Superelastic NiTi shape memory alloys (SMAs) are increasingly used in a broad range of fields, from biomedical stents to vibration control devices in engineering structures.

This thesis investigates the nonlinear vibration of a mass-damper-spring system with a superelastic SMA bar providing the restoring force under isothermal and non-isothermal conditions.

First, to reveal the effects of two key features of SMAs (nonlinearity and hysteresis), a piecewise linear hysteretic model is developed to describe the force-displacement relation without considering the thermal effect, and then the average method (or harmonic balance method) is used to solve the nonlinear and hysteretic equation of motion. Approximate analytical expressions of the steady-state amplitude and phase are obtai...[ Read more ]

Superelastic NiTi shape memory alloys (SMAs) are increasingly used in a broad range of fields, from biomedical stents to vibration control devices in engineering structures.

This thesis investigates the nonlinear vibration of a mass-damper-spring system with a superelastic SMA bar providing the restoring force under isothermal and non-isothermal conditions.

First, to reveal the effects of two key features of SMAs (nonlinearity and hysteresis), a piecewise linear hysteretic model is developed to describe the force-displacement relation without considering the thermal effect, and then the average method (or harmonic balance method) is used to solve the nonlinear and hysteretic equation of motion. Approximate analytical expressions of the steady-state amplitude and phase are obtained, from which the frequency response curves (FRCs) are plotted. It is shown that the softening nonlinearity bends the FRC to the left and subsequent hardening nonlinearity bends it to the right leading to S-shaped FRCs, while the hysteresis has little influence on the bend but can significantly suppress the response.

Second, a one-dimensional thermo-mechanically coupled model is proposed based on the first and second laws of thermodynamics to investigate the thermo-mechanical coupling in phase transitions of an SMA bar under uniaxial tensile loading. Fully coupled mechanical and thermal field equations are established to reveal the strong coupling phenomena. Scaling the heat equation results in a dimensionless quantity interpreted as the ratio of the characteristic time of loading to that of convective heat transfer, and the competition between the two timescales accounts for the effects of loading rate, geometrical shape and size, and the ambient conditions.

Finally, the thermo-mechanical response of a mass-damper-SMA-spring system under harmonic excitation is simulated with the developed thermo-mechanical model used to describe the thermo-mechanical behavior of the SMA bar. Specifically, the effect of thermo-mechanical coupling on the frequency response curves are studied by changing the the heat transfer coefficient. It is shown that, generally, both the strain and temperature can reach stable sinusoidal response, but the frequency of temperature change is twice that of strain variation and the excitation frequency. As the heat transfer coefficient decreases, the structure of the FRC evolves from that with double bends in isothermal case to the upright one in the adiabatic case.

keywords: shape memory alloy, hysteresis, softening, hardening, nonlinear vibration, jump phenomenon, thermo-mechanical coupling, thermodynamic driving force, phase transition, latent heat, loading rate effect, thermo-mechanical vibration.