2DOF (ODE) response in MATLAB
17 ビュー (過去 30 日間)
古いコメントを表示
Im trying to find the response to the 2DOF for the following system, ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/283820/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/283820/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/283821/image.png)
initial conditions:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/283822/image.png)
with the the following force applied to m2
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/283823/image.png)
I obtained the eqm, and tried to solve the ODE's using dsolove however the code doesnt work, Im not sure if this is because of wrong equation of motion, or Im taking the wrong approach. Also im wondering how to implement lsim command to solve this problem. I would appriciate the help. Thanks very much!
% finding force
F0=5;
T=1;
t=0:0.01:1;
F1=-F0*(t/T)+F0;
plot(t,F1)
hold on
t2=1:0.01:2
F2=F0*(t2/T)-F0;
plot(t2,F2)
hold on
t3=3:0.01:10
F3=F0;
F2=[F1,F2,F3];
hold off
% solving problem
syms x1(t) x2(t) F1 F2
m1=1;m2=2;c1=0;c2=0;k1=4;k2=4;k0=0.5;F1=F1;F2=F3;
eq1=F2==m2*(diff(x2,2)-diff(x1,2))+c2*(diff(x2,1)-diff(x1,1))+k2*(x2-x1);
eq2=F1==m1*diff(x1,2)+c1*diff(x1,1)+k1*x1;
Dx1=diff(x1);Dx2=diff(x2);
[X1(t),X2(t)]=dsolve([eq1 eq2],[x1(0)==0,Dx1(0)==0,x2(0)==0,Dx2(0)==0]);
t1=0:0.01:10;
Force=F2;
x1=subs(X2(t),{t,F2,F1},{t1,Force,0})
plot(t,X2(t));legend('X1(t)','X2(t)')
0 件のコメント
回答 (1 件)
Ameer Hamza
2020 年 4 月 12 日
編集済み: Ameer Hamza
2020 年 4 月 12 日
In MATLAB, ode45 solver can be used to solve such equations numerically. Since you are solving these equations symbolically, the following correct the error in your code
% finding force
F0=5;
T=1;
t=0:0.01:1;
F1=-F0*(t/T)+F0;
plot(t,F1)
hold on
t2=1:0.01:2
F2=F0*(t2/T)-F0;
plot(t2,F2)
hold on
t3=3:0.01:10;
F3=F0;
F2=[F1,F2,F3];
hold off
% solving problem
syms x1(t) x2(t) F1 F2
m1=1;m2=2;c1=0;c2=0;k1=4;k2=4;k0=0.5;F1=F1;F2=F3;
eq1=F2==m2*(diff(x2,2)-diff(x1,2))+c2*(diff(x2,1)-diff(x1,1))+k2*(x2-x1);
eq2=F1==m1*diff(x1,2)+c1*diff(x1,1)+k1*x1;
Dx1=diff(x1);Dx2=diff(x2);
[X1(t),X2(t)]=dsolve([eq1 eq2],[x1(0)==0,Dx1(0)==0,x2(0)==0,Dx2(0)==0]);
t1=0:0.01:10;
Force=F2;
x1(t)=subs(X2(t),{t,F2,F1},{t1,Force,0});
x2(t)=subs(X2(t),{t,F2,F1},{t1,Force,0});
plot(t1,x1(t), t1,x2(t));legend('X1(t)','X2(t)')
But the two variables x1, and x2 overlap. I am not sure if this is correct solution. If you can give the mathematical form of your equations, I can see if your equations are correctly implemented.
6 件のコメント
Ameer Hamza
2020 年 4 月 15 日
Glad to be of help. If you can apply ode45, then you already have knowledge about the state-space representation of your system of ODE.
参考
カテゴリ
Help Center および File Exchange で Ordinary Differential Equations についてさらに検索
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!