Overview

Since its inception, the finite element method has followed the tracks of other well established computational techniques, particularly the finite-difference method. The fluid mechanics applications remained limited to mostly steady-state flow applications in two-or three-dimensional domains, with one or more complicating real-flow effects (e.g., compressibility, turbulence, etc.) being part of the computational model. Differing in complexity and accuracy, the finite-elements themselves have been taken as fixed-geometry subdomains, and this is the critical point where the following analysis categorically differs.

In many real-life applications, the flow domain itself undergoes small timedependent changes (or distortions) that, in most cases, are periodic. The problem of wing flutter is an example of such a situation in the external aerodynamics discipline. The problem under focus here involves the vibration of a fluid-encompassed rotor in a confined-flow type of arrangement (Figure 16.1) and is known to have a major impact on the system's rotordynamic integrity.

Originally handled via finite-difference techniques, the solution strategy was to repeatedly solve the entire physical problemby marching in time while slightly altering the flow-domain geometry at each time level. Tedious as it was, this approach is hardly economical, nor is it based on prior knowledge of what controls the time increment and, often, what fluid/structure features are to be monitored. Prohibiting solid advances in addressing the problem, many believe, is that it was historically handled in either a fluid-dynamics or a mechanical-vibrations type of approach but not a combination of the two mentalities.