ODE45 for nonlinear problem

2020 6 14
1 个回答
更新时间：2020 7 22
2 次查看（30 天）

0 个投票

kindly check the below code....

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madhan ravi
madhan ravi 2020-6-14
Could you post the equation in LaTeX form?
chiyaan chandan
chiyaan chandan 2020-6-27
function code1_verification
t=0:0.05:50; % time scale
k1=100;
k2=50;
c1=0.2;
c2=0.4;
m1=10;
m2=20;
f1=@(t)(195*sin(t/2))/2 - 100*sin((4*t)/5)^3 + (5*cos(t/2) - 8*cos((4*t)/5))^3/5000;
f2=@(t)(8*cos((4*t)/5))/25 - 100*sin(t/2) - (16*sin((4*t)/5))/5 + 150*sin((4*t)/5)^3 - (5*cos(t/2) - 8*cos((4*t)/5))^3/5000;
[t,x]=ode45( @rhs, t, [0,0,0.5,0.8] );
function dxdt=rhs(t,x)
dxdt_1 = x(2);
dxdt_2 = (f1(t)-c1*(x(2)-x(4)).^3-k1*(x(1)-x(3).^3))/m1;
dxdt_3 = x(4);
dxdt_4 = (f2(t)+c1*(x(2)-x(4)).^3 + k1*(x(1)-x(3).^3)+ k2*x(3).^3 - c2*x(4))/m2;
dxdt=[dxdt_1; dxdt_2;dxdt_3;dxdt_4];
end
clf
subplot(211),plot(t,x(:,1));
legend('displacement')
hold on
subplot(212),plot(t,x(:,2));
legend('velocity')
xlabel('t'); ylabel('x');
end
--------------------------------------------------------------------------------------------------------------------------
i am not getting displacement and velocity profiles as sin(w*t) and w*cos(w*t) form respectively.
procedure
Two equations of motions are
m1*a1+c1*(v1-v2)^3+k1*(x1-x2^3)=f1..........(1)
m2*a2-c1*(v1-v2)^3-k1*(x1-x2^3)+k2*x2^3+c2*v2=f2..........(2)
i have considered
k1=100; k2=50; c1=0.2; c2=0.4; m1=10; m2=20;
displacement x1=sin(0.5*t)
velocity v1=0.5*cos(0.5*t)
Acceleration a1 =-0.5^2*sin(0.5*t);
displacement x2=sin(0.8*t)
velocity v2=0.8*cos(0.8*t)
Acceleration a2 = - 0.8^2*sin(0.8*t);
subtituted x1,v1,a1,x2,v2,a2 in above equation (1) and (2)
f1= (195*sin(t/2))/2 - 100*sin((4*t)/5)^3 + (5*cos(t/2) - 8*cos((4*t)/5))^3/5000
f2=8*cos((4*t)/5))/25 - 100*sin(t/2) - (16*sin((4*t)/5))/5 + 150*sin((4*t)/5)^3 - (5*cos(t/2)

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回答（1 个）

darova
darova 2020-6-14

0 个投票

  • avoid global. YOu can make nested function in your case
function linear_vs_nonlinear
% variables
% code
function SD_L=linear(t,s)
% code
end
end
  • you have 4 equations, but only 2 initial conditions
  • some operators are forgotten (multiplier i think)

6 个评论
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chiyaan chandan
chiyaan chandan 2020-6-27
编辑：darova 2020-6-28
function code1_verification
t=0:0.05:50; % time scale
k1=100;
k2=50;
c1=0.2;
c2=0.4;
m1=10;
m2=20;
f1=@(t)(195*sin(t/2))/2 - 100*sin((4*t)/5)^3 + (5*cos(t/2) - 8*cos((4*t)/5))^3/5000;
f2=@(t)(8*cos((4*t)/5))/25 - 100*sin(t/2) - (16*sin((4*t)/5))/5 + 150*sin((4*t)/5)^3 - (5*cos(t/2) - 8*cos((4*t)/5))^3/5000;
[t,x]=ode45( @rhs, t, [0,0,0.5,0.8] );
function dxdt=rhs(t,x)
dxdt_1 = x(2);
dxdt_2 = (f1(t)-c1*(x(2)-x(4)).^3-k1*(x(1)-x(3).^3))/m1;
dxdt_3 = x(4);
dxdt_4 = (f2(t)+c1*(x(2)-x(4)).^3 + k1*(x(1)-x(3).^3)+ k2*x(3).^3 - c2*x(4))/m2;
dxdt=[dxdt_1; dxdt_2;dxdt_3;dxdt_4];
end
clf
subplot(211),plot(t,x(:,1));
legend('displacement')
hold on
subplot(212),plot(t,x(:,2));
legend('velocity')
xlabel('t'); ylabel('x');
end
--------------------------------------------------------------------------------------------------------------------------
i am not getting displacement and velocity profiles as sin(w*t) and w*cos(w*t) form respectively.
procedure
Two equations of motions are
m1*a1+c1*(v1-v2)^3+k1*(x1-x2^3)=f1..........(1)
m2*a2-c1*(v1-v2)^3-k1*(x1-x2^3)+k2*x2^3+c2*v2=f2..........(2)
i have considered
k1=100; k2=50; c1=0.2; c2=0.4; m1=10; m2=20;
displacement x1=sin(0.5*t)
velocity v1=0.5*cos(0.5*t)
Acceleration a1 =-0.5^2*sin(0.5*t);
displacement x2=sin(0.8*t)
velocity v2=0.8*cos(0.8*t)
Acceleration a2 = - 0.8^2*sin(0.8*t);
subtituted x1,v1,a1,x2,v2,a2 in above equation (1) and (2)
f1= (195*sin(t/2))/2 - 100*sin((4*t)/5)^3 + (5*cos(t/2) - 8*cos((4*t)/5))^3/5000
f2=8*cos((4*t)/5))/25 - 100*sin(t/2) - (16*sin((4*t)/5))/5 + 150*sin((4*t)/5)^3 - (5*cos(t/2)
darova
darova 2020-6-28
The code looks correct. I think you formulas are strange. Why displacement and velocity are in power 3?
I didn't understand what if f? Where is expression for it and why did you substituted x,v and a?
chiyaan chandan
chiyaan chandan 2020-6-28
f1 and f2 are the forcing terms.
i calculated f1 and f2 by substituting know displacement, velocity and acceleration terms. so that i can verify my dispalcement plot esily with sin(w*t), velocity with w*cos(w*t) and acceleration with -w^2*sin(w*t).
darova
darova 2020-6-29
How do you know that ? Usually and are uknowns if you have ODE. and should be given
chiyaan chandan
chiyaan chandan 2020-7-22
To verify the results i assumed x1=sin(w1t), x2=sin(w2*t). Once the displcement, velocity and accelerations are obtained from the calculation. then that plot should show the sin(w1*t) form for diplacement, w1*cos(w1*t) for velocity. and -w1^2*sin(w1*t) for acceleration similarly for second system same form will be repeated by taking w2 value.
for this problem f1 and f2 are forcing terms are the time series input (acceleration vs time ) .before giving the that inputs. i need to check the results by appying the know forces. once it gives that as a output then i can go for the next step.

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