How can I make a graphical integration?

Hi guys I need help with graphical integration.

I have got data:

M = [82704 -107654 -151679 -36317 65017 149325 155528 26497 -47232 -30685 15002 88192 194927 226705 82704];

Angle = [0 15 30 60 90 120 150 180 210 240 270 300 330 345 360];

where M is moment of force [Nm] and Angle is angle of rotation [deg]

and I need to get graph of integration around value M=47535 Nm.

I have already solved numerical integration, but it is not enough for me. I need to get a graph of work [J] on y-axis and angle [deg] on x-axis with smooth curve.

I have tried to use cumtrapz but with nonsencial results.

Is here anybody who is able to help me?

Btw sorry for mistakes in English, not native.

I have already made this, but it is not working good...

M = [82704 -107654 -151679 -36317 65017 149325 155528 26497 -47232 -30685 15002 88192 194927 226705 82704];
Angle = [0 15 30 60 90 120 150 180 210 240 270 300 330 345 360];

figure
plot(Angle,M,'-*')
grid on
title('Moment')
xlabel('Angle[deg]')
ylabel('Moment[Nm]')

cmoment = cumtrapz(M);
M = table (Angle',cmoment','VariableNames',{'Angle','Work'})

plot(cmoment)
title('Work')

Answer 1

[darova]

What do you mean by "integration around value M = 47535". There several intersections:

a1 = linspace(min(A),max(A),100);    % mesh for angle
m1 = spline(A,M,a1);                 % moment values
plot(a1,cumtrapz(a1,m1))

[Karel Horký ml]

Hi,

it can be just a mistake of my misunderstanding the principle of graphical integration.What I found in my sources is: "Graphical integration - It determines the average (in this case M=47535) and the sizes of surfaces are rendered".

I am a bit confused about values of the moment (=x*10^5) and work (=x*10^7) because I have got some solved examples and there is work lower than moment everywhere, so I am going to try and find out...

Can I get a full script of a moment graph from U also please?

Thanks.

[darova]

Sure

I considered that work can be negative (minus sign)

[Karel Horký ml]

Thanks for the script.

There is no problem that work is negative. But I think there is a problem with dimension. The highest value of the moment is like Mmax = 2.26*10^5 Nm and the highest value of the work is about Amin = 1.5*10^7 J and it doesn't make sense for me. How i wrote before I have got some solved examples and there is Mmax = 120 Nm and Amax = 90 J in the first case and Mmax = 230Nm, Amax = -191J in the second case. So I am a bit worried and confused about these values with big difference...

[darova]

Try to convert units:

A = pi/180*A;        % angle in radians
M = 1E-3*M;          % moment in N*mm

    % average work/moment per RADIAN
J1 = trapz(A,M)/2/pi;        % original data integration
J2 = trapz(a1,m1)/2/pi;      % smoothed data integration

[Karel Horký ml]

When I use angle in radians it makes much more sense and the values seem also good.

I am still a bit uncertain about the end of the curve because I think that the values should fall down but not sure at all about that.

Anyway thank you for help. Helped me a lot.

[darova]

the moment at the end is with "+" sign. How the work can fall down?

Im going for Most Valuable Person

can you accept the question please?

[madhan ravi]

+1