Sinusoid vibration and random vibration testing are two acceptable ways of evaluating electronics against vibration damage. Most new platforms’ vibration specs have random vibration requirements, although some sinusoid vibration requirements still exist. But many older standards only list sinusoid vibration requirements.

It would be particularly useful to relate existing sinusoid vibration test results with more current random vibration test requirements. The significance, for example, comes when an older airplane needs to upgrade its legacy systems to a new avionics suite. In this case, the newly designed avionics system is tested by random vibration under MIL-STD-810F, but the spec available on the older airplane is written in terms of sinusoidal vibration testing under MIL-STD-810A. Will the new avionics survive the vibration requirement of the old airplane without expensive retesting?

One practical example would be an electronic device designed for the new Joint Strike Fighter (JSF) and qualified to meet certain modern random vibration requirements. But if the same device is to be mounted on a B-52, the airframe’s vibration specifications are probably stated in terms of sinusoid vibration. By using the appropriate equations, the device can be qualified by analysis. Therefore, expensive double qualification testing is eliminated and total cost of the product is reduced.

This is not an academic question: COTS engineers are troubled by this problem all the time. Finding a method to relate these two vibration methods will reduce or eliminate expensive repetitive testing and qualification.

Mathematical Differences

The characterizations of sinusoid and random vibration are based on two distinctly different sets of mathematics. Sinusoid vibration testing uses a single-frequency sinusoid wave to induce vibration in the specimen by changing the vibration frequency against a time variable. The upper and lower limit of the frequency, duration of sweep, amplitude or peak acceleration of the sine wave vibration will decide the severity of the vibration. The testing equipment can be an electro-dynamics shaker or simply a mechanical shaker.

Random vibration testing uses an electro-dynamics shaker to generate multiple random frequency vibration. The duration of the testing, Power Spectra Density (PSD) level of the vibration, and the upper and lower limit of the vibration frequency will decide the severity of the vibration. Repetitive Shock (RS) shaker equipment can also generate some random vibration. The power spectral density profile is very hard to control in RS shakers.

The challenge is to relate the testing results between the two methods. Often, attempts are made to compare the peak acceleration of the sine wave to the root mean square (RMS) acceleration of random vibration. However, peak sine acceleration is the maximum acceleration at one frequency only. Random RMS is the square root of the area under a spectral density curve. These are not equivalent.

Method

The proposed method to relate random and sinusoid vibration is based on the equivalent effective damage theory. In engineering practice, it is common to equal the dynamic load to a static acceleration load to simplify the calculation, if they all cause the similar damage to the structure. In the area of aircraft structural design, all loads were calculated in terms of static load. Dynamic load was considered in terms of static load factors. A different area has a different dynamic load, and therefore has different load factors. By using equivalent static load factors and treating the dynamic load as a static load, the structural analysis is simplified.

Avionics packaging engineers had been using equivalent damage theory for many years under the direction of MIL-STD-810. The military standard had allowed the testing engineers to use the equivalent testing scenario to replace the required testing scenarios if certain conditions had been met.

In the area of avionics equipment, most components are soldered to printed circuit boards (PCBs), and the deflection of the PCB is the dominating factor to the life of the equipment. Equations are established so that the static acceleration load will cause the PCB boards to have the same deflection as the vibration load.

Another simplification method is used in the following analogy. It has been documented that the PCB boards will deflect the most at the resonance points, under the vibration load (Figure 1). In vibration analysis, any driving-frequencies, which are between two half-power points, will cause the most effective damage. The half-power point is defined as being at the driven frequency f when current transmissibility is related to maximum transmissibility Q in the following formula.