Beam electrothermal actuators amplify the thermal expansion of pre-shaped beams and use the symmetrical structure to create a linear motion. These actuators, including V and Z shapes, are widely used in microsystems. Explicit analytical expressions are derived in this paper governing the structural deformation of these actuators due to electrothermal expansion and interaction with external lateral load. The analytical expressions are developed for an arbitrary initial shape of the actuator beams with symmetry and uniform cross-section. The modeling is based on the elastic beam theory, and all the modes of buckling are considered in the analytical solution. The solution and analytical expressions account for axial forces in tension and compression. The modeling considers the buckling with the third mode, which occurs at a certain limit of the axial compression and leads to significant variation in the stiffness of the actuator. This phenomenon is well studied for bistable pre-shaped beams, but related studies are limited for beam electrothermal actuators. As a case study, the V shape actuator is specifically investigated. The modeling shows very good agreement with finite element simulations and experimental data based on micro-machined in-plane silicon actuators. [2020-0262]

中文翻译：

---

梁式电热致动器的建模

横梁电热致动器放大预成型横梁的热膨胀，并利用对称结构产生线性运动。这些致动器，包括 V 形和 Z 形，广泛用于微系统。由于电热膨胀和与外部横向载荷的相互作用，本文导出了明确的解析表达式，用于控制这些致动器的结构变形。解析表达式是针对具有对称和均匀横截面的致动器梁的任意初始形状而开发的。建模基于弹性梁理论，在解析解中考虑了所有的屈曲模式。解和解析表达式考虑了拉伸和压缩中的轴向力。建模考虑了第三模态的屈曲，这发生在轴向压缩的某个极限并导致致动器刚度的显着变化。对于双稳态预成型梁，这种现象得到了很好的研究，但相关研究仅限于梁电热致动器。作为案例研究，专门研究了 V 形执行器。该建模与基于微加工面内硅致动器的有限元模拟和实验数据非常吻合。[2020-0262] 该建模与基于微加工面内硅致动器的有限元模拟和实验数据非常吻合。[2020-0262] 该建模与基于微加工面内硅致动器的有限元模拟和实验数据非常吻合。[2020-0262]