Effect of the frequency spacing on modal damping estimation of a double-layer grid

Although natural frequencies and mode shapes can be accurately measured by dynamic tests, error bounds in values of damping estimation can be large. Since damping strongly influences the design and control of structures, efforts are made to find the damping that has the least error. The random and bias errors are the two important types of error in damping estimation of structures via frequency domain methods. These errors can be reduced by choosing appropriate frequency spacing. In this study, the frequency spacing leading to the least bias and random errors for estimation of modal damping is determined. The complexity of the damping phenomenon on the one hand and complexity of the structural behavior of a double layer grid, on the other hand, led to this study. For this purpose, a double layer grid constructed from ball joint system was tested. the modal damping ratios related to the first 6 modes of a double layer grid with the ball jointed system were identified for different frequency spacing via two output only modal identification techniques; namely enhanced frequency domain decomposition (EFDD), curve fit frequency domain decomposition (CFDD). The modal damping ratio estimations identified through the two methods were then compared with the results of the input output identification method of Ibrahim time domain (ITD) as the reference value. The results showed that there is an almost linear relationship between the modal damping ratio estimations and the frequency spacing in each mode. At the frequency spacing of 0.0625 Hz, the modal damping ratios obtained from the output only methods showed the least difference (between 0 to 21.43%) with the reference values. At this frequency spacing, the root mean square deviation of modal damping estimations between enhanced frequency domain decomposition (EFDD) and curve-fit frequency domain decomposition (CFDD) with the corresponding reference values was 0.02.