Frederick Ward Williams

TL;DR: The optimal parameter γ−2cr of state feedback H ∞ control is shown to correspond to the fundamental Rayleigh quotient eigenvalue in structural stability or to structural vibration problems formulated in the prismatic domain.

TL;DR: In this paper, it was shown that both the natural frequencies of constrained systems can be calculated accurately using only moderately large artificial inertial parameters, e.g. which are only about 10 times that of the system mass and also that values about a million times more than this do not precipitate ill-conditioning when using 16 figure computer accuracy.

TL;DR: Exact substructuring was introduced into the recursive Newton method, with accuracy retained because the inverse iteration includes the substructure nodes as mentioned in this paper, and the benefits of using frequency squared, rather than frequency, as the eigenparameter.

TL;DR: In this article, a normalized member stiffness determinant is derived for beams with uncoupled axial and Bernoulli-Euler flexural behaviour, by methods applicable to any member possessing transcendental stiffnesses.

TL;DR: In this paper, the authors derived the member stiffness determinant for a vibrating, axially loaded, Timoshenko member, which is the first ever derivation of its stiffness matrix.