Parerga and Paralipomena

I have been catching up on my ultrasonics this morning and met with this abstract, helpfully prefixed to an article on "Vibration of Post-Buckled Homogeneous Circular Plates":

The dynamic behavior of an axisymmetric post-buckled circular plate with initial in-plane compression loading is investigated. The static von Karman plate equations are solved numerically for clamped boundary conditions. The static solution is presented for a range of transverse and in-plane loads. Lumped element modeling is used to calculate the mass and compliance of the plate from results of the static solution. The resonant frequency, sensitivity, and maximum linear transverse pressure are calculated for a variety of in-plane loads. These solutions can be used to predict the post-buckled behavior of micromachined plates.

Heaven knows it sounds right. But alas, here as elsewhere, gorgeous diction conceals faulty reasoning.

We have grown so accustomed to solving clamped boundary conditions numerically that it can be difficult to remember that the static von Karman equations are only approximately conformable to in-plane compression loading.

Now, if it were possible to calculate the compliance of the plate using nothing more than lumped element modeling, I'm sure we would all be as happy as kings.

But there is no getting around the fact that linear pressure predicts post-buckled behavior if, and only if, the range of vibration of the transverse loads exceeds their resonant frequency under un-clamped conditions -- and that, frankly, is so rare that I don't believe I have ever once seen it happen.

The sad thing is that this blunder deprives us of the pleasure we so keenly anticipated from the article itself.