Belated appreciation of Lisa Sievers' thesis

Abstract

In her 1987 thesis [1] and a follow-up paper in the IEEE Transactions of Automatic Control [2], Lisa Sievers described three dynamic multi-span models for lateral web behavior.

Convecting string with zero bending stiffness

Euler-Bernoulli beam with bending stiffness and no shear

Timoshenko beam with both bending and shear

The last two transferred the bending portion of lateral deformation across rollers. In the Timoshenko model, which included shear and is the main result of her work, only bending deformation is transferred.

Although she built on the work of everyone who preceded her, Lisa creatively reanalyzed everything she used and put it on a more rigorous mathematical footing. This deserves a wider appreciation.

Three notable features of the thesis are:

Use of Hamilton's method for deriving the governing equations. This is certainly not the first instance of its use in web handling. It is nevertheless an excellent example.

Derivation of the downstream boundary conditions for lateral velocity by application of the material derivative. So far as I know, this has never been done before.

Use of spectral separation to justify use of static web shape in a dynamic model. This is a good idea. However, results from it suggest that there is not as much separation as we might like.

In an effort to make the results of her thesis more accessible, this paper will review it and recast the Timoshenko model into a form which facilitates analytical comparison with Euler-Bernoulli beam models in current use.