Experimental identification of generalised proportional viscous damping matrix

A simple and easy-to-implement algorithm to identify a generalised proportional viscous damping matrix is developed in this work. The chief advantage of the pro-posed technique is that only a single drive-point frequency response function (FRF) measurement is needed. Such FRFs are routinely measured using the standard techniques of experimental modal analysis, such as impulse test. The practical utility of the proposed identification scheme is illustrated on three representative structures: (1) a free-free beam in °exural vibration, (2) a quasi-periodic three-cantilever structure made by inserting slots in a plate, in out-of-plane flexural vibration, and (3) a point-coupled-beam system. The finite element method is used to obtain the mass and stiffness matrices for each system and damping matrix is fitted to measured variation of the damping (modal damping factors) with the natural frequency of vibration. The fitted viscous damping matrix does accommodate for any smooth variation of damping with frequency, as opposed to the conventional proportional damping matrix. It is concluded that a more generalised viscous damping matrix, allowing for smooth variation of damping as a function of frequency, can be accommodated within the framework of standard finite element modelling and vibration analysis of linear systems.