Numerical Model For Vibration Damping Resulting From the First Order Phase Transformations
Linxiang X. Wang, Roderick V. N. Melnik
TL;DR
The paper addresses macroscale damping in a shape memory alloy (SMA) rod caused by first-order martensite phase transformations. It introduces a modified Ginzburg-Landau framework with a non-convex free energy $\mathcal{F}(\theta,\varepsilon)$ and thermo-mechanical coupling, yielding a coupled system for displacement $u$, strain $\varepsilon$, and temperature $\theta$, solved as a differential-algebraic problem using Chebyshev spectral discretization and backward differentiation in time. Results show that damping is markedly enhanced when phase transformations occur, due to hysteresis energy dissipation and energy conversion between mechanical and thermal forms; even without phase transformation, damping arises from thermo-mechanical coupling and viscosity. The framework provides a robust macro-scale tool for predicting SMA damper performance and guiding the design of vibration suppressors with tunable damping properties.
Abstract
A numerical model is constructed for modelling macroscale damping effects induced by the first order martensite phase transformations in a shape memory alloy rod. The model is constructed on the basis of the modified Landau-Ginzburg theory that couples nonlinear mechanical and thermal fields. The free energy function for the model is constructed as a double well function at low temperature, such that the external energy can be absorbed during the phase transformation and converted into thermal form. The Chebyshev spectral methods are employed together with backward differentiation for the numerical analysis of the problem. Computational experiments performed for different vibration energies demonstrate the importance of taking into account damping effects induced by phase transformations.