Optimum design of dynamic absorber for a random-excited machine mounted on a platelike structure foundation

The optimum design of a dynamic absorber for a machine mounted on a floor system is presented. The floor is considered to be a platelike structure. The transfer function is derived in closed-form. Based on the band-limited white-noise excitation, the optimum tuning and damping ratios of the absorber are determined by minimising the variance of response of the machine. Since the variance cannot be calculated directly by integrating the transfer function over the band-limited frequency range, the steepest descent method is used for determining these optimum parameters by iteration. The same procedure can be extended to deal with the cases of other multi degrees-of-freedom systems. The effects of mass ratios (i.e. absorber/machine and machine/floor), primary damping, frequency ratio and the thickness of plate on the design parameters are examined. The results show that the values of optimum tuning are much different from those of the rigid foundation case. To have a small variance, it is better to keep the frequency ratio ω₁ (defined as the frequency of primary system divided by half of the lowest natural frequency of the floor) in the range 1 < ω₁ < 1.5, and have the mass ratio μ and the primary damping ratio ζ₁ are both greater than 0.1.