= Ali Imam
{c}
<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.<The Decoupling of Damped Linear Systems in Oscillatory Free Vibration by Fai Ma, Ali Imam and Matthias Morzfeld>[Title page, Abstract and Introduction]{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.<The Decoupling of Damped Linear Systems in Free or Forced Vibration by Fai Ma, Matthias Morzfeld and Ali Imam>[Title page and Abstract: nonoscillatory and forced cases]{ref}
A simple original scalar illustration is
$$
\ddot y+2\dot y+5y=f(t).
$$
Setting $y=e^{-t}z$ 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.
Back to article page
