Abstract
A new optimum design method for dynamic vibration absorbers is proposed for cases when the dynamic characteristics of the primary system vary by a considerable amount and the excitation frequency fluctuates in a small range. When the excitation frequency is constant, it is well known that an undamped dynamic vibration absorber is very effective for attenuating the vibration amplitude of the primary system. However, when the excitation frequency fluctuates in a small range, such an undamped absorber does not always suppress the vibration amplitude. In this paper, we show that the upper limit of the vibration amplitude of the primary system can be easily estimated using the imaginary part of the dynamic stiffness of the absorber. We derive very simple equations that give the optimum natural frequency and damping ratio of the absorber for a given excitation frequency range when the excitation force amplitude is proportional to the square of the frequency and vibration is evaluated using velocity amplitude. Calculation results of the frequency response for some examples of absorbers designed by the proposed method are demonstrated, which show the usefulness of the proposed method.
