There is some confusion about the various tests available to the vibration testing engineer. Difficulties encountered usually center on the differences between sinusoidal vibration (sine testing) and random vibration testing.
Strike a tuning fork and the sound you hear is the result of a single sinusoidal wave produced at a particular frequency as shown in Figure 1. The simplest musical tones are sine waves at particular frequencies. More complicated musical sounds arise from over- laying sine waves of different frequencies at the same time. Sine waves are important in more areas than music. Every structure can vibrate and has particular frequencies (resonance frequencies) in which it vibrates with the greatest amplitude. Therefore sinusoidal vibration testing is important to help understand how any structure vibrates naturally.
The vibration testing industry has made good use of sine vibra- tions to help assess the frequencies at which a particular device under test (DUT) resonates. These frequencies are important to the vibration testing engineer, because they are the frequencies at which the DUT vibrates with the greatest amplitude and, therefore, may be the most harmful to the DUT.
Because “real-world” vibrations are not sinusoidal, sine testing has a limited place in the vibration testing industry. Part of the usefulness of sine testing is its simplicity, so it’s a good point of entry into the study of vibrations.
Sine testing is used primarily to determine damage to structures. The best pro-sine arguments are to search for product resonances and then to dwell on one or more of them to determine modal properties and to determine fatigue life associated with each mode.1
Aside from testing a product to find and dwell at its resonance frequencies to determine fatigue life, one might also use sine testing to determine damage to equipment. A sine sweep prior to any shock or random vibration test will identify the dominant resonances of the tested equipment. Repeating the sine test after otherwise abusing a product should produce the same test results unless the DUT has been damaged. Any differences in the sweeps indicate damage to the equipment – perhaps something as simple as a shift in the natural resonanance frequencies that might suggest a few loose bolts need to be tightened.
Random Vibration
Vibrations found in everyday life scenarios (a vehicle on a typi- cal roadway, the firing of a rocket or an airplane wing in turbulent air flow) are not repetitive or predictable like sinusoidal wave- forms. Consider the acceleration waveform shown in Figure 2 for dashboard vibration of a vehicle traveling on Chicago Drive near Hudsonville, MI. Note that the vibrations are by no means repeti- tive. So there is an important need for tests that are not repetitive or predictable. Random vibration testing accomplishes this.
Random vs. Sine. Sinusoidal vibration tests are not as help- ful as random testing, because a sine test focusses upon a single frequency at any one time. A random vibration test, on the other hand, excites all the frequencies in a defined spectrum at any given time. Consider Tustin’s description of random vibration – “I’ve heard people describe a continuous spectrum, say 10-2000 Hz, as 1990 sine waves 1 Hz apart. No, that is close but not quite cor- rect. Sine waves have constant amplitude and phase, cycle after cycle. Suppose that there were 1990 of them. Would the totality be random? No. For the totality to be random, the amplitude and starting phase of each slice would have to vary randomly, unpre- dictably. Unpredictable variations are what we mean by random. Broad-spectrum random vibration contains not sinusoids but rather a continuum of vibrations.”1
Advantages of Random Vibration Testing. One of the main goals or uses of random vibration testing in industry is to bring a DUT to failure. For example, a company might desire to find out how a particular product may fail because of various environmental