I need help with The logarithmic decrement, The undamped natural frequency ,The damped natural frequency ,The damping ratio please

G03.csv file is an excle file which is attach bellow that file contains the vibration measurement data and the corresponding time (from an initial time seconds) when each measurement data was taken.

Use Matlab software to determine the following from the given data:

1. The logarithmic decrement
2. The undamped natural frequency
3. The damped natural frequency
4. The damping ratio

please i need your help. i have tried to do the coding but its not working could you please have a look into it, the code as follow :

clc
clear all
close all
load G03.mat
z=importdata('G03.mat'); 
Veloc = G03.VarName2;
Time = G03.VarName1;
Time = z(:,1);  
Veloc = z(:,2);  
n_peaks=351;  
%Vector length of interest 
t_new = Time(imax(1:n_peaks));  
y_new = ymax(1:n_peaks);  
t_new(1)=[];%Remove first point - Due to impact  
y_new(1)=[];   
%---Calculate Logarithmic Decrement,  undamped natural frequency, damped natural frequency, damping ratio
Log_Dec = zeros(length(n_peaks));  
for nn = 1:n_peaks-2 %We go to '-2' because length(n_peaks) = since we ignore first one
    Log_Dec(nn)= log(y_new(nn)/y_new(nn+1));  
end  
Mean_dec = mean(Log_Dec); %Calculate Average Logarithmic Decrement  
%Damping  
damp_ratio_logdec = 1/sqrt(1+((2*pi/(Mean_dec))^2)); %Assesses Damping Constant 

Answer 1

[Mathieu NOE]

hello

this would be my suggestion - damping ratio of 0.4 is found coherent with the fast decay

plot will show the two successive peaks (using findpeaks) - that's why the computation of the log decrement is also performed with only one period distance between peaks (and there will be indeed no averaging as we have here only two peaks)

code :

clc
clear all
close all
z = csvread('G03.csv');

Time = z(:,1);  
Veloc = z(:,2);  

[Ypk,Xpk,Wpk,Ppk] = findpeaks(Veloc);
plot(Time,Veloc,Time(Xpk),Ypk,'dr');
n_peaks=numel(Xpk);  

%Vector length of interest 
t_new = Time(Xpk);  
y_new = Ypk;  
%---Calculate Logarithmic Decrement,  undamped natural frequency, damped natural frequency, damping ratio
Log_Dec = zeros(length(n_peaks));  
for nn = 1:n_peaks-1 %
    Log_Dec(nn)= log(y_new(nn)/y_new(nn+1));  % computed with n = 1 periods apart
end  
Mean_dec = mean(Log_Dec); %Calculate Average Logarithmic Decrement  
%Damping  
damp_ratio_logdec = 1/sqrt(1+((2*pi/(Mean_dec))^2)); %Assesses Damping Constant