Computational modeling of vibration damping in SMA wires

Abstract.Through a mathematical and computational model of the physical behavior of shape memory alloy wires, this study shows that localized heating and cooling of such materials provide an effective means of damping vibrational energy. The thermally induced pseudo-elastic behavior of a shape memory wire is modeled using a continuum thermodynamic model and solved computationally as described by the authors in [23]. Computational experiments confirm that up to $80\%$ of an initial shock of vibrational energy can be eliminated at the onset of a thermally-induced phase transformation through the use of spatially-distributed transformation regions along the length of a shape memory alloy wire.

[1]  J. Málek.  Weak and Measure-valued Solutions to Evolutionary PDEs , 1996 .

[2]  F. Falk.  LANDAU THEORY AND MARTENSITIC PHASE TRANSITIONS , 1982 .

[3]  J. Sprekels,et al.  Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys , 1988 .

[4]  C. Dafermos.  Hyberbolic Conservation Laws in Continuum Physics , 2000 .

[5]  Donald A. French,et al.  Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems , 1994 .

[6]  Roderick V. N. Melnik,et al.  Computational Models for Materials with Shape Memory: Towards a Systematic Description of Coupled Phenomena , 2002, International Conference on Computational Science.

[7]  Gero Friesecke,et al.  Implicit time discretization and global existence for a quasi-linear evolution equation with nonconvex energy , 1997 .

[8]  Petr Kloucek,et al.  On thermodynamic active control of shape memory alloy wires , 2003, Syst. Control. Lett..

[9]  Stuart S. Antman,et al.  The Parabolic-Hyperbolic System Governing the Spatial Motion of Nonlinearly Viscoelastic Rods , 2005 .

[10]  Fritz Falk,et al.  Three-Dimensional Landau Theory Describing the Martensitic Phase Transformation of Shape-Memory Alloys , 1993 .

[11]  B. Hulme.  One-step piecewise polynomial Galerkin methods for initial value problems , 1972 .

[12]  V. A. Likhachev.  Structure-Analitycal Theory of Martensitic Unelasticity , 1995 .

[13]  A. F. Devonshire.  Theory of ferroelectrics , 1954 .

[14]  Donald A. French,et al.  A continuous space-time finite element method for the wave equation , 1996, Math. Comput..

[15]  J. K. Knowles,et al.  Implications of viscosity and strain-gradient effects for the kinetics of propagating phase boundaries in solids , 1991 .

[16]  James K. Knowles,et al.  On the driving traction acting on a surface of strain discontinuity in a continuum , 1990 .

[17]  D. Reynolds.  A nonlinear thermodynamic model for phase transitions in shape memory alloy wires , 2003 .

[18]  M. Brokate,et al.  Phase Transitions and Hysteresis , 1994 .

[19]  Stefan Seelecke,et al.  Shape memory alloy actuators in smart structures: Modeling and simulation , 2004 .

[20]  F. Falk,et al.  Three-Dimensional Landau Theory Describing the Martensitic Phase Transformation of Shape-Memory Alloys , 1990 .

[21]  P. Klouček,et al.  The computational modeling of nonequilibrium thermodynamics of the martensitic transformations , 1998 .

[22]  S. Seelecke,et al.  Quasiplasticity and pseudoelasticity in shape memory alloys , 1994 .

[23]  P. Kloucek,et al.  On the modeling and computations of nonlinear thermodynamics in SMA wires , 2006 .

[24]  Lev Davidovich Landau,et al.  THE FUNDAMENTAL PRINCIPLES OF STATISTICAL PHYSICS , 1980 .

[25]  Stefan Seelecke,et al.  Modeling the dynamic behavior of shape memory alloys , 2002 .

[26]  P. Klouček,et al.  The computation of the dynamics of the martensitic transformation , 1994 .

[27]  Convergence of a second-order scheme for semilinear hyperbolic equations in 2+1 dimensions , 1991 .

[28]  Stuart S. Antman,et al.  Quasilinear Hyperbolic–Parabolic Equations of One-Dimensional Viscoelasticity , 1996 .

[29]  S. Antman.  Physically unacceptable viscous stresses , 1998 .