This study focuses on the optimum design of the damped dynamic vibration absorber (DVA) for damped primary systems. Different from the conventional way, the DVA damper is connected between the absorber mass and the ground. Two numerical approaches are employed. The first approach solves a set of nonlinear equations established by the Chebyshev’s equioscillation theorem. The second approach minimizes a compound objective subject to a set of the constraints. First the two methods are applied to classical systems and the results are compared with those from the analytical solutions. Then the modified Chebyshev’s equioscillation theorem method is applied to find the optimum damped DVAs for the damped primary system. Various results are obtained and analyzed.

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