Substructuring with Geometrically Nonlinear Subcomponents


With its matte-black finish and squat, stealthy shape, the Lockheed SR-71 Blackbird reconnaissance aircraft has for more than three decades held the world record as the fastest air-breathing manned aircraft. In service with the U.S. Air Force from 1964 to 1998, the craft could streak across the globe at Mach 3-plus, or more than 2,200 miles per hour. Since it was retired over a decade ago, no vehicle has been able to even match that speed, but that doesn’t mean that the US Air Force wouldn’t like to create vehicles that could top that speed, flying at hypersonic speeds of Mach 5 or maybe even in excess of Mach 10.

One major barrier is the fact that the air flowing over the aircraft at that speed generates a lot of heat, says Matt Allen, an assistant professor of engineering physics. “At these speeds the panels of the plane heat significantly, causing them to expand and buckle,” he says. “Then the turbulent air passing over the panels can cause them to snap between different equilibria. This is type of vibration is highly nonlinear, and so the analysis tools that are used to design conventional aircraft don’t work for these vehicles.”

Using computer models to simulate what might happen under those circumstances is difficult and time-consuming. With his award, Allen is developing analytical tools that will enable him to create simplified models for each panel and then to predict how the vehicle will behave when these panels are assembled onto the aircraft. “Our work will help to understand and predict the large-amplitude vibrations that would cause the panels to fail,” he says.

The supersonic Blackbird had a titanium body, but even titanium could not take the heat required for Mach 10, and past efforts to beef up a vehicle for those speeds have produced designs that were too heavy to be practical. “We hope that the tools that we’re developing will allow us to redesign key components to avoid damaging vibrations while also minimizing weight,” says Allen.

While Allen’s current project is focusing on hypersonic vehicles, he also has an eye towards other applications, such as cars and wind turbines, where noise and vibration are important. “These substructuring methods allow us to think of a system as an assembly of parts, which can be advantageous, for example, in the automotive industry where one company makes the electronics, one company makes the frame, one company makes the seat, and so on,” he says. “With these methods you can predict how noisy the vehicle will be after all of those parts are assembled, or whether it might have a resonance that will cause things to break prematurely.”