Hi Jasem,
To develop MATLAB code for the instantaneous integration of dissipated energy in a viscous damper, you can refer the following code. The below sample MATLAB code assumes an example position data (x = sin(t)) and an example value for the damping coefficient ‘c’.
% Define parameters
C = 0.5; % Damping coefficient (example value)
t = linspace(0, 10, 1000); % Time vector from 0 to 10 seconds
X = sin(t); % Example position data (replace with your actual data)
% Calculate velocity (dX/dt)
dX_dt = gradient(X, t); % Numerical differentiation to get velocity
% Calculate the dissipated energy
W = zeros(size(t)); % Initialize energy array
for i = 1:length(t)
if i > 1
W(i) = trapz(t(1:i), (C * dX_dt(1:i)).^2); % Integrate using trapezoidal rule
end
end
Adjust the damping coefficient (‘c’) and the position data (‘x’) as required. The ‘gradient’ function computes the derivate of the position data with time to obtain the velocity. The ‘trapz’ function then performs numerical integration using the trapezoidal rule, accumulating energy over time. If you have specific time intervals ‘t_1’ and ‘t_2’ , you can adjust the integration limits accordingly. For more information about the functions used, refer the following documentations:
