Minimum Foundation Mass for Vibration Control

This note utilizes the analog models of forced vibration to express the mass of foundation block in terms of damping ratio and thereafter obtains the expression for the minimum foundation mass required to limit vertical machine vibration amplitude to a prescribed limit. The resulting formula, which accounts for internal damping, is constrained by the limitations of the original analog solutions. Moreover, formulas are derived for determining the damping ratio for conditions different from optimum that enable the evaluation of the nonoptimum foundation mass required to limit vibration. Since the ideal optimum solution may not be practical, an expression has been derived for the best nonoptimum foundation mass. The method presented in this note is believed to be easier to implement and to yield smaller foundation blocks than the existing traditional method, and thus will enable cheaper machine foundations to be constructed. It is believed that the proposed optimal solution may lead to the near elimination of machine vibration nuisance produced by high-frequency machines during operation.