“Introduction:

Resonance, which is the result of the excitation of a natural frequency, is a common root cause of excessive machine and structural vibration. Operating machinery that produces dynamic forces at frequencies near natural frequencies can result in a significant amplification of vibration.

Figure 1 contains a simple approximation for a structural-mechanical vibrating system that consists of the mass (m) of a machine supported by a structure approximated by two springs, each having stiffness (k). The total stiffness of the structure would then be 2k. This approximation is presented as an academic exercise in order to illustrate the difference in the response of machine structures to static loading versus dynamic loading. Most structural-mechanical systems are too complex to be treated as such a simple vibrating system.

Figure 2 is a curve illustrating the effects of resonant amplification. The amplification increases as the frequency ratio increases from the origin toward 1.0. At a frequency ratio of 1.0, the magnification factor without damping is infinite. The magnification factor then begins to decrease as the frequency ratio increases beyond 1.0. At ratios above 1.414, vibration is attenuated instead of amplified.

Very stiff structures will have higher natural frequencies and lower frequency ratios. Thus, stiff structures will be subject to some amount of resonant amplification, albeit in most cases the magnitude of the amplification is minimal. Also, since the amplitude of vibration without amplification is usually low due to the stiffness of the structure, the resultant amplified vibration is typically acceptable.

The design of the structural support members and foundations should include a calculation of the natural frequencies and mode shapes. Natural frequencies that are in the neighborhood of frequencies of dynamic forces produced by a machine should be altered by structural modification to preclude the excitation of resonance.

The evaluation of structural natural frequencies is even more important for equipment operating with variable frequency control devices. Dynamic forces will be produced by equipment over a wide range of frequencies instead of at discrete frequencies. This increases the probability of resonance unless the structures are properly evaluated.

"Impact Testing:

Impact testing is a common method used to determine the natural frequencies of machines and structures. Although an impact test can be performed using a single-channel analyzer, this paper is limited to the discussion of multi-channel impact testing. A multi-channel impact test requires an instrumented force hammer, at least one response transducer, and a multi-channel analyzer with cross channel functionality.”