A modeling and uncertainty quantification framework for a flexible structure with macrofiber composite actuators operating in hysteretic regimes

Abstract

Macrofiber composites are low cost, durable, and flexible piezoceramic devices that are presently being considered for applications that include shape control of airfoils for improved flight performance, vibration, and noise suppression and energy harvesting. However, macrofiber composites also exhibit hysteresis and constitutive nonlinearities that need to be incorporated in models and model-based control designs to achieve their full capability. In this article, we combine constitutive relations, constructed using the homogenized energy model for ferroelectric hysteresis, with Euler–Bernoulli theory to construct a dynamic macrofiber composite model that quantifies a range of rate-dependent hysteretic behavior of macrofiber composites. Using homogenizing strategies, the macrofiber composite patch is treated as a monolithic material with effective parameters. We initially calibrate the model by estimating parameters through a least squares fit to a subset of the measured data. We find that the estimated parameters yield very accurate fits for quasi-static hysteresis. The estimated parameters also provide reasonably accurate predictions for a range of frequencies that include the first two harmonics. Second, we employ an adaptive Markov chain Monte Carlo algorithm to construct densities and analyze the correlation between parameters. The kernel density estimates derived from the Markov chain Monte Carlo chains imply that most of the model parameters exhibit non-Gaussian distributions.

Thermoacoustic modeling and uncertainty analysis of two-dimensional conductive membranes

“…Bayesian statistics are introduced to quantify material parameter uncertainty and the propagation of uncertainty when inversely identifying graphene TA model parameters in light of sound pressure data. This technique has shown to provide new insights into complex field coupled mechanics of other functional materials and adaptive structures 17,18 as well as a broader range of problems in weather and climate predictions, nuclear reactor design, and hydrology. 19 A three parameter TA model is often implemented based on prior results summarized by Arnold and Crandall.…”

Characterization of piezoelectric macrofiber composite actuated winglets

“…It is also observed that there is an increase in the amplitudes of oscillations from 0°to 8°, which may be due to change in the aerodynamic loads at higher angles. The results also show that despite the wellknown hysteresis of piezoelectric MFC actuation [31], this behavior does not lead to measurably higher-order harmonics of the winglet actuator. It should be noted that future analysis of fluid-structure vortex interactions may require feedback control of both internal hysteretic constitutive behavior and compensation to external flow disturbances [32,33].…”

Data-Driven Design of Sliding Mode Controllers for Ferroelectric Actuators

“…These methods construct a Markov chain which has the posterior distribution as its equilibrium distribution, bypassing the need for directly evaluating the integral in the denominator. This approach is used in Crews et al [2012] to estimate the parameters for a shape-memory alloy system and in Hu et al [2013] to estimate the parameters for an actuator constructed from macro-fiber composites.…”