I'm reading a document describing the procedure to do a random vibration test. In it, a PSD (Power Density Curve) curve is defined, and there's a note at the bottom of the curve:

Total acceleration effective: 50 to 500 Hz = 2.0G

What does it mean? Thanks.


1 Answer 1


For a discrete system with $N$ degrees of freedom, the displacement can be expressed as $$ \mathbf{u}(t) = \sum_{i=1}^N \boldsymbol{\Phi}_i \Gamma_i s_i(\omega_i, t) $$ where $\boldsymbol{\Phi}_i$ is the mode shape, $\Gamma_i$ is the participation factor, and $s_i$ is a function of the modal frequency, $\omega_i$.

The second derivative of the displacement, $\ddot{\mathbf{u}}$ (with respect to time, $t$) gives the total acceleration. Some corrections are needed when all the $N$ modes are not known.

In your case, the modes chosen are only between 50 Hz and 500 Hz. Therefore, the term effective has been used.

To get the g value, the acceleration ($\ddot{\mathbf{u}}$) is divided by the acceleration due to gravity.


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