For the purposes of examining its transverse (vertical) vibration, a bridge may be modeled as a rectangular cross-section, clamped/clamped beam. The direct response of the bridge at its mid-point needs to be damped. The two side rails of the bridge may also be considered to be clamped/clamped beams of rectangular crosssection. It is proposed to insert some rubber between the rails and the bridge at their mid-points. It is required to minimize the maximum mid-point response of the bridge up to a frequency twice the first natural frequency of the bridge without rails.
The two rubber inserts behave as mass less springs and hysteretic damping elements, each with a characteristic k (1+i). Each team will be given values for L, Bb, Db, Br and . The object is to minimize the maximum response by finding the optimum values of Dr and k. The material of the bridge and rails is the same with density = 7800 kg/m3 and elastic modulus E = 2 1011 N/m2. Parameters are L=10m, Bb =1.5m, Db= 0.25m, Br=0.085m, Alpha= 0.2