Mode shape construction provides way for understanding of diaphragm resonator damping mechanism

Because of their sensitivity advantages and ability to be scaled down the nanoscale, mechanical resonators have found widespread use in biology, medicine, and chemistry. Many of these devices, however, must be used in a fluid medium, where energy dissipation strongly affects their use of frequency changes to measure a target molecule. The mechanism for this damping is still not fully understood, but new work provides a way for those in the research community to investigate how local environmental factors affect diaphragm-structured resonators.

A technique presented by Dong, Ma, and Wang better understands how the resonators are affected by fluid medium and thermal stress. Constructing the mode shape of the diaphragm using a set of polynomial functions, they determined the frequency parameter, nondimensional added virtual mass incremental (NAVMI) factor, and quality factor of the diaphragm.

“The introduction of these approximate mode shapes can hugely simplify the fluid-interaction problem and reduce dramatically the difficulty of theoretical calculation,” said Ma.

Because of its effects on the NAVMI and quality factors, the group found that thermal stress should be accounted for in sensor design. They validated the approach’s reliability with numerical examples and comparisons with a finite element model.

While the approach streamlined determining the theoretical calculations, it does not always accurately predict vibration responses of the fluid structure at higher vibration modes, likely due to the assumption it makes that fluid loading cannot change mode shapes. Ma said the group hopes the paper will stoke interest in the theory for micromechanical and nanomechanical resonators. The group looks to use mode shapes to investigate the dominant fluid interaction-related damping for higher vibration modes.

Source: “The dynamic characteristics of micro-diaphragms subjected to thermal stress when coupled with a fluid,” by Ming Dong, Shujun Ma, and Shiliang Wang, Journal of Applied Physics (2018). The article can be accessed at https://doi.org/10.1063/1.5045272 .