Post-buckling of micromachined beams
Post-buckling of micromachined beams
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DOI：
10.1109/memsys.1994.555620
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发表时间：
1994-01
期刊：
影响因子：
--
通讯作者：
Weileun Fang;J. A. Wickert
中科院分区：
文献类型：
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作者：
Weileun Fang;J. A. Wickert
采用解析和实验相结合的方法，研究了微细加工梁在屈曲前、屈曲过渡和屈曲后载荷范围内，在规定的面内压应力作用下的静态变形。通过建立梁的压应力与面外变形的非线性关系模型，预测了梁在屈曲后的有限幅值。此外，该模型还明确考虑了微小缺陷(包括制造缺陷、几何不规则性或非理想载荷)对梁在近屈曲区域行为的净影响。作为应用，采用传统的体微加工方法制作了固支二氧化硅光束，并用三维光学轮廓术测量了其偏转轮廓。将测量结果与模型预测的屈曲后的振幅和形状进行比较，并与现有的不包括非线性和缺陷影响的更简单的模型进行比较。结果表明，在考虑缺陷的情况下，梁从屈曲前到屈曲后的转变过程中，梁的离面振幅持续增长，与临界荷载下的突然分叉形成鲜明对比。通过考虑这一行为，可以改进制造梁的薄膜中残余应力的估计，并可以预测常见的后屈曲微机械结构的幅值。
The static deformation of micromachined beams under prescribed in-plane compressive stress is studied by analytical and experimental means over the pre-buckling, transition, and post-buckling load ranges. The finite amplitude of the beam in its post-buckled state is predicted by modeling the non-linear dependence of its compressive stress on the out-of-plane deformation. In addition, the model explicitly considers the net effect of slight imperfections, which can include fabrication defects, geometric irregularities, or non-ideal loading, on the beam's behavior in the near-buckling regime. As an application, clamped-clamped silicon dioxide beams are fabricated through conventional bulk micromachining, and their deflected profiles are measured through three-dimensional optical profilometry. The measurements are compared to the post-buckled amplitudes and shapes that are predicted by the model, and by existing simpler models that do not include the effects of both non-linearity and imperfection. As borne out by the data, when imperfections are considered, the beams exhibit continuous growth of the out-of-plane amplitude during transition from the prebuckled state to a post-buckled one, in contrast to sudden bifurcation at a critical load. By accounting for this behavior, the estimate of residual stress in the thin film from which the beams are fabricated can be improved, and the amplitude of common post-buckled micromachined structures can be predicted.