Pseudoelastic SMA Spring Elements for Passive Vibration Isolation: Part I

Abstract

In this work, the effect of pseudoelastic response of shape memory alloys (SMAs) on passive vibration isolation has been investigated. This study has been conducted by developing, modeling, and experimentally validating a SMA-based vibration isolation device. This device consists of layers of preconstrained SMA tubes undergoing pseudoelastic transformations under transverse dynamic loading. These SMA tubes are referred to as SMA spring elements in this study. To accurately model the nonlinear hysteretic response of SMA tubes present in this device, at first a Preisach model (an empirical model based on system identification) has been adapted to represent the structural response of a single SMA tube. The modified Preisach model has then been utilized to model the SMA-based vibration isolation device. Since this device also represents a nonlinear hysteretic dynamical system, a physically based simplified SMA model suitable for performing extensive parametric studies on such dynamical systems has also been developed. Both the simplified SMA model and the Preisach model have been used to perform experimental correlations with the results obtained from actual testing of the device. Based on the studies conducted, it has been shown that SMA based vibration isolation devices can overcome performance trade-offs inherent in typical softening spring-damper vibration isolation systems. This work is presented as a two-part paper. Part I of this study presents the modification of the Preisach model for representing SMA pseudoelastic tube response together with the implemented identification methodology. Part I also presents the development of a physically based simplified SMA model followed by model comparisons with the actual tube response. Part II of this work covers extensive parametric study of a pseudoelastic SMA spring-mass system using both models developed in Part I. Part II also presents numerical simulations of a dynamic system based on the prototype device, results of actual testing of the device and correlations of the experimental cases with the model predictions.

Get full access to this article

View all access options for this article.

References

Abeyaratne, R. and Knowles, J.K. 1994. “Dynamics of Propagating Phase Boundaries: Thermoelastic Solids with Heat Conduction,” Archive for Rational Mechanics and Analysis, 126(3): 203–230 .

Achenbach, M. and Muller, I. 1985. “Simulation of Material Behaviour of Alloys with Shape Memory,” Arch. Mech., 35: 537–585 .

Banks, H., Kurdila, A. and Webb, G. 1996a. “Identification of Hysteretic Control Influence Operators Representing Smart Actuators: Formulation,” Tech. Rep. CRSC-TR96-14, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC .

Banks, H., Smith, R. and Wang, Y. 1996b. Smart Material Structures: Modeling, Estimation and Control, John Wiley & Sons, Paris .

Banks, H., Kurdila, A. and Webb, G. 1997. “Identification of Hysteretic Control Influence Operators Representing Smart Actuators: Convergent Approximations,” Tech. Rep. CRSCTR97-7, Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC .

Beranek, L.L. and Vér, I.L. (eds) 1992. Noise and Vibration Control Engineering, John Wiley and Sons, New York .

Bernardini, D. and Vestroni, F. 2002. “Non-isothermal Oscillations of Pseudoelastic Devices,” International Journal of Non-Linear Mechanics, Submitted for Publication.

Bo, Z. and Lagoudas, D.C. 1999a. “Thermomechanical Modeling of Polycrystalline SMAs under Cyclic Loading, Part IV: Modeling of Minor Hysteresis Loops,” International Journal of Engineering Science, 37: 1205–1249 .

Bo, Z. and Lagoudas, D.C. 1999b. “Thermomechanical Modeling of Polycrystalline SMAs under Cyclic Loading, Part IV: Modeling of Minor Hysteresis Loops,” International Journal of Engineering Science, 37: 1174–1204 .

10.

Brinson, L.C. 1993. “One-dimensional Constitutive Behavior of Shape Memory Alloys: Thermomechanical Derivation with Non-constant Material Functions and Redefined Martensite Internal Variable,” Journal of Intelligent Material Systems and Structures, 4: 229–242 .

11.

Brokate, M. 1994. “Hysteresis Operators.,” In: Visintin, A. (ed.), Phase Transitions and Hysteresis, Lecture Notes in Mathematics, Vol. 1584, pp. 1–48, Springer-Verlag, Berlin, Germany .

12.

Collet, M., Foltete, E. and Lexcellent, C. 2001. “Analysis of the Behavior of a Shape Memory Alloy Beam under Dynamic Loading,” European Journal of Mechanics and Solids, 20: 615–630 .

13.

Feng, Z.C. and Li, D.Z. 1996. “Dynamics of a Mechanical System with a Shape Memory Alloy Bar,” Journal of Intelligent Material Systems and Structures, 7: 399–410 .

14.

Fosdick, R. and Ketema, Y. 1998. “Shape Memory Alloys for Passive Vibration Damping,” Journal of Intelligent Systems and Structures, 9: 854–870 .

15.

Ge, P. and Jouaneh, M. 1995. “Modeling of Hysteresis in Piezoceramic Actuators,” Precision Engineering, 17: 211–221 .

16.

Gorbet, R.B., Morris, K.A. and Wang, D.W.L. (1997). “Stability of Control Systems for the Preisach Hysteresis Model,” In: Proc. IEEE International Conf. on Robotics and Automation, Albuquerque, NM, Vol. 1, pp. 241–247 .

17.

Gorbet, R.B., Wang, D.L. and Morris, K.A. 1998. “Preisach Model Identification of a Two-wire SMA Actuator,” In: Proc. IEEE International Conf. on Robotics and Automation, Leuven, Belgium, Vol. 3, pp. 2161–2617 .

18.

Graesser, E. and Cozzarelli, F. 1991. “Shape-memory Alloys as New Materials for Aseismic Isolation,” Journal of Engineering Materials, 117(11), 2590–2608 .

19.

Harris, C.M. (ed.) 1996. Shock and Vibration Handbook, McGraw-Hill, New York .

20.

HKS 1997. ABAQUS/Standard User's Manual, Karlsson and Sorrensen, Inc., Hibbit .

21.

Hughes, D. 1997. “Piezoceramic and SMA Hysteresis Modeling and Compensation,” Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, NY.

22.

Hughes, D. and Wen, J. 1994. “Preisach Modeling and Compensation for Smart Material Hysteresis,” SPIE Active Materials and Smart Structures, 2427: 50–64 .

23.

Huo, Y.Z. 1991. “Preisach Model for the Hysteresis in Shape Memory Alloys,” In: Boehler, J.P. and Khan, A.S. (eds), Proc. Of Plasticity’91: The Third Int. Symp. on Plasticity and Its Current Applications, Grenoble, France, Elsevier, London, pp. 552–555 .

24.

Inman, D. 2001. Engineering Vibration, Prentice-Hall, Inc., Upper Saddle River, New Jersey .

25.

Ivshin, Y. and Pence, T.J. 1994. “A Thermomechanical Model for a One-variant Shape Memory Material,” Journal of Intelligent Material Systems and Structures, 5: 455–473 .

26.

Khan, M.M. 2002. “Modeling of Shape Memory Alloy (SMA) Spring Elements for Passive Vibration Isolation using Simplified SMA Model and Preisach Model,” Master’s Thesis, Texas A & M University, College Station, TX.

27.

Khan, M.M. and Lagoudas, D.C. 2002. “Modeling of Shape Memory Alloy Pseudoelastic Spring Elements using Preisach Model for Passive Vibration Isolation,” In: SPIE Conference on Modeling, Signal Processing and Control in Smart Structures, San Diego, CA.

28.

Krasnoselskii, M. and Pokrovskii, A. 1983. Systems with Hysteresis, Springer-Verlag, Heidelberg, Germany .

29.

Lacarbonara, W., Bernardini, D. and Vestroni, F. 2001. “Periodic and Nonperiodic Thermomechanical Reponses of Shape Memory Oscillators,” In: Proc. Conf. ASME Design Engineering Technical Conference, Pittsburgh, PA.

30.

Lagoudas, D. and Bhattacharyya, A. 1997. “On the Correspondence between Micromechanical Models for Isothermal Pseudoelastic Response of Shape Memory Alloys and the Preisach Model for Hysteresis,” Math. Mech. Solids, 2(4), 405–440 .

31.

Lagoudas, D.C. and Bo, Z. 1999. “Thermomechanical Modeling of Polycrystalline SMAs under Cyclic Loading, Part I-IV: Material Characterization and Experimental Results for a Stable Transformation Cycle,” International Journal of Engineering Science, 37.

32.

Lagoudas, D.C., Bo, Z. and Qidwai, M.A. 1996. “A Unified Thermodynamic Constitutive Model for SMA and Finite Element Analysis of Active Metal Matrix Composites,” Mechanics of Composite Materials and Structures, 3, 153–179 .

33.

Lagoudas, D.C., Khan, M.M. and Mayes, J.J. 2001a. “Modelling of Shape Memory Alloy Springs for Passive Vibration Isolation,” In: Proc. Conf. ASME International Mechanical Engineering Congress and Exposition, New York, NY.

34.

Lagoudas, D.C., Khan, M.M., Mayes, J.J. and Henderson, B.K. 2002. “Parametric Study and Experimental Correlation of an SMA Based Damping and Passive Vibration Isolation Device,” In: Proc. Conf. ASME International Mechanical Engineering Congress and Exposition, New Orleans, LA.

35.

Lagoudas, D.C., Mayes, J.J. and Khan, M.M. 2001b. “Simplified Shape Memory Alloy (SMA) Material Model for Vibration Isolation,” In: SPIE Conference on Modeling, Signal Processing and Control in Smart Structures.

36.

Liang, C. and Rogers, C.A. 1990. “One-dimensional Thermomechanical Constitutive Relations for Shape Memory Materials,” Journal of Intelligent Material Systems and Structures, 1: 207–234 .

37.

Malovrh, B. and Gandhi, F. 2001. “Mechanism-based Phenomenological Models for the Pseudoelastic Hysteresis Behavior of Shape Memory Alloys,” Journal of Intelligent Material Systems and Structures, 12(1): 2130-2130 .

38.

Mayergoyz, I. 1991. Mathematical Models of Hysteresis, Springer-Verlag, New York .

39.

Mayes, J.J. and Lagoudas, D.C. 2001. “An Experimental Investigation of Shape Memory Alloy Springs for Passive Vibration Isolation,” In: Proc. Conf. AIAA Space 2001 Conference and Exposition, Albuquerque, NM, Submitted.

40.

Miyazaki, S., Imai, T., Igo, Y. and Otsuka, K. 1997. “Effect of Cyclic Deformation on the Pseudoelasticity Characteristics of Ti-Ni Alloys,” Metallurgical Transactions, 42(7): 115–120 .

41.

Ortin, J. 1992. “Preisach Modeling of Hysteresis for a Pseudoelastic Cu-Zn-Al Single-crystal,” Journal of Applied Physics, 71(3): 1454–1461 .

42.

Otsuka, K. and Shimizu, K. 1986. “Pseudoelasticity and Shape Memory Effects in Alloys,” International Metals Review, 31(3), 93–114 .

43.

Otsuka, K. and Wayman, C.M. 1999. “Introduction” In: Otsuka, K. and Wayman, C.M. (eds), Shape Memory Alloys, Chap. 2. 27–48, Cambridge University Press, Cambridge, United Kingdom .

44.

Ozdemir, H. 1976. “Nonlinear Transient Dynamic Analysis of Yielding Structures,” Ph.D. Thesis, University of California at Berkeley.

45.

Patoor, E., Eberhardt, A. and Berveiller, M. 1987. “Potentiel Pseudoelastique et plasticite de transformation martensitique dans les mono et polycristaux metalliques,” Acta Metallurgica, 35:2779–2789.

46.

Preisach, F. 1935. Uber die magnetische nachwirkung, Zeitschrift fur Physik, 94:277–302.

47.

Qidwai, M.A. and Lagoudas, D.C. 2000. “Numerical Implementation of a Shape Memory Alloy Thermomechanical Constitutive Model using Return Mapping Algorithms,” International Journal for Numerical Methods in Engineering, 47: 1123–1168 .

48.

Raniecki, B., Lexcellent, C. and Tanaka, K. 1992. “Thermodynamic Models of Pseudoelastic Behaviour of Shape Memory Alloys,” Arch. of Mech., 3.

49.

Seelecke, S. 2002. “Modeling the Dynamic Behavior of Shape Memory Alloys,” International Journal of Non-Linear Mechanics, 37(8): 1363–1374 .

50.

Song, C.L., Brandon, J.A. and Featherston, C.A. 1999. “Estimation of Hysteretic Properties for Pseudoelastic Materials,” In: Proceedings of 2nd International Conference of Identification in Engineering Systems, Swansea, Wales, pp. 210–219 .

51.

Tanaka, K. 1986. “A Thermomechanical Sketch of Shape Memory Effect: One-dimensional Tensile Behavior,” Res Mechanica, 18: 251–263 .

52.

Thomson, P., Balas, G.J. and Leo, P.H. 1995. “The Use of Shape Memory Alloys for Passive Structural Damping,” Smart Materials and Structures, 4(1): 36–41 .

53.

Visintin, A. 1994. Differential Models of Hysteresis, Springer-Verlag, Berlin, Germany .

54.

Wayman, C.M. 1983. “Phase Transformations, Nondiffusive,” In: Cahn, R.W. and Haasen, P. (eds), Physical Metallurgy, pp. 1031–1075, North-Holland Physics Publishing, New York .

55.

Webb, G. 1998. “Adaptive Identification and Compensation for a Class of Hysteresis Operators,” Ph.D. Thesis, Texas A & M University, College Station, TX.

56.

Webb, G., Kurdila, A. and Lagoudas, D. 1998. “Hysteresis Modeling of SMA Actuators for Control Applications,” Journal of Intelligent Material Systems and Structures, 9(6): 432–447 .

57.

Yiu, Y.C. and Regelbrugge, M.E. 1995. “Shape-memory Alloy Isolators for Vibration Suppression in Space Applications,” In: Proc. 36th AIAA/ASME/ASCE/AHS/ASC Conf. Structures, Structural Dynamics, and Materials, pp. 3390–3398 . AIAA-95-1120-CP.

Pseudoelastic SMA Spring Elements for Passive Vibration Isolation: Part I – Modeling

Abstract

Get full access to this article

References