Multimodal Analysis of Driven Nanobeams with Arbitrary Tension in a Viscous Fluid

We investigate the driven dynamics of a long and slender nanoscale beam with tension that is immersed in a viscous fluid. The beam motion is driven by a harmonic force that is applied over the spatial region near its fixed ends. We develop a multimode theoretical description that is valid for all values of tension, includes the coupling of the beam dynamics with the spatially varying drive force, and can be used for a Newtonian fluid. The fluid dynamics are modeled using the hydrodynamic function of an oscillating blade. Using our theoretical description, we quantify the dynamics over a wide range of conditions. We directly compare the theoretical predictions with experimental measurements for a beam under very high tension that is driven electrothermally and placed in air and water. We compare theory with experiment for the first several modes of oscillation which shows good agreement. For very high tension, we demonstrate the benefit of modeling the system as an oscillating string immersed in a fluid.