标题： 计算纳米梁在粘性流体中的多模随机动力学 显示英文标题

标题： Computing the multimodal stochastic dynamics of a nanobeam in a viscous fluid

摘要： 小弹性物体在流体中的随机动力学对于许多重要的新兴技术至关重要。 现在可以仅通过布朗运动来测量和利用弹性结构的高阶运动模式。 尽管存在针对理想条件的理论描述，但计算实验复杂条件下的随机多模态动力学非常具有挑战性。 我们展示了使用确定性有限元计算与涨落耗散定理相结合的方法，探索双固定梁的多模态随机动力学时，这是可能实现的。 我们采用了一种非常通用且灵活的有限元计算方法，仅通过单一确定性模拟即可同时量化多个模式的随机动力学。 我们考虑了梁内固有张力以及附近刚性边界通过粘性流体相互作用对动力学的影响。 我们量化了梁浸没在空气或水中时前十一阶弯曲模式的随机动力学。 在可能的情况下，我们将数值结果与理论进行比较，发现非常一致。 我们量化了计算方法的局限性，并描述了其适用范围。 这些结果为研究粘性流体中缺乏理论描述的复杂三维弹性结构的随机动力学奠定了基础。 显示英文摘要

摘要： The stochastic dynamics of small elastic objects in fluid are central to many important and emerging technologies. It is now possible to measure and use the higher modes of motion of elastic structures when driven by Brownian motion alone. Although theoretical descriptions exist for idealized conditions, computing the stochastic multimodal dynamics for the complex conditions of experiment is very challenging. We show that this is possible using deterministic finite element calculations with the fluctuation dissipation theorem by exploring the multimodal stochastic dynamics of a doubly-clamped nanobeam. We use a very general, and flexible, finite-element computational approach to quantify the stochastic dynamics of multiple modes simultaneously using only a single deterministic simulation. We include the experimentally relevant features of an intrinsic tension in the beam and the influence of a nearby rigid boundary on the dynamics through viscous fluid interactions. We quantify the stochastic dynamics of the first eleven flexural modes of the beam when immersed in air or water. We compare the numerical results with theory, where possible, and find excellent agreement. We quantify the limitations of the computational approach and describe its range of applicability. These results pave the way for computational studies of the stochastic dynamics of complex 3D elastic structures in a viscous fluid where theoretical descriptions are not available.