Stochastic dynamics of micron-scale doubly clamped beams in a viscous fluid.
Stochastic dynamics of micron-scale doubly clamped beams in a viscous fluid.
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粘性流体中微米级双钳梁的随机动力学。
DOI：
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发表时间：
2009
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通讯作者：
M. Paul
中科院分区：
文献类型：
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作者：
M. M. Villa;M. Paul
研究了双固支微米尺度光束在布朗运动驱动下在粘性流体中的随机动力学行为。我们使用热力学的方法来计算梁位移的平衡波动，只需要确定性的计算。从自相关和噪声谱的计算，我们量化的光束动力学的质量因子和谐振频率的基本弯曲模式在很宽的范围内的实验可访问的几何形状。我们认为梁均匀的矩形横截面和探索增加的品质因数和谐振频率的基线几何形状是不同的，通过增加宽度，增加厚度，并减少长度。通过将光束的宽度或高度增加三倍，品质因数几乎增加一倍。通过减小梁的长度可以得到更大的改进，但是这受到附加流体耗散模式的出现的限制。总体而言，更宽和更厚的梁的随机动力学预测的二维近似理论超出了预期的基础上的假设，而较短的梁需要更详细的分析。
We study the stochastic dynamics of doubly clamped micron-scale beams in a viscous fluid driven by Brownian motion. We use a thermodynamic approach to compute the equilibrium fluctuations in beam displacement that requires only deterministic calculations. From calculations of the autocorrelations and noise spectra we quantify the beam dynamics by the quality factor and resonant frequency of the fundamental flexural mode over a wide range of experimentally accessible geometries. We consider beams with uniform rectangular cross section and explore the increased quality factor and resonant frequency as a baseline geometry is varied by increasing the width, increasing the thickness, and decreasing the length. The quality factor is nearly doubled by tripling either the width or the height of the beam. Much larger improvements are found by decreasing the beam length, however this is limited by the appearance of additional modes of fluid dissipation. Overall, the stochastic dynamics of the wider and thicker beams are well predicted by a two-dimensional approximate theory beyond what may be expected based upon the underlying assumptions, whereas the shorter beams require a more detailed analysis.