Using Theory, Simulation, and Experiment to Probe the Multimodal Thermal Noise Spectrum of a Nanobeam in Fluid Near a Wall

Technology continues to push towards smaller objects to develop increasingly sensitive sensors. By immersing these sensors in a fluid, the resonant frequencies and quality factors shift, and the presence of a nearby wall influences the fluid-solid interaction. To understand these differences, we examine the dynamics of a doubly-clamped beam under high tension in air or water. We explore the Brownian noise spectrum of the beam displacements using theory, simulation, and experiment. We provide a deterministic theoretical description using the fluctuation-dissipation theorem, where the dissipation is due to the viscous fluid. Additionally, we use a finite element approach to study the 3D fluid-solid interaction between the elastic beam and the surrounding fluid. We compare our simulations and experiments using different models of the hydrodynamic function to investigate the effects of a nearby wall on the thermal noise spectrum. We examine the first eleven modes of the noise spectrum, finding excellent agreement between theory, simulation, and experiment. We find that a nearby wall influences the noise spectrum for frequencies with a corresponding Stokes' length greater than 1/5 of the separation between the wall and the beam for the parameters we explore.