# Accelerance FRF with modal FRF?

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Ricardo Néstor Aguilar on 2 Aug 2022
Hello, I'm trying to compute the accelerance FRF based on acceleration and modal hammer force signal.
I use the script of Manuel Lozano (script link) and the matlab modalFRF function, but I have diferences in magnitude and shape.
clc; clear; close all;
a = readtable ('aceleracion.csv').Var2; %Aceleration in [g]
f = readtable ('fuerza.csv').Var2; %Force in [N]
%% Using the code of https://la.mathworks.com/matlabcentral/answers/530968-what-s-wrong-with-my-frf
N = length(a); %length of signal
fs = 10000; %sampling frequency [Hz]
df = fs/N; %frequency resolution
fn = fs/2; %nyquist frequency
frequencies = linspace(0,fn,N/2+1);
Y = fft(a);
X = fft (f);
FRF = (Y./X); %Accelerance
Ymag = abs(FRF/N);
Ymag = Ymag(1:N/2+1);
Ymag(2:end-1) = 2*Ymag(2:end-1); % double magnitudes except c0
%% Using modalfrf function
winlen = size(a,1);
[FRF,f] = modalfrf(f, a, fs, winlen);
FRF = abs(FRF);
%% Plot
figure
plot(frequencies,Ymag, f, FRF)
set(gca,'YScale','log')
xlabel('frequency [Hz]')
ylabel('Magnitude [g/N]')
legend ('Using FFT', 'Using Matlab ModalFRF');
grid on I have also calculated the accelerance function using commercial software based on LabVIEW language. It can be seen that there is no coincidence either. Does anyone done this comparison? can someone tell me where is the error?

Paul on 2 Aug 2022
Edited: Paul on 2 Aug 2022
The two blue curves look pretty close, perhaps just off by a scale factor (except for the dip at ~600 Hz?). Those curves are the accelerance at least according to how Ymag is computed and the statement about what LabView computes. However, modalfrf always computes the receptance. So perhaps the output of modalfrf needs to be multplied by -omega^2 (omega in rad/sec) to get the accelerance? Worth a try anyway to see if that better aligns the curves.
Then still need to figure out the scale factor.. To sort that out, I think you'll really need to understand more precisely what LabView and modalfrf are really computing.

### More Answers (1)

Ricardo Néstor Aguilar on 2 Aug 2022
It seems that, changing Ymag = abs(FRF/N) by Ymag = abs(FRF), removing Ymag(2:end-1) = 2*Ymag(2:end-1); and adding Ymag = Ymag./(2*pi*frequencies').^2; the curve fit to the output of modalFRF.
clc; clear; close all;
a = readtable ('aceleracion.csv').Var2; %Aceleration in [g]
f = readtable ('fuerza.csv').Var2; %Force in [N]
%% Using the code of https://la.mathworks.com/matlabcentral/answers/530968-what-s-wrong-with-my-frf
N = length(a); %length of signal
fs = 10000; %sampling frequency [Hz]
df = fs/N; %frequency resolution
fn = fs/2; %nyquist frequency
frequencies = linspace(0,fn,N/2+1);
Y = fft(a);
X = fft (f);
FRF = (Y./X); %Accelerance
Ymag = abs(FRF);
Ymag = Ymag(1:N/2+1);
Ymag = Ymag./(2*pi*frequencies').^2;
%% Using modalfrf function
winlen = size(a,1);
[FRF,frec] = modalfrf(f, a, fs, winlen,'Sensor','acc');
FRF = abs(FRF);
%% Plot
figure
plot(frequencies,Ymag, frec, FRF,'-.')
set(gca,'YScale','log')
xlabel('frequency [Hz]')
ylabel('Magnitude [g/N]')
legend ('Using FFT', 'Using Matlab ModalFRF');
grid on ##### 2 CommentsShowHide 1 older comment
Ricardo Néstor Aguilar on 2 Aug 2022
Thanks for your help!

R2020a

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