Changing the Effective Mass to Control Resonance Problems

Resonant frequency problems are often encountered in mechanical systems. When this occurs, the level of vibration is generally quite high, and this in turn often causes premature failure of machine components. Often, attempts are made to address the problem by reducing the forcing function. Such courses of action include dynamic balancing of rotating elements and aligning coupled components. It is very important to maintain good balance and alignment. However, in the case of a resonant condition, the primary problem is generally not the magnitude of the forcing function. The problem is that a forcing function, which may be of modest magnitude, matches a system resonance or natural frequency. In such a case, the amplification factor of the vibration can be many fold. The amplification factor is the ratio of the peak dynamic displacement imparted on a system by an oscillating force with a given peak magnitude compared with the displacement imparted by a static force of the same magnitude. Figure 1 is a plot of the amplification factor versus resonant frequency ratio for several systems each with a different level of damping. The resonant frequency ratio is the ratio of the forcing frequency to the resonant frequency. A value of one indicates that the system is at resonance. The simple equation for resonant frequency is: