On the damping ratio of multi‐degree‐of‐freedom systems

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Abstract
The damping parameter is commonly used when assessing a vibration system or analysing dynamical response, as well as reducing vibration levels. A basic step towards analysing a damped system is to solve its complex eigenvalues. However, the solution is computer‐time‐consuming. An alternative way is to get the damping ratio matrix so that the behaviour of the system in each mode can be determined. This paper presents a simple means of identifying the corresponding relation between the mode number and its damping ratio by a matrix perturbation method which leads to the transformation perturbation or TP method. The equivalence of the complex eigenproblem of damped systems and transformed damping matrix in calculating the damping ratios is also discussed.

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