## Aeroelasticity

Aeroelasticity is the field devoted to the study of how unsteady aerodynamic forces interact with flexible structures. If you've ever seen a stop sign oscillating in a high wind, you've seen an example of aeroelasticity. It turns out that airplanes can exhibit this kind of behavior as well (it's generally bad when it happens). I spent part of my time as a civilian engineer (about five years) with the U.S. Air Force working on aeroelasticity problems. My Ph.D. dissertation topic was a method for designing scaled wind tunnel models.

The image above depicts the image plane holography setup I used to test the structure for an aeroelastically scaled wing structure. The laser is at the upper left and the rest of the optical components split the beam, expand the two legs, and recombine them at the plate holder in the foreground.

The image above depicts what a typical result looks like. It is a double exposure hologram in which a small static load was applied between the first and second exposures. Each fringe is a line of constant out of plane deformation.

The pictures above show a large aeroelastically scaled model in a NASA wind tunnel beore and after a catastrophic flutter incident. (Photo courtesty of NASA).

## Optimization

Strictly speaking, optimization is the field devoted to finding minima and maxima of functions. It is essentially the practical application of the calculus of variations. It sounds pretty dry, but is extremely cool when applied to design problems. If the function being minimized is the weight of a structure like an airplane wing, the result can be very useful. The wing must be able to do specific things like produce lift and withstand aerodynamic loads, but shouldn't be any heavier than is absolutely necessary. The thing being minimized (weight) is called the objective function. The performance requirements (lift and max stress) are called constraints.

For reasons we may never understand, nature always minimizes things. For structures under a static load, strain energy is minimized. This is a plot showing the strain energy as a function of the angles of deformation on a simplified model of a simple bow. The bow has been strung, but not drawn. The minimum strain energy occurs when the discrete springs are deformed about 12 and 15 degrees.

## Photomechanics

Photomechanics is the field of using optical test methods to measure the behavior of solid structures. There are many different methods in use and several companies making test equipment. Probably the most common piece of commercail equipment is the laser vibrometer. I have worked with wet holography, electronic speckle pattern interferometry (ESPI - the electronic analog of holography), laser vibrometry and high speed video.

The image above depicts a photoelasticity test on a piece of transparent plastic with a machined slot. The plastic is sandwhiched between two polarizing sheets and a load is applied. The birefringent properties of the plastic create fringes showing lines of constant strain.

The image above shows scanning laser vibrometer test on an archtop guitar I made. The shaker is visible behind the instrument and the vibrometer scan head is in the left foreground.

The image above is a screen shot of an ESPI system showing thermal strains on a slotted plate. I made the system using a high resolution digital camera with a computer interface. I did the software using LabView.