Various formulas for optimal design of a series-type double-mass dynamic vibration absorber

The author had previously reported the optimal design formulas for a series-type double-mass dynamic vibration absorber (DVA) to be installed in a damped primary system. At that time, only one formula giving the exact optimal design conditions for the DVA was reported for each optimization criterion. Each formula was obtained by solving a set of simultaneous algebraic equations consisting of four or five equations. The usual method for solving simultaneous equations is to reduce the number of unknowns in these equations one by one, and finally derived a single higher-order (cubic or quartic) equation consisting of a single unknown. Depending on which variables are left at the last equation, completely different solutions calculating the optimal designing values of the DVA can be obtained for each criterion. Because these are the solutions to the same optimization problem, numerical calculations will return to us the same values. However, the derived multiple solutions cannot be derived from one solution to the other through algebraic operations. In this article, some of those solutions will be presented.