 62.2 58.1 54.4 64.0 67.4 66.2 acquired in the range between 0 and 75Hz. In Fig.8, single-point FRF’s are presented around the targeted frequency (66Hz).Theyhave been acquired for different values of the current running along the SMAwire. Themeasurement point has been the one at the middle of the plate, the most representative in the selected range. Because of the presence of the dynamic absorber, at the target frequency band two new peaks have appeared instead of the original one; an anti-resonance in between can also be seen. The absorber is perfectly tuned for a 1.9Acurrent.Themaximumvelocity attenuation of around 20dB has been attained at 66Hz. Fig. 8. Case 1 – single point FRF acquired at different current Global results are instead reported in Fig.9, where ameasure of the vibra- tion energy has been evaluated as the mean value of the velocities, recorded A shape memory alloys... 147 in 40 points and homogeneously distributed on the plate. In this case, the attained attenuation at 66Hz is also evident (a 10dB reduction can be ap- preciated) as well as the appearance of other two peaks. Fig. 9. Case 1 – structural vibration energy (40 measurement points): non-activated vs. activated (I =1.9A) ATDVA 7.2. SMA-embedded fibreglass panel The plate has been left free on the longest and clamped along the shor- test edges, through a specific device aimed at fixing its embedded wires, too. First, an experimental campaign has been carried out without activating the embedded SMAwires. As expected, the presence of the absorber, placed once again at the plate centre, has not significantly affected the panel response in terms of both mode shapes and natural frequencies, due to the limited amo- unt of addedmass and stiffness. A very light ATDVA system has been in fact implemented in this case. FRF’s have been then evaluated.With respect to the former experimental setup, a hammer has been used instead of the shaker (Fig.10). A single-point excitation has been performed and the system response in terms of veloci- ty v(t)hasbeenacquiredover 117points, uniformlydistributed (Fig.10), thro- ugh a laser vibrometer and normalised with respect to the input force F(t). The absorber has been then activated through a current. The target system resonance frequencyhas been set at 196Hz.As before, the relatedmode shape has associated with a large displacement at the middle of the plate. Again, the internal tension of the wire has been controlled through varia- tion of its temperature, inducedby a current. In this case, the feedback control loop has been based on temperature information, acquired by the thermoco- uple. 148 B. Tiseo et al. Fig. 10. Case 2 – fibreglass panel: test rig andmeasurement points; experimental setup block diagram As the wire-mass system eigenfrequency approaches the panel resonance, its contribution to the structural response at that band, as expected, becomes more and more evident. This effect is maximized at the ”tuning frequency”, where the isolated mass-wire system and themain structure exhibit the same eigenvalue. Zooming on 196Hz (Fig.11), the ATDVA-induced response peak moves towards higher values as a function of the growing temperature. The figure refers to a single acquisition point (central point of the plate). Fig. 11. Case 2 – single point FRF acquired at different wire temperatures After that, the plate kinetic energy (measured over the aforementioned 117 acquisition points) is computed (Fig.12). The global energy attenuation levelmaybe estimated in around 5dB in thenarrowband 186-206Hz (roughly corresponding to the ATDVA influence band). If the half-power bandwidth is considered, the attenuation rises to more than 10dB. A shape memory alloys... 149 Fig. 12. Case 2 – structural vibration energy (117measurement points): non-activated vs. activated ATDVA At the end, in order to verify the effect of the proposed semi-active control device on the smart panel when it is activated, another test has been perfor- med. It has been aimed at evaluating the capabilities of theATDVA to further affect the dynamic response of such an adjustable stiffness structural element, whose characteristics and behaviour are detailed in bibliography. Fig. 13. Case 2 – action of ATDVA on the activated smart panel Before, a selected panel natural frequency has been shifted, by heating the panel embedded wires: the panel natural frequencies have been globally mo- ved towards higher values. In detail, by considering a 2A current, a frequency increase of about 4Hz has been achieved. The ATDVA has been then tuned at the target frequency with the purpose of attaining a further tonal mitiga- tion (Fig.13). The eigenfrequency at 196Hz has been again considered as the reference one. 150 B. Tiseo et al. 8. ATDVA: conclusion In this paper, the design and implementation of an SMA-based ATDVA have been investigated. This device uses an SMA wire as a tensioned adaptive spring element. By heating it up, a change in the structural stiffness occurs and a concomitant device frequency shift is attained. The current is generally used to activate the system. The absorber architecture is completed with a concentrated mass placed at the middle of the wire. Two absorber configurations have been implemented and tested on two different reference structures that are both of interest for aeronautical appli- cations: an aluminium and a fibreglass smart plate, instrumented with SMA wires. A feedback control has been implemented to stabilise the absorber tem- perature, resulting it strongly dependent on the environmental conditions. Promising results have been achieved in both the applications. In the first case, an energy attenuation of about 10dBat the targeted frequency has been attained. Similar results occurred in the second case. To verify the ATDVA, its effect on the activated smart panel has been of a certain interest, dealingwith a variable stiffness structure. After the embed- ded SMA wires have produced a suitable panel natural frequencies shift, the ATDVA still showed its capability in further modification of the structural dynamic response and achievement of the desired tonal response reduction. The compact, simple and light systemherein presented, easily embeddable in complex structures like honeycomb plates, has shown good potentialities for practical applications. Further investigation activities should be addressed towards deeper com- prehension of the effects, recorded also far from the targeted frequency band. In fact, relevant FRF variations appeared as the device has been turned on. Optimisation of the architecturemaybeanother point of interest; designpara- meters to be taken into account are thewire length and diameter, the concen- trated mass value, the supporting frame structure and configuration, and so on. Also, multiple systems for multi-tone control can be addressed in further examinations. In the end, some complications could arise if, for certain expe- riences, nonlinear behaviour of the device would be detected. In the current investigations, standing the low levels of excitation produced, inorder toattain repeatable results fromthe experimental point of viewand thenavoid anykind of non-linearity, these effectswerenot evident. It is to say that lowvibration le- vels are the typical operative conditions where these objects are thought to be applied for practical applications. On the other hand, the employed SMAma- A shape memory alloys... 151 terial elements are reliable and have shown good and predictable performance in different applications, investigated by the authors. Specific high actuation level tests could be designed in order to face this eventual aspect. References 1. Ameduri S., Diodati G., Concilio A., 2005, An SMA embedded anisotro- pic panels aimed at controlling vibration due to variable regimes sources, 8th Conference Dynamic System, Theory and Application, Lodz, Poland 2. Baz A., 1990, Active vibration control of flexible beams using shape memory actuators, Journal of Sound and Vibration, ??, ?, 437-456 3. Blevins R., 1979, Formulas for Natural Frequencies and Mode Shapes, R.E. Krieger Publishing Co., Florida 4. Dayuo J., Brennan M.J., 2002, Global control of structural vibration using multiple-tuned vibration neutralizer, Journal of Sound and Vibration, 258, 2, 345-357 5. Elahainia M.H., 2005, A temperature-based controller for a shape memory alloy actuator, Journal of Vibration and Acoustics, 127/285 6. ElahainiaM.H.,KooJ.H.,AhmadianM., 2004,Shapememoryalloy tuned vibration absorbers: robustness analysis, Proc. of IMECE 04, Anaheim (CA), USA 7. Estéve S.J., 2004, Control of sound transmission into payload fairings using distributed vibration absorbers and Helmotz resonators, Submitted to the Fa- culty of Virginia Polytechnic Institute and State University for the Degree of Mechanical Engineering 8. Hartog J.P.D., 1956,Mechanical Vibrations, McGraw-Hill Book Company 9. HuangM., FullerC.R., 1997,The effect of dynamic absorbers on the forced vibration of a cylindrical shell and its coupled interior sound field, Journal of Sound and Vibration, 200, 4, 401-418 10. Hunt J.B., 1979,Dynamic Vibration Absorbers, Mechanical Engineering Pu- blications Ltd. 11. Inman D.J., 1989, Vibration With Control Measurements And Stability, Prentice-Hall International Inc. 12. Korenev B.G., Reznikov L.M., 1993, Dynamic Vibration Absorbers, John Wiley and Sons Ltd. 152 B. Tiseo et al. 13. LiangC., RogersA., 1990,One dimensional thermo-mechanical constitutive relations for shapememorymaterials, Journal of Intelligent Materials Systems and Structures, 1, 201-233 14. Otsuka C., Waymann M., 2002, Shape Memory Materials, Cambridge Uni- versity Press, UK 15. Rustighi E., BrennanM.J.,MaceB.R., 2005b,Real time control of shape memory alloy adaptive tuned vibration absorber, Smart Materials and Struc- tures, 14, 1184-1195 16. Rustighi E., Brennan M.J., Mace B.R., 2005a, A shape memory alloy adaptive tunedvibrationabsorber:designand implementation,SmartMaterials and Structures, 14, 19-28 17. Tanaka K., Kobayashi S., Sato Y., 1986, Thermo-mechanics of transfor- mationpseudo-elasticity and shapememory effect in alloys, Int. J. of Plasticity, 2, 59-72 18. TDVAApplication, Designed by Cameron Hold Sworth Associates-Consulting Civil and Structural Engineers. Description available at http://www.cameron- holdsworth.co.uk/absorber.html (Last seenMay 2008) 19. Tiseo B., Koopmann G.A., Concilio A., 2005, A SMAbased adaptive tu- neable vibration absorber, 11th AIAA/CEAS Aeroacoustics Conference, Mon- terey (CA), USA 20. Tiseo B., Gianvito A., Concilio A., 2006, Smart tuneable dynamic vibra- tion absorber, 12th AIAA/CEAS Aeroacoustics Conference, Cambridge (MA), USA 21. Williams K., Chiu G., Bernhard R., 2002, Adaptive passive absorbers using shape memory alloys, Journal of Sound and Vibration, 249, 5, 835-848 Zastosowanie adaptacyjnego dynamicznego eliminatora drgań ze stopem z pamięcią kształtu do tonalnego sterowania drganiami Streszczenie Wpracy omówiono nowymodel adaptacyjnego i dostrajalnego eliminatora drgań (ATDVA) opartego na wykorzystaniu stopu z pamięcią kształtu (SMA). Posiadając właściwości adaptacyjne, eliminator taki umożliwia śledzenie jakościowych i ilościo- wych zmianwodpowiedzi dynamicznej układu, do którego został zastosowany.Archi- tektura eliminatora jest wyjątkowo prosta: konstrukcja zawiera obustronnie utwier- dzony drut SMA i masę skupioną. Dla celów porównawczych rozważono dwa układy A shape memory alloys... 153 drgające: aluminium panel stosowany w aeronautyce i kompozytowy panel zawiera- jący włókna szklane. Pierwszą część artykułu poświęcono omówieniu zaproponowa- nej koncepcji sterowania drganiami i prezentacji najważniejszychwłaściwości stopów z pamięcią kształtu. Następnie przedstawiono sposób realizacji badań i charaktery- stykę układu do eliminacji drgań w kontekście zaplanowanych doświadczeń. Osta- tecznie opisano praktyczne wdrożenie eliminatora, przybliżono przebieg wykonanych eksperymentów i zaprezentowano otrzymane wyniki analizy, opatrując je dyskusją i wskazaniem dalszych kroków badawczych. Manuscript received March 16, 2009; accepted for print April 19, 2009