THESIS
2015
iv leaves, v-xi, 84 pages : illustrations ; 30 cm
Abstract
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...[
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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.
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