The design of pseudoelastic shape memory alloy (SMA) passive damping devices for structural vibration is dependent
on the geometry of the SMA. By changing the effective radius size of an attached SMA element, one simultaneously
changes the nonlinear stiffness and damping contributed to the system by the SMA. In order to identify the coupled
nonlinear dynamic behavior, this work focuses on the steady state frequency response functions of a simple SDOF
system with an attached SMA element under base excitation. An equivalent linearization method is used to produce a
qualitative representation of the frequency response of the structure for multiple radius sizes and excitation amplitudes.
These results are then compared to corresponding frequency response functions produced from the Seelecke, Muller,
and Achenbach SMA model. These results give insight into jump phenomenon, hysteretic damping effects, and identify
the stable branches of the nonlinear frequency response. Additionally, optimal radius sizes are presented for a range of
harmonic excitation amplitudes and frequencies. These results lead to an initial investigation into the physical
mechanisms responsible for choosing optimal radius sizes for an arbitrary excitation.
Previous work at NASA Langley Research Center (LaRC) involved fabrication and testing of composite beams with embedded, pre-strained shape memory alloy (SMA) ribbons within the beam structures. That study also provided comparison of experimental results with numerical predictions from a research code making use of a new thermoelastic model for shape memory alloy hybrid composite (SMAHC) structures. The previous work showed qualitative validation of the numerical model. However, deficiencies in the experimental-numerical correlation were noted and hypotheses for the discrepancies were given for further investigation. The goal of this work is to refine the experimental measurement and numerical modeling approaches in order to better understand the discrepancies, improve the correlation between prediction and measurement, and provide rigorous quantitative validation of the numerical analysis/design tool. The experimental investigation is refined by a more thorough test procedure and incorporation of higher fidelity measurements such as infrared thermography and projection moire interferometry. The numerical results are produced by a recently commercialized version of the constitutive model as implemented in ABAQUS and are refined by incorporation of additional measured parameters such as geometric imperfection. Thermal buckling, post-buckling, and random responses to thermal and inertial (base acceleration) loads are studied. The results demonstrate the effectiveness of SMAHC structures in controlling static and dynamic responses by adaptive stiffening. Excellent agreement is achieved between the predicted and measured results of the static and dynamic thermomechanical response, thereby providing quantitative validation of the numerical tool.