 Ali Imam

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.