The Dynamics of a Micron Scale Beam Driven by Synthetic Noise in a Fluid

As nanotechnology rapidly advances, the role of nonlinear dynamics and the influence of dissipation will become increasingly important -- even when the dynamics are driven by molecular collisions. As a means to study this regime while using currently accessible microscale systems, we use a noisy electrothermal drive whose magnitude can be varied to explore the linear and nonlinear dynamics of a micron scale beam immersed in fluid. The electrothermal actuation is a synthetic noise force that we have tailored to generate beam dynamics that approximate Brownian driven motion. In the linear regime, we use the fluctuation-dissipation theorem to quantify the ability of the synthetic noise to generate driven Brownian dynamics. We use deterministic and stochastic numerical approaches to describe the beam dynamics that are valid in the linear and nonlinear regimes. We explore extensions of these approaches to include the variations in mass loading and damping that occur for oscillators in a viscous fluid. Theory, numerics, and experiment will be compared where possible to highlight new physical insights into the strongly driven dynamics of small elastic structures in fluid.