With Richard Farris and Steve Mazur, several years ago, we developed a vibrational technique for stress measurement in films. Under ideal conditions membrane vibration modes depend only on the stress, film thickness, and density. By analyzing non-ideal conditions, one can extract all the stress components and material moduli. An interesting point is that this is a rare technique that provides a direct measurement of the 2D stress tensor. Most other techniques measure strains to infer the stress.
The figure below shows calculated and observed mode shapes in a polymeric membrane. The corresponding natural frequencies can be used to calculate the stress.