“Negative” concepts lead to positive results for Waikato researcher

Whether there is negative mass in the universe or not, the mathematical concept of negative mass, once called by a journal reviewer as “black magic”, has helped a University of Waikato Researcher solve vibration problems.

Now the novel concept of “negative structures” has resulted in Associate Professor Ilanko Ilanko, from the Faculty of Science and Engineering, receiving a $795,000 Marsden Research award to develop a theoretical framework and explore the range of applications.

Ilanko was awarded the grant to look at Negative structures, superposition and penalty parameters for dynamic analysis.

Vibrating Structures

His research aims to develop a new methodology for predicting the vibration behaviour of complex structures using the concept of negative structures – imaginary structures that have negative physical properties: negative mass and negative elastic stiffness.

Just as mathematicians use ‘imaginary numbers’ to solve equations, engineers could use the idea of negative structures to solve vibration problems says Ilanko. Applications of the theory could include creating optimal design of perforated brake discs.

Ilanko’s previous research into negative mass was born following a mistake made in his PhD, where an equation mistakenly using negative mass produced a correct answer. The unexpected answer sparked his interest and the protestations of academics provided inspiration to pursue the topic.

He has published mathematical proofs to support the use of “negative mass” to model rigid supports and connections with potential for applications such as the analysis of aircraft wing and fuselage assembly. These were published in the Journal of Sound and Vibration and the Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science in 2008.

The new proposal of negative structures is an evolution of his work with negative mass. “Mathematically the concept of is a very useful application. Preliminary studies suggest that voids could be simulated by embedding imaginary negative structures into positive structures.”

“For example, a circular plate of negative mass and negative stiffness can be embedded in a larger rectangular plate to simulate a plate with a hole. Negative structures are identical to their positive counterparts, and their vibrational modes can be easily found.”

International Collaborations

In this venture, Ilanko will be joined by a postdoctoral fellow, a PhD student and three Associate Investigators, Professors Peter Hagedorn of Technical University of Darmstadt in Germany, Harm Askes of University of Sheffield and David Kennedy of Cardiff University.

The Marsden Fund is administered by the Royal Society of New Zealand on behalf of the Marsden Fund Council, and funded by the New Zealand Government. It supports projects in the sciences, technology, engineering and maths, social sciences and the humanities.

The University of Waikato won four Marsden Research grants.