How Do You Solve a 2nd Order ODE Using Matlab?

[amir99civil]

Dear All,

I have a Problem about a 2nd order ode. I don't know how it can be solved with Matlab. If someone know about it then please let me know. I need to get the values of x & y. All other values are known.

The equation is:

[ M + mf mf
mf mf ][ ¨x
¨y ]+
[ C 0
0 cf ][ x˙
y˙ ]+[ K 0
0 kf][ x
y ] = [ Fe(t)
0 ]

Thanks a lot

 

[Data]

you are going to have to make the equation more clear. What are all the 0s? Try to put it up in tex.

 

[Mute]

I think this is how it's supposed to look:
$$\left(<br /> \begin{array}{cc}<br /> M + m_f & m_f \\<br /> m_f & m_f<br /> \end{array}<br /> \right)<br /> \left(<br /> \begin{array}{cc}<br /> \ddot{x} \\<br /> \ddot{y}<br /> \end{array}<br /> \right) +<br /> \left(<br /> \begin{array}{cc}<br /> C & 0 \\<br /> 0 & c_f<br /> \end{array}<br /> \right)<br /> \left(<br /> \begin{array}{cc}<br /> x\\<br /> y<br /> \end{array}<br /> \right) +<br /> \left(<br /> \begin{array}{cc}<br /> K & 0 \\<br /> 0 & k_f<br /> \end{array}<br /> \right) =<br /> \left(<br /> \begin{array}{cc}<br /> F_{e}(t)\\<br /> 0<br /> \end{array}<br /> \right)$$

I don't know how to use MATLAB to solve it, though.

 

[J77]

There should be an $$\dot{x}$$ after the damping terms (c's) and an $$x$$ after the stiffness terms (k's)...

For the simulation, first write it in first-order form.

It's quite simple to solve this forced msk system as an IVP in Matlab, check the help files on odes...

 

[amir99civil]

yes. This is an equation of motion for a Tuned Liquid Column Damper with (xdot & ydot) after damping terms and (x & y) after the stiffness matrix.I don't know how i can handle the matrics if i change it to first order. If you know something then please explain a little more about the problem. How to handle the matrics to get a first order system.

The zeros 0s are 0.There is no entry where there is zero.

 

[J77]

Write:

$$u=\dot{x}$$ and $$v=\dot{y}$$

then...

$$\dot{u}=\ddot{x}$$ and $$\dot{v}=\ddot{y}$$

ie. you now have 4 first-order equations.