 Fai Ma

Fai Ma is a professor of applied mechanics at UC Berkeley whose listed research includes uncertain dynamical systems, vibration, damping and hysteresis.^[ref] His work with Ali Imam and Matthias Morzfeld develops ways to decouple linear structural dynamics models with damping beyond the conventional assumption of proportional damping.

Their 2009 paper treats oscillatory free vibration. In an undamped real normal mode, all physical coordinates share one time-dependent amplitude with fixed real ratios; generic nonclassical damping can introduce relative phase differences. The paper uses phase information to construct a time-varying decoupling transformation, recovering classical modal analysis in its applicable special case.^[ref]

For an original illustration of the obstacle, consider two coordinate signalsAt $t=\pi /4$, $x_1=0$ while $x_2\ne 0$, so these signals cannot be a single fixed real vector multiplied by one scalar time function. A phase-aware representation must carry more information than that undamped-mode picture.

The 2010 continuation coauthored by Fai Ma, Matthias Morzfeld and Ali Imam extends the treatment to nonoscillatory free response and forced vibration. Together the two papers connect damping, the damped quadratic eigenvalue problem and coordinate transformations, while distinguishing a system's actual decoupling from an approximation that merely discards off-diagonal modal damping coupling.^[ref]

University profile: me.berkeley.edu/people/fai-ma/