The requirements for random vibration testing are defined by the frequency-acceleration power spectral density (PSD for short) curve and its tolerance range. Therefore, in addition to meeting the basic requirements of a sinusoidal vibration shaker, a random vibration shaker has several specific technical specifications.

**I. Acceleration power spectral density control capability (dB)**

Broadband random vibration power spectrum reproduction is the most widely used and most frequently used vibration test in the modern vibration test, and on the basis of broadband random vibration test there are also “broadband + narrowband” “broadband + sine” and other random vibration tests, so the control error of the broadband random vibration power spectrum is a very important technical index.

The acceleration power spectrum density control capability is expressed in terms of power spectrum control accuracy (dB), which is the degree of fluctuation of the measured power spectrum curve around the set power spectrum curve in the whole frequency range, and the maximum fluctuation value is taken to indicate the random vibration test system and velocity power spectrum density control capability.

**II. Acceleration total root mean square value of control error (dB)**

The maximum exciting force of random vibration is the product of the total root mean square value of acceleration and the total mass of the “armature+ fixture + specimen” combination, thus indicating the state of total random vibration energy.

As the root mean square of the acceleration is the open square root of the area below the power spectrum density curve, the root mean square of the acceleration must be within the control error as long as the acceleration power spectrum curve is within the control error.

**III. Peak acceleration values for random vibration tests**

As the amplitude probability density function of random vibration through smooth states meets the requirements of the Gaussian normal distribution, the probability of peak acceleration at a few frequency points in the time domain waveform is very low, and the corresponding current transient peak time is very short, which will hardly cause excessive heating of the armature, so the peak acceleration achieved by random vibration can theoretically be three times the average value of acceleration during the sinusoidal vibration test. In practice, this can be (2.0 to 2.5) times the average acceleration in a sine test.

**IV. Maximum displacement of random vibration tests**

The displacement in the low frequency band of random vibration is limited by the maximum displacement of the shaker, often because the maximum displacement of the shaker cannot meet the requirements of the large displacement in the low frequency, there is clipping of the low frequency vibration waveform, introducing some high frequency spurious signals to the actual collected time domain waveform, affecting the control accuracy of the power spectrum curve. The correct estimation of the amount of vibration displacement in the low frequency band should be based on the acceleration power spectrum density curve, find the random vibration displacement spectrum density curve through two integration operations, calculate the square root mean displacement and multiply it by 3 to get the corresponding maximum peak displacement.

In engineering implementation, the maximum peak displacement in the low frequency band of random vibration can be estimated for a flat power spectrum curve within the operating frequency range according to the following equation. For the downward sloping power spectrum in the low frequency band, it can also be used, but the estimated maximum displacement may be slightly higher than the maximum peak displacement in the actual vibration, which is more conducive to the safety of the experiment and reduces the risk of waveform clipping at peaks.

X_{p-p} — maximum peak displacement, mm

W_{0}— Power spectrum (PSD) value at frequency F_{0}, g^{2}/Hz

F_{0} — Frequency value in the low frequency band, Hz