crystal

In collaborations with industrial engineers on the design and analysis of quartz crystal plate resonators, which involves the high frequency vibrations of piezoelectric plates with Mindlin plate equations, we have to go through the details of plate equations for every stages in the analysis.  In addition, complications and bias fields are also considered.  We have put together our papers and written a draft of a book detailing essential equations and methods.  We now share this draft with you if you would like to read some documents to know insights on this particular subject.