Santillan Explores Dynamics of Extremely Flexible Structures


santillan.jpgYou might call mechanical engineering graduate student Sophia Santillan a non-linear thinker. In fact, the native of Amarillo, Texas, conducts cutting edge research on the non-linear behavior of structures whose strength paradoxically depends on being extremely flimsy.

The buckled beams she studies--thin strips of flexible, bent plastic--might one day lead to the replacement of the metal springs more traditionally used as shock absorbers in some automobiles or other machinery, Santillan said. Her lightweight materials might have a particular advantage in aerodynamic systems, for example, where heft can be a considerable burden.

While the notion may be simple, the underlying investigation her work requires could hardly be more mathematically complex. Unlike traditional coiled springs--which behave in a linear fashion, meaning that the amount of force placed upon them directly corresponds to the amount they compress–— Santillan’s buckled beams behave in a manner much less readily predictable.

“In some cases, decreasing the beams’ deflection requires an increase in the required force,” Santillan said. “Their behavior also depends on their precise orientation and the weight of the structures, among other factors.”

Mathematical descriptions of their dynamics therefore require notoriously difficult to solve nonlinear partial differential equations that encapsulate the way the structures deflect and vibrate when shaken at different frequencies or intensities.

Such equations were essentially unsolvable before the advent of greater computing power, noted Santillan’s adviser Professor Lawrence Virgin, who recently moved from the mechanical engineering and materials science department to become chair of the civil and environmental engineering department.

“It’s now possible to analyze all sorts of interesting behavior that couldn’t be appreciated before,” Virgin said of Santillan’s work. “Our research is at the cutting edge of exploring the potential uses and applications, to consider the circumstances under which such structures, that can accept extreme deflection without breaking, might be beneficial.”

Santillan tests her mathematical models against the beams’ actual behavior as observed in the Dynamics, Stability & Vibration Laboratory in Duke’s Hudson Hall.

In the lab one morning, Santillan demonstrated just what her buckled beams can do. She peered over a shaker table to examine two bent pieces of clear plastic fastened securely on either side of a metal mass. When the stage shook slowly, the plastic bobbed from side to side with the metal plate sliding smoothly back and forth. After turning up the vibrations, which stemmed from one side of the stage, the nearer plastic beam shook harder. The metal mass and opposite beam, on the other hand, remained completely still.

That behavior demonstrates the beams’ possible utility as “vibration isolators,” Santillan said. Just as the beams protected the metal plate from vigorous shaking, they could protect any sensitive piece of machinery from damaging vibrations.

Santillan’s models could provide the foundation for designing a buckled beam made of essentially any elastic material in place of springs in future suspension systems. Differences in material properties are easily accounted for by including a measure of their elasticity.

The mathematical models she is creating might even apply to biological or other systems as well, she added. For example, her buckled beam model could describe the twisting and torsion of strands of DNA or the behavior of pipelines along the seabed as they expand or contract upon heating or cooling.

Santillan earlier studied another non-linear system: a thin strip bent so far that the two ends came together, forming a loop in the shape of a teardrop. One application of such a pinched loop is in measuring the “tackiness” of adhesive tapes – how well they stick and the manner in which they separate again, Santillan said. The tack is measured as the force required to separate two ends of such a loop. She reported those findings in the Journal of Sound and Vibration in November 2005.

For Santillan, it’s the math behind such practical problems that she finds most intriguing.

“I’ve always liked math, and engineering is an application of math,” she said.

Santillan first learned of the work conducted in Professor Virgin’s lab during an independent study as an undergraduate double major in mechanical engineering and math at Duke. After receiving her bachelor’s degree in 2001, Santillan spent two years teaching high school math before the urge to learn more herself landed her back at Duke.

“I figured out that I love teaching,” Santillan said, “but I wanted to come back to graduate school before I didn’t have the time.”

“I also was interested in doing research in the nonlinear dynamics area–— an area I learned a little about as an undergrad and always thought was really interesting.”

Although Santillan said she was always “really mathy,” she hadn’t always planned on a career in engineering. In fact, as an accomplished competitive pianist in high school, Santillan had thought she would pursue music at Northwestern. She applied to Duke on a whim, she said, not expecting to get in.

She was obviously wrong about that and enrolled at Duke’s Trinity College as an undergraduate, only later transferring in to the Pratt School. After completing her doctorate in December 2006 or May 2007, she plans to continue conducting math-based research and teaching at the college level.