Height Adjustment of 3-D Axisymmetric Microumbrella Shells for Tailoring Wineglass Frequency

This paper proposes to adjust shell heights of slim-stemmed microumbrella shells by a low-cost foaming process for regulating wineglass frequency. Titanium hydride (TiH
₂
) is used as the foaming agents. They are sealed in the cavities of the bonded glass and silicon wafers and release H
₂
to drive the softened wafer glass into axisymmetric microumbrella shells at high temperatures. An analytical model coupled with a finite-element model is built to relate the mass of foaming agents to shell height. Results show that the difference between the analytical model and the finite-element model for the mass of foaming agents of shaping a hemispherical umbrella shell is within 15%. The finite-element model for the shell height exhibits <12% errors with the foaming experiments. The
$n = 2$
wineglass frequency of glass umbrella shells with different aspect ratios (shell height/shell radius) is predicted to be from 10 to 50 kHz, demonstrating nonnegligible impact of shell heights on the frequencies. Experiment results indicate that changing aspect ratios of the umbrella shells by the foaming process is an effective way to obtain the desirable working frequency. With a combination of selecting thicknesses of the micromachined glass layer and changing shell heights, this foaming process can achieve a broader spectrum of resonant frequencies, which makes the axisymmetric umbrella shells suitable for a wide range of vibration applications.