About the use of shape memory alloys in vibration damping.

Gillich, Gilbert Rainer ; Amariei, Daniel ; Gillich, Nicoleta 等

1. INTRODUCTION

Constructions are normally not sensitive to vibrations. However, they can be affected; light to strong damages can appear, depending on the vibration parameters. More than that, optimal functioning of sensitive equipment depends on low level of vibrations. Regulations are different in various counties (Bratu & Gillich, 2006).

Shape Memory Alloys (SMAs) have the ability to change their shape, stiffness, natural frequency, damping coefficient and other mechanical characteristics in response to a change in temperature and/or stress. SMAs exhibit two phenomena, known as: shape memory effect and superelasticity or pseudoelasticity. These characteristics are a result of a phase transformation between different crystallographic structures of the materials known as the martensite and austenite phases. A SMA is easily deformed in its low-temperature martensitic condition and is returned to its initial shape by heating above the austenite start temperature (As). At temperatures above the austenite finish temperature (Af) pseudoelastic behaviour is observed (Graesser & Cozzarelli, 1991).

This makes SMAs proper to be used as passive damping devices due to their inherent energy dissipation, resulted from the hysteretic phase transformation between austenite and martensite. A study on the use of SMAs for passive structural damping was performed, where three different quasi-static models of hysteresis were reviewed and compared with an experimental investigation of a cantilevered beam constrained by two SMA wires (Thomson et al., 1995). Thermal effects in the SMA constitutive behaviour has to be considered (Fosdick & Ketema, 1998), for instance by including an "averaged" thermal rate dependency. It is possible to realize a physically based SMA model identified from an SMA helical spring response (Yiu & Regelbrugge, 1995). The dynamical behaviour of a SMA bar in a single degree of freedom spring mass damper system was also studied (Feng & Li 1996), where a modified plasticity model (Graesser & Cozzarelli 1991) was used to model the pseudoelastic response of an SMA bar.

2. PSEUDOELASTIC EFFECT

The pseudoelastic behaviour is defined as inducing detwinned martensite from austenite by thermo-mechanical loading. A simplified model that requires specific transition points (points 1-4) representing martensitic and austenitic start and finish temperatures, where begins and ends the transformations is presented in figure 1.

In addition to the change in material properties and large recoverable strain during pseudoelastic transformation, hysteresis is also an indicator for energy dissipation during the transformations. This energy dissipation is proportional to the degree of transformation completed during a loading cycle for both complete and incomplete, or partial transformations. These partial transformations are referred to as minor loop hysteresis cycles (figure 2) and complete or full transformations are referred to as major loop hysteresis cycles (Figure 3).

The hysteresis behaviour (represented by points 1 to 4 in figures 2 and 3) along with the stiffness change (represented by [k.sub.F] and [k.sub.R] in figure 2 and [k.sub.A-M], [k.sub.M], [k.sub.M-A] and [k.sub.A], characteristic for each state phase, in figure 3) of the material during the pseudoelastic phase transformations confirm the availability for our SMA spring-mass system to be used as damping and vibration isolation device.

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3. ISOLATED WORKSTATION

Sensitive equipment, for proper use and avoid of defects, needs a good isolation against vibrations. Classical solutions are: the use of tables with heavy plates or implementation of dumpers in the table's structure. These solutions are inadequate because of the high weight or expensive.

The authors have developed for the use in the own university a workstation, schematic illustrated in figure 4, based on the pseudoelastic behaviour of SMAs. The structure is a rigid one, on which are placed two mobile plates assigning a pre-compression of the SMA elements placed between the two mobile plates and the structure. We have tested elements with three different forms: spring, cylinder and semi-cylinder, the last providing the best isolation. Finally we placed them parallel to the long side of the plates, with the open side orientated to the stiff mounting plate.

To determinate the natural frequencies a simplified mechanical model was used (figure 5), where linear springs, frictional and slip elements are used to describe the behaviour in austenitic or martensitic domains or during the austenitic to martensitic respectively martensitic to austenitic transformations. In the figure 5, d [greater than or equal to] 0 represents the load cycle, d<0 the unload cycle. The four stiffness values [k.sub.A], [k.sub.M], [k.sub.A-M] and [k.sub.M-A] can be determined experimental, the values for [k.sub.I], [k.sub.II] and [k.sub.III] for load and unload cycles by calculus.

Experiments regarding the influence of pre-compression have been made to find a good isolation. Tri-axial transducers placed on the structure and the upper mobile plate have determined the transmissibility of vibrations. We obtained good results in isolation in vertical field, but worst in horizontal field.

Next approaches will be focused to find out shapes which permit isolation in all directions, or if the results are unsatisfying, constructive solutions for integration of SMA elements designed to isolate in all directions. Meantime, theoretical background will be improved, in order to permit accurate design of this kind of isolating workplaces.

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4. CONCLUSION

Elements from SMA are proper devices for vibration damping/isolation. Different models describing them, respecting shape, dynamic behaviour and/or temperature changes are available in the literature. Based on that, the authors have developed a work station for sensitive equipment for own use (electron microscopy). The best results for the spring form were obtained for semi-cylindrical elements, having the open side orientated to the stiff plate. Precompression of the spring can affect, positively or negatively the damping performances of the system. The excitation level defines the type of the loop; a higher level determines a major loop, being the favourable situation, while a low level determines a minor loop, where the behaviour of the SMA element is close to them of a linear spring. Because of the fact that the mass intended to be isolated has an important role in the effectiveness of the system, it can be concluded that the performance of the damping system is given by a combination of four parameters: form of the SMA, excitation level, mass and pre-compression. As future research the authors intend to develop specific form-dependent models for the SMA elements.

5. REFERENCES

Amariei, D.; Gillich, G.R.; Frunzaverde, D. & Miclosina, C. (2008). Study on the behavior of Ni-Ti Shape Memory Alloys in order to highlight the Memory Effect, IEEE International Conference on Automation, Quality Testing and Robotics AQTR 2008, pp. 517-524, Cluj, May 2008

Bratu, P. & Gillich, G.R. (2006). Reference Values in Evaluating Effects of Vibrations on Buildings and Persons. Annals of "Eftimie Murgu" University Resita. Engineering Fascicule, Vol XIII, Nr. 1, October 2006, pp. 111-116, ISSN 1453-7394

Feng Z.C. & Li, D.Z. (1996). Dynamics of a mechanical system with a shape memory alloy bar. Journal of Intelligent Material Systems and Structures, 7(4), July 1996, pp. 399-410, ISSN 1530-8138.

Fosdick, R & Ketema, Y. (1998). Shape memory alloys for passive vibration damping. Journal of Intelligent Material Systems and Structures, 9(10), October 1998, pp. 854-870, ISSN 1530-8138.

Graesser, E.J. & Cozzarelli, F.A. (1991). Shape-Memory Alloys as New Materials for Aseismic Isolation, Journal of Engineering Mechanics, 117(11), November 1991, pp. 2590-2608, ISSN 0733-9399

Thomson, P.; Balas, G.J. & Leo. P.H. (1995). The use of shape memory alloys for passive structural damping, Smart Materials and Structures, 4(1), March 1995, pp. 36-41, ISSN 0964-1726

Yiu, Y.C. & Regelbrugge, M.E. (1995) Shape-memory alloy isolators for vibration suppression in space applications. Proceedings of the 36th AIAA/ASME/ASCE/AHS/ASC Conference: Structures, Structural Dynamics, and Materials, pp. 3390-3398, New Orleans, April 1995.