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