ABSTRACT
In Chapter 10 we discussed a method for the solution of undamped and damped free-vibration problems which involved a transformation of the equations to a set of coordinates called modal coordinates or normal coordinates. Modal coordinate transformation uncouples the equations of undamped free vibrations so that the problem reduces to the solution of a set of N independent second-order differential equations. In the case when damping is present, modal transformation will uncouple the equations of motion only provided that the damping matrix satisfies the orthogonality condition. In practice, because the nature of physical characteristics that determine damping are difficult to define or to measure, damping is usually best specified in terms of modal damping ratios, an approach which while implying that the damping matrix does satisfy the orthogonality conditions, does not require an explicit determination of the matrix.
