“Computational Civil Engineering - "Intersections" International Journal

230 C. C. ComisuThe response should be measured at enough points on the superstructure to ensurethat all modes will display their resonant characteristics in the response curve of atleast one of the points.The first piece of information that can be extracted from an amplitude responsecurve is the natural frequencies of the specimen, which are usually identified as thefrequencies where peaks are attained – and thus the name peak-amplitude method.Theoretically, the peaks do not occur exactly at the natural frequencies but at afrequency displaced slightly on one or the other side of them. This is partly due tothe damping which couples the modes (non-proportional damping) and partly dueto the contribution from the other off-resonant modes at that frequency. The lattercontribution will still be there, even if the damping does not couple the motion inthe principal modes. However, if the system is lightly damped and the naturalfrequencies are widely spaced, these errors would be relatively small compared tothe experimental errors involved in locating the peaks.The second piece of information that can be extracted from a response curve is theamount of damping in a particular mode [2]. Damping is determined from thesharpness of the peak (fig. 4) and is normally measured in terms of the Loss Factorgiven byω1−ω2η =ωwhere ω 0 is the natural frequency and ω 1 and ω 2 are frequencies on either side ofthe natural frequency where the peak amplitude is reduced by a factor of 2 .Other parameters in terms of which damping is quoted are all related to each otherand are given by:0wherecccc=2 ⋅ m ⋅ω 0cc is the critical dampingδ is the logarithmic decrement2 ⋅ c δ Eη = = =c π 2 π wcis the dimensionless damping ratioE is the energy dissipated per cycle at resonancew is the energy stored in the system.