Transport Vibration – Should You Be Concerned? Part 2

A helpful way to think of vibration is in terms of sound. Though the audible frequency spectrum is higher than the transport vibration spectrum – sound is vibration. The simplest way to think of vibration is in-terms of a sinusoidal signal. Strumming a guitar string results in a sinusoidal tone – honking a horn and even traveling over rumble strips on the side of the road results in a temporary burst of sinusoidal vibration. In the test lab, we often describe vibration as rumbling (low frequencies), rattling (mid frequencies) or ringing (high frequencies). Those descriptions are based upon the sinusoidal characteristic of the sound.

In the example below, we’re showing a measured sinusoidal vibration signal with a 1G input. Frequency is described in terms of Hertz-Hz, which means cycles per second. We can determine the frequency of the signal by counting the number of repetitive cycles that occur over a period of one second. In the example below, we’ve highlighted one complete “cycle” evident in the entire 1-second signal. If we count the number of those cycles in that 1-second example, we determine that this signal has a 5 Hz sinusoidal characteristic.

Graph of sinusoidal vibration signals with complete cycle identified.

However, constant amplitude, sinusoidal signals are not common in real-world transport vibration. Below, is a view of that 5 Hz signal side-by-side with a sample of real-world transport vibration. One looks clean while the other looks comparably messy – or noisy.

Graphs of sinusoidal and random vibration signals.That messy signal is what we call random vibration. Though it may appear messy, the random signal can be thought of as being made up from many sinusoidal wavelets. Additionally, the amplitude of those wavelets changes, or varies over time. For example, truck trailers transmit vibration into cargo that originates from the road, wheels (mid frequency), suspension (low frequency) and the rigid-body structural members (high frequency). Each of those inputs possess their own sinusoidal signatures, and that cumulative input is simultaneously transmitted through the floor and into the cargo. All of those sine wavelets overlay and combine to create what looks to be a random signal.

So – how would you go about analyzing a random bunch of mixed up sine tones and amplitudes?

Luckily – automated analysis techniques allow us to decompose the random vibration signals to have a look at the original frequency content and amplitudes. You can think of it like sending the random signal through a filter – the filter is sensitive to a specific frequency and can tell you if that frequency is present – and at what levels/intensities. The trick is to create a bank of filters that can observe an entire frequency spectrum where each filter identifies and reports if that frequency is present and at what levels.

For transport vibration, we can do this with a Power Spectral Density (PSD) analysis. In simple terms – we pull all the individual sinusoidal frequency content out of the random signal – then determine the intensity for each frequency. In the example below, we’re illustrating a 5 Hz signal being pulled from the random signal and the average intensity of that signal being plotted on the PSD. Now imagine repeating that process for 1 Hz, 2 Hz, 3, Hz, 10 Hz, 20 Hz, 50 Hz, etc. The specific frequency resolution of the analysis determines the number of frequency-vs-amplitude breakpoints that would be used to define the PSD.5 Hz signal pulled from random signal, averaged intensity plotted as PSD breakpoint.

Hundreds, or even thousands of individual frequency analysis lines are often computed from each time-history signal. Plotting all those individual frequency-vs-amplitude breakpoints together as one curve results in the representative PSD plot.

To assemble a PSD summary representative of a specific mode or segment of transport – requires analysis of thousands of individual events – which are then statistically combined to provide a representative view of the frequency and amplitude content (energy) present within that mode.

PSDs are defined by their individual shape and intensity. We can think of them as representative of an environmental signature. For instance, a truck PSD looks different than a rail PSD. Air transport PSDs are different from intermodal transport equipment. Transport Vibration PSD profiles are what many of us use to drive laboratory pre-shipment testing and simulation – all in an effort to validate protective packaging designs and solutions.


In Part 3, we’ll discuss resonant, or natural frequency and why you need to be concerned with it from a safe transport perspective.