How to calculate the damping ratio of beat time?

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Yijing LU 2023-4-25

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https://ww2.mathworks.cn/matlabcentral/answers/1952754-how-to-calculate-the-damping-ratio-of-beat-time

T12.xlsx

I applied an initial displacement to the top of the structure, but found that the result showed the phenomenon of beating vibration. The data collected were as follows. How to calculate the damping ratio of the structure with such data? The function I used calculated an envelope that was not what I wanted, and the envelope I wanted to fit is shown in Figure 2.

% Set the Excel file path and file name to read
filename = 'C:\Users\user\Desktop\FJTJ\半功率法求解阻尼比\T12.xlsx';
% Read data in Excel files
Data = xlsread(filename);
dt=(Data(5,1)-Data(2,1))/3 % Time step of the sample
fs=1/dt  % Sampling frequency
t = Data(:,1);
Signal = Data(:,2);
plot(t,Signal)
% The ceil function is rounded up and rounded up
samples=ceil(120/dt); 
t_use = t(2001:samples);
Signal_use = Signal(2001:samples);
% Calculate the envelope
env = abs(hilbert(Signal_use)); 
plot(t_use, Signal_use, 'b'); hold on;
plot(t_use, env, 'r', 'LineWidth', 2);
xlabel('Time (s)');
ylabel('Amplitude');
legend('Signal', 'Envelope');