Date of Award


Publication Type

Master Thesis

Degree Name



Mechanical, Automotive, and Materials Engineering

First Advisor

J. Ahamed




The dynamic performance of the micro-resonator depends on the loss mechanism. As most of the nergy is lost from air damping in the ambient pressure, creating a vacuum condition around the micro-resonator will mitigate the energy loss. This paper presents numerical and analytical modeling techniques to understand the effect of vacuum level on energy loss in micro-resonator. Two vacuum region were investigated; the first region is in the pressure range of 1-10 Pa, while the second region is in the pressure range of 20-100 Pa. Both were investigated in the medium vacuum pressure regime. Analytical and numerical results were compared at these two pressure regions with previous experimental literature study. The goal was to graphically compare the previous and current work and find similar trend relationships ie. if the pressure decreases, the measured quantity Q/Qmax exponentially increases. There is a qualitative good agreement between the analytical and numerical model with a vacuum sealed pacakging platform. Both the squeeze film damping and slide film damping are present in the cavity and the squeeze film damping is the dominating energy loss. The air gaps between moving structure and fixed fingers create the squeeze film damping and cause energy loss difference, while the smaller air gaps between them generate large damping force and reduce the performance of the micro-resonator. In contrast, the larger air gaps exist between them generate smaller damping force and less influence on micro-resonator (fewer energy losses from the resonator). The air damping is classified into three damping regimes: viscous damping, molecular damping, and intrinsic damping. The pressure between 1-100 Pa is in the molecular damping regimes (medium vacuum), and air damping is the dominating loss in the low to medium vacuum. Furthermore, intrinsic losses, such as anchor loss and thermoelastic damping loss, are dominating at a high vacuum in the pressure range of 0.1 to 10-5 Pa.