A modeling and uncertainty quantification framework for a flexible structure with macrofiber composite actuators operating in hysteretic regimes
A modeling and uncertainty quantification framework for a flexible structure with macrofiber composite actuators operating in hysteretic regimes
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具有在滞后状态下运行的粗纤维复合材料执行器的柔性结构的建模和不确定性量化框架
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发表时间：
2014
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通讯作者：
W. Oates
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作者：
Zhengzheng Hu;Ralph C. Smith;N. Burch;M. Hays;W. Oates
长纤维复合材料是低成本、耐用且柔性的压电陶瓷装置，其目前被考虑用于包括翼型的形状控制以改善飞行性能、振动和噪声抑制以及能量收集的应用。然而，粗纤维复合材料也表现出滞后和本构非线性，需要纳入模型和基于模型的控制设计，以实现其全部功能。在这篇文章中，我们联合收割机本构关系，构造使用均匀化的能量模型的铁电滞后，与欧拉-伯努利理论，构建一个动态的粗纤维复合材料模型，量化的一系列率相关的滞后行为的粗纤维复合材料。采用优化策略，将粗纤维复合材料补片作为具有有效参数的整体材料处理。我们最初通过对测量数据的子集进行最小二乘拟合来估计参数，从而校准模型。我们发现，估计的参数产生非常准确的适合准静态滞后。所估计的参数还为包括前两个谐波的频率范围提供合理准确的预测。其次，我们采用自适应马尔可夫链蒙特卡罗算法来构建密度和分析参数之间的相关性。从马尔可夫链蒙特卡罗链的核密度估计意味着大多数模型参数表现出非高斯分布。
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.