How to produce a noise spectrum from an rms velocity specification?

Dear all,

For a dynamic model I am looking at the appropriate input to analyse the performance under the influence of floor vibrations.

The norm is an ISO VC-C floor spectrum as displayed in the image. However, I am stuck in the derivation of going from a rms velocity to a (displacement) noise signal in the time domain. Any help on how to achive this (in Matlab) would be greatly appreciated.

Answer 1

[Mathieu NOE]

hello

maybe this ?

here we generate 10 frequencies (sine waves) of 10 periods each

I took a simple case where the spectrum is flat , but it works too if you can give amplitude vs frequency

% "flat" amplitude spectrum sinus waves 
freqs = logspace(0,2,10); % from 1 to 100 Hz , log spaced values 
fs = 1000; % sampling rate (>> 100 Hz)
dt = 1/fs;
velocity_rms_amplitude = 0.78e-6; % 0.78 micro m /s 

% init some arrays
t_all = [];
displ_all = [];
t_shift = 0;
    
for ci = 1 : numel(freqs)
    f = freqs(ci);
    nb_periods = 10; 
    t = (0:dt:nb_periods/f)' + t_shift ;
    vel = velocity_rms_amplitude*cos(2*pi*f*(t-t_shift));
    displ = cumtrapz(t,vel); % velocity to displacement integration
    % concat all signals 
    t_end = t(end);
    t_all = [t_all; t];
    displ_all = [displ_all; displ];
    t_shift = t(end) + dt;
end



plot(t_all,displ_all)