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Ali Imam is a coauthor of work on decoupling linear structural dynamics models with damping in mechanical engineering. The exact byline and UC Berkeley Mechanical Engineering affiliation appear in the 2009 paper with Fai Ma and Matthias Morzfeld on oscillatory free vibration. That work studies how nonclassical damping prevents the usual undamped normal modes from yielding independent scalar equations, and develops a time-varying transformation using modal phase information.^[ref]

Ali Imam also coauthored the 2010 continuation with Fai Ma and Matthias Morzfeld, treating nonoscillatory free motion and forced vibration. The distinction matters because a change of variables must transform applied forces as well as the free equations.^[ref]

A simple original scalar illustration isSetting $y=e^{-t}z$ gives $\ddot{z}+4z=e^{t}f(t)$. The exponential removes the first-derivative term, but changes the forcing. Thus a free-motion simplification cannot simply be reused with the old right-hand side in a forced calculation. The scalar example highlights why a transformation developed for free vibration needs a corresponding treatment of external forcing.

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/