How to solve the coupled second order differential equations by using "ODE45"?

Hello,

I try to solve the coupled second order differential equations with ODE45.

But my answer was weird.

My system is two defree of freedom system including spring and damper.

So, the equations are

m1*x1'' + (c1+c2)*x1' + (k1+k2)*x1 - c2*x2' - k2*x2 = 0;

m2*x2'' + x2*x2' + k2*x2 - c2*x1' - k2*x1 = F(t);

And I changed the above equations,

x1'' = v1' = ...

x2'' = v2' = ...

Here are my code..

% mx1'' = -(k1+k2)x1 - (c1+c2)x1' + k2 x2 + c2 x2' 
% mx2'' = -k2 x2 - c2 x2' + k2 x1 + c2 x1' + F

tspan = linspace(0,10*pi,2000);
h = tspan(2) - tspan(1);

xini = [0; 0; 0; 0];

[t,x] = ode45(@T2_func, tspan, xini);

------ Function ------
function dxdt = T2_func(t,x)

%%Constants
m1 = 1;   % [kg]
m2 = 1;   % [kg]

k1 = 10;  % [N/m]
k2 = 10;  % [N/m]

c1 = 1;   % [Ns/m]
c2 = 1;   % [Ns/m]

%%Force
p = 10 * ones(1,length(t));   % [N]

%%Matrix
F = zeros(2, length(t));
F(2,:) = p/m2;

K11 = -(k1+k2)/m1;
K12 = k2/m1;
K21 = -k2/m2;
K22 = k2/m2;
Kmat = [K11 K12; K21 K22];

C11 = -(c1+c2)/m1;
C12 = c2/m1;
C21 = -c2/m2;
C22 = c2/m2;
Cmat = [C11 C12; C21 C22];

%%Function
dxdt = zeros(4,1);
dxdt(1) = x(2);
dxdt(2) = - Kmat(1,1)*x(1) - Cmat(1,1)*x(2) + Kmat(1,2)*x(3) + Cmat(1,2)*x(4) + F(1);
dxdt(3) = x(4);
dxdt(4) = - Kmat(2,1)*x(3) - Cmat(2,1)*x(4) + Kmat(2,2)*x(1) + Cmat(2,2)*x(2) + F(2);

Thank you.

Answer 1

[Torsten]

You already included the correct signs of the coefficients in the definition of Kmat and Cmat. Thus all terms in dxdt(2) and dxdt(4) must have a "+" sign.

Furthermore, in your original set of equations, K11 = -k1/m1 instead of K11 = -(k1+k2)/m1.

Additionally, t in T2_func will always be a scalar. Thus

%%Force
p = 10 ;   % [N]

%%Matrix
F(1) = 0; 
F(2) = p/m2;

Best wishes

Torsten.

[HYEOKJUNE LEE]

Thanks for answer,

You mentioned, K- matrix. And that is my fault.. so I modified my script, and plus I also modified C- matrix.

And, through your answer, my code be working correctly. Thank you very much.

[HYEOKJUNE LEE]

Torsten, I have more question. When the force is related with the time, then how can I make a code?

You mentioned, "time" in a function scription must be scalar. But the force term could be dependent with the time.

How could I handle this problem?

Best regardes, Lee.