Understanding Random Vibration Testing and Sine Testing

What is Random Vibration Testing?

There has always been some confusion concerning the various tests offered to the vibration testing engineer by the vibration test labs. Difficulties encountered usually concentrate on the differences between sinusoidal vibration (sine testing) and random vibration testing.

Strike a tuning fork and the sound you will hear would be of a single sinusoidal wave produced at a specific frequency. The most basic musical tones are sine waves at specific frequencies. More complex musical sounds arise from over-laying sine waves of varied frequencies simultaneously. Sine waves are necessary in other areas than music.

Every structure can vibrate and possess specific frequencies (resonance frequencies) wherein it vibrates using the greatest amplitude. Therefore, sinusoidal vibration testing goes a long way in helping us comprehend how any structure vibrates naturally.

The vibration testing industry uses sine vibration to assess the frequencies at which a device under test (DUT) resonates. These frequencies are vital to the vibration testing engineer, as they are the frequencies at which the DUT vibrates with the greatest amplitude and therefore, could be the most damaging to the DUT.

Because “real-world” vibrations aren’t generally sinusoidal, sine testing plays a limited role in the vibration testing industry. One of the usefulness of sine testing is to identify product resonances in order to dwell on one or more of them to discover modal properties and to determine fatigue life related to each mode.

Aside from testing a product to identify and dwell at its resonance frequencies to ascertain fatigue life, you may also use sine testing to determine damage to equipment. A sine sweep ahead of any shock or random vibration test will determine the dominant resonances of the tested equipment. Repeating the sine test after otherwise abusing a product should obtain the same test results unless the DUT has been damaged.

Any differences in the sweeps indicate damage in the equipment, perhaps simple thing like a shift in the natural resonance frequencies which could suggest a few loose bolts ought to be tightened or the sample was permanently damaged.

Random vibrations are seen in daily life scenarios (an automobile on a typical roadway, the firing of a rocket or an airplane wing in turbulent air flow) aren’t certainly repetitive or predictable like sinusoidal wave forms.

Random vs. Sine.

Sinusoidal vibration tests typically are not as helpful as random testing in certain condition since a sine test focuses on single frequency consistently. A random vibration test, however, always excites all the frequencies within a defined spectrum.  Wayne Tustin’s had a good lay person’s description of random vibration:

sine vibration testing

“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 correct. 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, unpredictably. Unpredictable variations are what we mean by random. Broad-spectrum random vibration contains not sinusoids but rather a continuum of vibrations.”

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, unpredictably. Unpredictable variations are what we mean by random. Broad-spectrum random vibration contains not sinusoids but rather a continuum of vibrations.”

The Advantages of Random Vibration Testing.

The goals or uses of random vibration testing in industry usually is to evaluate the durability of the DUT and to check if a DUT will either work or fail under extreme conditions which it might be exposed to during its lifecycle.

For instance, a manufacturer may want to see how their product may fail on account of various environmental vibrations it will probably encounter during its life. The manufacturer will simulate these vibrations on a shaker and operate their product under those conditions.

Testing the product to failure will inform the manufacturer of several attributes of their product’s weaknesses and the best way to improve it.
Random vibration testing is usually the key testing technique for this type of application because all frequencies are exited at the same time hence creating more realistic representation of what occurs in the “real-world”.

The Power Spectral Density Function (PSD)

To perform random testing, a random test spectrum needs to be defined. Real-time data acquisition utilizes spectrum-averaging to create a statistical approximation of the vibration spectrum. Generally, the random vibration spectrum profile is defined as a power spectral density (PSD) plot.

The form of a PSD plot defines the average acceleration of the random signal at any frequency. The area under this curve is called the signal’s mean square (g2) and its square root is equal to the acceleration’s overall root-mean-square (RMS) value often abbreviated.

A random test is conducted by using closed-loop feedback to introduce the random vibration of a single location (for example the shaker table) to exhibit a desired PSD. The PSD demonstrates how hard the shaker is working, but it doesn’t give any direct information regarding the forces experienced in the DUT.

The g2/Hz PSD is a statistical measurement of the motion experienced at the Control point on the test object – this is crucial to remember. Considering that the PSD is the result of an averaging process, an infinite number of different time waveforms could have generated such a PSD.

Additional Random Vibration Testing Alternatives

Modern test and measurement systems are blessed with inexpensive memory. Recently, it has become feasible to record a long-time history and then play it back as a shake-test Control reference. Vibration Research pioneered such Field Data Replication (FDR) testing few years ago. While FDR is the preferred solution for many cases, this does not substitute random vibration testing. FDR provides an exact simulation of one instance of the environment.

Random provides a statistical average of that environment. Where FDR might exactly capture what one driver experiences while driving a prescribed route, random represents the average of thousands of different drivers attempting to follow the same course. While an FDR recording uses large quantities of memory, a random reference requires very little.

Sine-on-random tests may prove useful to simulate a specific environment with random and tonal components, such as an aircraft package shelf experiencing both random airloads and engine harmonics. Random-on-random tests superimpose narrow-band random noise on broadband random noise.

Such tests are claimed useful to simulate aircraft gunfire reactions. Both types of tests are designed to model a particular class of environment and both are “tricky” to design.


Overall, random vibration testing is an invaluable general-purpose tool for environmental vibration simulation. It is more efficient, more precise, and more realistic for this purpose than sine testing.