Homogenized Energy Model and Markov Chain Monte Carlo Simulations for Macro Fiber Composites Operating in Broadband Regimes

Macro Fiber Composites (MFCs), comprised of PZT fibers, are being considered for a variety of applications due to their flexibility and relatively low production costs. Like other PZT actuators, MFCs also exhibit hysteresis and constitutive nonlinearities that must be characterized in models and control designs to achieve the full potential. Here we use an Euler-Bernoulli beam model coupled with the homogenized energy strain model to predict the structural/hysteretic response of a thin cantilever beam with an MFC patch attached during a series of frequency sweep experiments. Optimization routines are employed to optimized both MFC parameters and beam parameters using a subset of displacement data. The posterior probability distribution of each model parameter is estimated using Markov Chain Monte Carlo simulations. Finally, we present model predictions with quantified uncertainties.