The fundamental question we aim to address is as follows:
Given all the components of a system, how do we put these components together in order to obtain a desired response? In the context of a mechanical system, the objective is to connect the masses with springs in a suitable way such that a desired response can be obtained for a given set of input forces acting on the masses. In the simplest of the scenarios, this problem further reduces to the objective of finding a suitable interconnection of the masses using the given springs such that the smallest non-zero natural frequency of the interconnection is maximized.
Journal Publications:
H. Nagarajan, S. Rathinam and S. Darbha, Synthesizing Robust Communication Networks for Unmanned Aerial Vehicles with Resource Constraints. ASME Journal of Dynamic Systems and Control, Accepted August 2014. (pdf)
H. Nagarajan, P. Wei, S. Rathinam and D. Sun, Heuristics for Synthesizing Robust Networks with a Diameter Constraint, Mathematical Problems in Engineering, vol. 2014 (2014), Article ID 326-963, 11 pages. (pdf)
H. Nagarajan, S. Rathinam, S. Darba and K. Rajagopal, Algorithms for Synthesizing Mechanical Systems with Maximal Natural Frequencies, Nonlinear Analysis Series B: Real World Applications, vol. 13, Issue 5, October 2012, Pages 2154-2162. (pdf)
Book Chapter:
H. Nagarajan, S. Rathinam, S. Darba and K. Rajagopal, Algorithms for .finding diameter constrained graphs with maximum algebraic connectivity, Dynamics of Information Systems: Mathematical Foundations, 2012, vol. 20, Springer Proceedings in Mathematics & Statistics, Editors: Alexey Sorokin, Robert Murphey, My T. Thai, Panos M. Pardalos.
Conference Publications:
H. Nagarajan, P. Wei, S. Rathinam, and D. Sun, Air transportation network robustness optimization under limited legs itinerary constraint. The 5th International Conference on Research in Air Transportation, Berkeley, CA, May 22-25, 2012.
H. Nagarajan, S. Rathinam and S. Darbha, Synthesizing Robust Communication Networks for Unmanned Aerial Vehicles with Resource Constraints. ASME Dynamic Systems and Control Conference, Ft. Lauderdale, FL, USA, October 2012.