What is Random Vibration?
There is a degree of confusion about the different kinds of vibration tests available to the vibration testing engineer. Difficulties encountered usually center on the difference between sinusoidal vibration (sine testing) and random vibration testing. Sinusoidal Vibration (Sine):

Strike a tuning fork or pluck a guitar string and the sound you hear is the result of a single sinusoidal wave produced at a particular frequency (Figure 1). Simple musical tones are sine waves (simple, repetitive, oscillating motion of the air) at a particular frequency. More complicated musical sounds arise from overlaying a number of sine waves of different frequencies at the same time. Sine waves are important in more areas than music. Every substance vibrates and has particular frequencies (resonant frequencies) in which it vibrates with the greatest amplitude. Therefore sine wave vibration is important to help understand how any substance vibrates naturally. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

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Figure 1: Representation of a sinusoidal wave. Note its repeatability and predictability. The vibration testing industry has made good use of sine vibrations to help assess the frequencies at which a particular device under test (DUT) resonates. These resonant frequencies are important to the vibration testing engineer because these resonant frequencies are the frequencies at which the DUT vibrates with the greatest amplitude; and therefore, are the frequencies that are most harmful to the DUT. Because “real-world” vibrations are not pure sine vibrations, sine testing has a limited place in the vibration testing industry. Part of the usefulness of sine testing is its simplicity, and therefore, it is a good point of entry into the study of vibrations. Sine testing is used primarily to determine damage to equipment or product. According to Tustin “The best pro-sine reasons are to search for product resonances and then to dwell on one or more of those resonances to: 1. Study modal responses; 2. Determine fatigue life in each mode.”1

Besides testing a product to find and dwell at its resonant frequencies to determine fatigue life, one might also use sine testing to determine damage to one’s equipment. A sine sweep prior to any shock or random test will identify any resonances of the equipment. Running a sine test after testing a product should produce the same data graphs. Any differences in the sweeps indicates damage to the equipment – perhaps something as simple as a shift in the natural resonant frequencies, possibly suggesting a few loose bolts that need to be tightened.

Random Vibration:
Vibrations found in everyday life scenarios (vehicle on common roadway; rocket in take-off, or an airplane wing in turbulent airflow) are not repetitive or predictable like the sinusoidal wave. Consider the acceleration waveform for dashboard vibration found in a vehicle traveling on Chicago Drive near Hudsonville, MI (Figure 2). Note that the vibrations are by no means repetitive.

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Acceleration Waveform: Dashboard Vibration: Real Test 2
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Figure 2 – Data collected on vehicle dashboard in Hudsonville, MI Thus, there is an important place in our testing of products for a test that is not repetitive or predictable. Random testing accomplishes this.

Random vs. Sine:
Sinusoidal vibration tests are not as helpful as random testing is, because a sine test essentially consists of a single frequency in time. A random vibration test, on the other hand, consists of all...

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