Optimization of Multiple Tuned Mass Dampers for Road Bridges Taking into Account Bridge-Vehicle Interaction, Random Pavement Roughness, and Uncertainties

Table 4

Results of the proposed optimization procedure for 50 km/h.

Scenario	TMD mass (kg)	TMD optimized parameters k (N/m); c (Ns/m)	Maximum vertical displacement (mm)	Dynamic amplification factor
Static case	—	—	0.3132	—
Without TMD	—	—	0.6026	1.924
1	mtmd1 = 4498.2	ktmd1 = 21198202.49	0.4477	1.429
		ctmd1 = 56064.90
2	mtmd1 = 2249.1	ktmd1 = 6730864.37	0.3867	1.235
		ctmd1 = 1516.19
	mtmd2 = 2249.1	ktmd2 = 11187204.86
		ctmd2 = 202.916
3	mtmd1 = 1499.4	ktmd1 = 4598993.93	0.3867	1.235
		ctmd1 = 1122.01
	mtmd2 = 1499.4	ktmd2 = 6925434.17
		ctmd2 = 2501.31
	mtmd3 = 1499.4	ktmd3 = 7598713.09
		ctmd3 = 168.309