78 J. Jahanpour et al. 0 5 10 15 20 -1000 -500 0 500 1000 Transmitted Force (N) Time (s) 0 2 4 6 8 10 -1000 -500 0 500 1000 Transmitted Force (N) Time (s) 0 2 4 6 8 10 -100 -50 0 50 100 Displacement (mm) Time (s) 0 5 10 15 -1000 -500 0 500 1000 Transmitted Force (N) Time (s) a b c d Fig. 8.5 Comparison between the transmitted force by the system in a linear system and nonlinear system with NDD damper with resonant external force as F D50N for (a) " D0:05 and ı D0 (b) " D0:05 and ı D1 (c) " D0:5 and ı D1 (d) " D0:05 and ı D2: (red line) approximate analytical solution of the system with the NDD damper; (blue line) numerical solution of the system with the NDD damper; (dark line) analytical solution of the system with the linear damper confirm that utilizing the NDD damper in the resonant-excited system not only causes more vibration amplitude reduction rather than the traditional linear damper but also provides the lower force transmitted to the base compared to the linear damper, where an undesired significant higher transmitted force is produced. A.1 Appendix ˛1 D 4 2 2 C1 ˛2 D 4 4 4 2 ˇ ˛3 D 6 4 2 2 ˇ2 ˛4 D 4 4 ˇ3 ˛5 D 4 ˇ4 (8.41)
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