Variational method for modeling static and dynamic stresses in a resonator disc with mounts

Abstract

The authors establish calculational procedures implemented in a desk top computer program which provide adequate solutions for most problems of interest in reasonable computation times. It uses variational calculus to approximate the displacements in the quartz crystal. Body forces are included to represent acceleration. The mounting structures are included as point boundary conditions represented by spring matrices, relating deflections and rotations to the forces and moments from the mount reactions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>