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

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Emadaddin Abdo Mohammed  Alazzani
Answered: Mathieu NOE on 1 Dec 2021
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

Answers (1)

Mathieu NOE
Mathieu NOE on 1 Dec 2021
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

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