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<Fai Ma> is a professor of applied mechanics at UC Berkeley whose listed research includes uncertain <dynamical systems>, vibration, <damping> and <hysteresis>.<Fai Ma faculty profile by UC Berkeley>[Name, faculty title and Research Description]{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.<The Decoupling of Damped Linear Systems in Oscillatory Free Vibration by Fai Ma, Ali Imam and Matthias Morzfeld>[Abstract and §§4–5, phase relations and decoupling]{ref}

For an original illustration of the obstacle, consider two coordinate signals
$$
x_1(t)=e^{-t}\cos2t,\qquad x_2(t)=2e^{-t}\cos(2t-\pi/4).
$$
At $t=\pi/4$, $x_1=0$ while $x_2\ne0$, 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>.<The Decoupling of Damped Linear Systems in Free or Forced Vibration by Fai Ma, Matthias Morzfeld and Ali Imam>[Abstract and Introduction, extension to nonoscillatory and forced response]{ref}

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


 Fai Ma (source code)