Duhamel's Integral with conv

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James Browne 2022-2-26

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https://ww2.mathworks.cn/matlabcentral/answers/1658885-duhamel-s-integral-with-conv

编辑： Walter Roberson 2022-2-27

duhammel_formula.jpg

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Hi,

Following on from this question ( https://au.mathworks.com/matlabcentral/answers/392931-duhamel-s-integral-in-matlab?s_tid=srchtitle )

I am also having some problems solving duhammels integral using the conv funciton. I am comparing the results with a simulink spring damper system to try and get correlation.

I am trying to solve the equation attached from "structual dynamics, theory and applications" by Tedesco et al.

I have tried to start very simple with a constant force.

f_ext = 100000; %N
%% System details
m = 400;                %kg
k = 100000;          %n/m
nf = sqrt(k/m);  % = 15.8114 rad/s

I am using a time of 5 seconds with dt = 0.001;

t = [0:dt:5]

i tried using:

h = sin(nf*t); 
f_duhammel = ones(length(t),1)*f_ext; %this is just creating a force vector that is constant for time
convolution  = conv(f_duhammel,h,"same");
duhammel = 1/(m*omega)*convolution;
figure()
plot(duhammel)

however the plot doesn't look like my simple simulink model.

later in my text book they show for a constant force

x = (f_ext/k)*(1-cos(omega*t));

This matched the dispalcement from my simulink model, so I know my issue is with the convel fucntion in matlab rather than something I am doing incorrectly in simulink.

If anyone has done this before in matlab, are they able to assist me?

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Torsten 2022-2-26

Then why do you use conv ?

Use trapz instead.

James Browne 2022-2-27

Because I specifically wanted to undertand how the conv fuction works and use it in matlab. I already have a numerical method in a simulink model, so I can solve the problem that way.

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