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首页> 外文期刊>Journal of intelligent material systems and structures >Modeling of a Nonlinear Euler-Bernoulli Flexible Beam Actuated by Two Active Shape Memory Alloy Actuators
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Modeling of a Nonlinear Euler-Bernoulli Flexible Beam Actuated by Two Active Shape Memory Alloy Actuators

机译：由两个主动形状记忆合金驱动器驱动的非线性Euler-Bernoulli柔性梁的建模

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There are two different ways of using shape memory alloy (SMA) wire as an actuator for shape control of flexible structures: it can be either embedded within the composite laminate or externally attached to the structure. As the actuator can be placed at different offset distances from the beam, external actuators produce more bending moment and, consequently, considerabnle shape changes with the same magnitude of actuation force compared with the embedded type. Such a configuration also provides faster heat transfer rate owing to convection, which is very important in shape control applications that require a high-frequency response of SMA actuators. Although combination and physics-based modeling of externally attached SMA actuator wires and strips have been considered by many researchers, these studies have some drawbacks, which, if neglected, result in a number of errors in the theoretical results compared with experimental results. These shortcomings are considering the linear Euler-Bernoulli beam theory, not deriving the actuation force of the SMA from the constitutive equations, and taking into account the effect of only one SMA wire actuation force on, for example, the structure. These assumptions may lead to erroneous theoretical modeling results compared with experimental results. In this study, the aforementioned difficulties of attaching SMA actuators to the smart structures have been addressed. In other words, instead of linear beam theory, nonlinear beam theory is used in system modeling and, therefore, the proposed method and results are valid in large deflection and rotation behavior of beam. Also, in comparison to many other analyses that the effect of only one SMA wire is investigated, in the present research the effect of all active and inactive SMA wires is considered. Accordingly, the result of this paper can easily be generalized to the structure with several SMA wire actuations. Moreover, with the purpose of having practical applications in modeling and control, the heat transfer equations of all SMA wires are considered in the analysis and, as a result, the control inputs of the presented model are SMA wire electric currents rather than SMA temperatures. First, a flexible beam actuated by two active SMA actuators is modeled. Then, the Brinson constitutive equations and thermoelectric equations for SMA materials are coupled with the nonlinear beam behavior, and the coupled system of equations is numerically solved for some particular practical cases. Finally, the numerical results of the model simulation are verified against the experimental results using a test setup to validate the proposed model prediction. The implemented method used in this paper can be easily extended to the more complex smart structure with numerous externally attached SMA wires.
机译：使用形状记忆合金（SMA）线作为执行器来控制柔性结构的形状有两种不同的方法：它既可以嵌入复合材料层压板中，也可以外部连接到结构上。由于可以将致动器放置在距梁不同的偏移距离处，因此与嵌入式相比，外部致动器会产生更大的弯矩，因此，在相同的致动力大小下，可以考虑出现明显的形状变化。由于对流，这种配置还提供了更快的传热速率，这在需要SMA执行器高频响应的形状控制应用中非常重要。尽管许多研究人员已经考虑了外部连接的SMA执行器导线和条带的组合和基于物理的建模，但是这些研究仍存在一些缺陷，如果忽略这些缺陷，则会导致理论结果与实验结果相比出现许多错误。这些缺点是在考虑线性Euler-Bernoulli梁理论，而不是从本构方程推导SMA的作用力，并且仅考虑了一种SMA导线作用力对结构的影响。与实验结果相比，这些假设可能导致错误的理论建模结果。在这项研究中，已解决了将SMA执行器连接到智能结构的上述困难。换句话说，代替线性梁理论，非线性梁理论被用于系统建模，因此，所提出的方法和结果对于梁的大挠度和旋转行为是有效的。而且，与许多其他分析（仅研究一根SMA线的影响）相比，在本研究中，考虑了所有活动和非活动SMA线的影响。因此，本文的结果可以很容易地推广到具有几种SMA导线驱动的结构。此外，为了在建模和控制中具有实际应用的目的，在分析中考虑了所有SMA线的传热方程，结果，所提供模型的控制输入是SMA线电流而不是SMA温度。首先，对由两个有源SMA致动器致动的柔性梁进行建模。然后，将SMA材料的Brinson本构方程和热电方程与非线性射束行为耦合，并针对某些特殊的实际情况对方程的耦合系统进行了数值求解。最后，使用测试设置对模型仿真的数值结果与实验结果进行验证，以验证所提出的模型预测。本文中使用的已实现方法可以轻松地扩展到具有大量外部连接的SMA导线的更复杂的智能结构。

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