Lagrangian framework for systems composed of high-loss and lossless components
Abstract
Using a Lagrangian mechanics approach, we construct a framework to study the dissipative properties of systems composed of two components one of which is highly lossy and the other is lossless. We have shown in our previous work that for such a composite system the modes split into two distinct classes, high-loss and low-loss, according to their dissipative behavior. A principal result of this paper is that for any such dissipative Lagrangian system, with losses accounted by a Rayleigh dissipative function, a rather universal phenomenon occurs, namely, selective overdamping: The high-loss modes are all overdamped, i.e., non-oscillatory, as are an equal number of low-loss modes, but the rest of the low-loss modes remain oscillatory each with an extremely high quality factor that actually increases as the loss of the lossy component increases. We prove this result using a new time dynamical characterization of overdamping in terms of a virial theorem for dissipative systems and the breaking of an equipartition of energy.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 01, 2014
- Source ID
- 10.1063/1.4884298
Entities
People
- Aaron Welters
- Alexander Figotin
Organizations
- Air Force Office of Scientific Research
- Massachusetts Institute of Technology
- University of California, Irvine