144 O. Avci 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0 5 10152025303540455055 Calculated Modal Damping Ratio Sinusoidal Excitation Amplitude (lbs) Stage 2 Stage 1 Fig. 18.4 Nonlinear damping behavior for both stages of the laboratory structure For the back-calculations of the modal damping ratios, when the effective weight values of 0.470 W and 0.502 W are used for Stages 1 and 2, respectively, the corresponding damping ratios are found for each sinusoidal test run, using Eq. (18.26). Table 18.2 presents the calculated damping ratios for Stage 1 and Table 18.3 presents the calculated damping ratios for Stage 2. Studying the results of Tables 18.2 and 18.3 it is observed that as the sine excitation amplitude is increasing, the damping ratio value is also increasing. This is the nonlinear behavior of the damping and it is plotted in Fig. 18.4. It must be emphasized that the damping ratio values for Stage 1 and 2 are very close and showing the same trend for the amplitude dependent behavior. It is shown that for very low excitations, the damping ratio value can go as low as 0.5% while for increased excitations, the damping ratio value is around 1%. 18.5 Verification of Nonlinear Damping After the amplitude dependent characteristics of damping has been shown in the previous sections, the finite element models can be re-run for the acceleration responses. The sinusoidal excitations of Stages 1 and 2 are simulated in the FE software with the calculated modal damping ratios presented in Tables 18.2 and 18.3. The corresponding acceleration predictions by the FE model are also shown in Tables 18.2 and 18.3. It is observed that the modal damping ratios introduced for different level of excitations result in very good correlation with the FE model acceleration predictions and measured accelerations. The acceleration predictions are within 4% of the measured data for Stage 1 and within 3% for Stage 2. Since matching the test acceleration responses with the FE model predictions has been a challenge in floor vibrations research, the successful verification of the nonlinear damping in the laboratory environment builds more confidence in FE models for matching the measured accelerations. 18.6 Conclusions The amplitude dependent nature of damping is investigated in this paper based on experimental and analytical work conducted on a laboratory structure. Damping values per various excitation levels are verified; as a result, measured acceleration values matched the FE model predictions utilizing the effective mass calculations for resonant cases. This strengthens the existing confidence on FE models for acceleration predictions in floor vibrations serviceability. References 1. Jeary, A.P.: The description and measurement of nonlinear damping in structures. J. Wind Eng. Ind. Aerodyn. 59, 103–114 (1996). doi:10.1016/0167-6105(96)00002-5 2. Li, Q.S., Yang, K., Wong, C.K., Jeary, A.P.: The effect of amplitude-dependent damping on wind-induced vibrations of a super tall building. J. Wind Eng. Ind. Aerodyn. 91, 1175–1198 (2003). doi:10.1016/S0167-6105(03)00080-1
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