Acoustic radiation of MEMS and NEMS resonators in fluids

Here, we study the acoustic radiation generated by the vibration of miniaturized doubly clamped and cantilever beam resonators in viscous fluids. Acoustic radiation results in an increase in dissipation and consequently a decrease in the resonator's quality factor. We find that dissipation due to acoustic radiation is negligible when the acoustic wavelength in the fluid is much larger than the bending wavelength. In this regime, dissipation is primarily due to the viscous losses in the fluid and may be predicted with the two-dimensional cylinder approximation in the absence of axial flow and substrate effects. In contrast, when the bending wavelength approaches the length of the acoustic wavelength, acoustic radiation becomes prominent. In this regime, dissipation due to acoustic radiation can no longer be neglected, and the cylinder approximation inaccurately characterizes the total energy loss in the system. Experiments are performed with microcantilevers of varying lengths in Ar and N 2 to observe trends in the acoustic wavelength of the fluid and bending wavelength. Additional experimental results from doubly clamped nanoelectromechanical system beams are also presented. Experimental results illustrate an increase in dissipation, which is further analyzed with the use of three-dimensional finite element models. With the numerical simulations, we calculate the radiation efficiency of the measured devices and analyze the pressure fields generated by the vibrating resonators. This analysis allows one to estimate the effects of acoustic radiation for any resonator.