Analytical method for suboptimal design of dynamic absorber for parametrically excited system

Parametric excitation is induced due to systemically unstable equilibrium states and often results in undesired vibration in mechanical systems. Many researchers have shown that the use of a dynamic absorber with an appropriate natural frequency and damping ratio is effective for suppressing parametric excitation. However, unlike the situation in a forced vibration system, it is difficult to find analytical expressions to determine the optimal design of the dynamic absorber for a parametrically excited system, which inevitably makes the design inefficient. This study developed a method for obtaining analytical suboptimal designs, specifically approximate optimal designs, for a dynamic absorber for parametric excitation through two kinds of free vibration systems constructed by approximating the original system. A comparison between the results for the suboptimal designs and an accurate optimal design demonstrated that an effective suboptimal design is achieved using a free vibration system that has an appropriate negative damping term derived from the instability of the original parametrically excited system. The developed approach is expected to provide an efficient option for suppressing parametric excitation.