I need to to solve this coupled ODEs. I have written the code but not really getting any output. Any help would be appreciated!

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Jayanth Palat 2021-6-10

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评论： Jayanth Palat 2021-6-12

在 MATLAB Online 中打开

function [time, x, xdot, y] = bluff
meff = 0.0114; %Effective mass (kg)
ceff = 0.0212; %Effective damping (N/(m/s))
keff = 8.86;   %Effective stiffnes (N/m)
thet = 0.000019758; %Electromechanical coefficient (N/V)
Cp = 0.0000000157; %Capacitance
rho = 1.225; %air density (kg/m3)
u = 10; %wind velocity(m/s)
stip = 0.0118; %exposed area of the bluff body(m2)
L = 0.15 ; %length of the beam
a1 = 2.3;  %empirical coefficient for the aerodynamic force calculation
R = 1050000; %load resistance (ohm)
%values
x0 = 1; xdot0 = 0; y0 = 1;
t0 = 0; tf = 60;
%Time span
tspan = [t0, tf];
%initial conditions
IC = [x0, xdot0,y0];
% [sdot] = g(t,s)
sdot = @(t, s) [s(2);
    (-ceff*s(2) - keff*s(1) - thet*s(3) + 0.5*rho*stip*(a1*((s(2)/u)+(1.5*s(1)/L))*u^2))/meff;
    thet*s(2)/Cp - s(3)/(R*Cp)];
%Call ode45 solver
[time, state_values] = ode45(sdot,tspan,IC);
%Extract individual values
x = state_values(:,1);
xdot = state_values(:,2);
y = state_values(:,3);
%plot x(t) and y(t)
figure(1)
clf
plot(time,x), title('Displacement'), xlabel('time(s)'), ylabel('displacement(m)')
figure(2)
clf
plot(time,y), title ('Voltage generation'), xlabel('time(s)'), ylabel('Output voltage(V)')
end

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Jayanth Palat 2021-6-11

编辑：Walter Roberson 2021-6-11

在 MATLAB Online 中打开

So how do I change the code to get the required output?

function [time, w, wdot, v] = bluff
meff = 0.0114; %Effective mass (kg)
ceff = 0.0212; %Effective damping (N/(m/s))
keff = 8.86;   %Effective stiffnes (N/m)
thet = 0.000019758; %Electromechanical coefficient (N/V)
Cp = 0.0000000157; %Capacitance
rho =1.225 ; %air density (kg/m3)
u = 10; %wind velocity(m/s)
stip = 0.0118; %exposed area of the bluff body(m2)
L = 0.15 ; %length of the beam
a1 = 2.3; a3 = -18 ; %empirical coefficient for the aerodynamic force calculation
R = 1050000; %load resistance (ohm)
q = R*Cp ;
%values
x0 = 0; xdot0 = 0; y0 = 0;
t0 = 0; tf = 60;
%Time span
tspan = [t0, tf];
%initial conditions
IC = [x0, xdot0,y0];
% [sdot] = g(t,s)
sdot = @(t, s) [s(2);
    -ceff*s(2)/meff - keff*s(1)/meff - thet*s(3)/meff + 0.5*rho*stip*u*u*(a1*((s(2)/u)+(1.5*s(1)/L))+a3*((s(2)/u)+(1.5*s(1)/L))^3)/meff ;
    thet*s(2)/Cp - s(3)/q];
%Call ode45 solver
[time, state_values] = ode45(sdot,tspan,IC);
%Extract individual values
w = state_values(:,1);
wdot = state_values(:,2);
v = state_values(:,3);
%plot x(t) and y(t)
figure(1)
clf
plot(time,w), title('Displacement'), xlabel('time(s)'), ylabel('displacement(m)')
figure(2)
clf
plot(time,v), title ('Voltage generation'), xlabel('time(s)'), ylabel('Output voltage(V)')
end

Walter Roberson 2021-6-11

You divide by Cp but Cp is about Pi / 2e8 . When you divide by that, values are magnified a lot.

You might have better success if y0 were a lot smaller.

Jayanth Palat 2021-6-12

y0?

Walter, y0 = 0. Thats the initial condition.

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回答（1 个）

Lewis Fer 2021-6-11

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Hello, I am having troubles solving a system of second order nonlinear equations with boundary conditions using MATALB

Here is the equations:

f''(t)=3*f(t)*g(t) -g(t)+5*t;

g''(t)=-4f(t)*g(t)+f(t)-7*t;

the boundary conditions are: f'(0)=0 et h'(o)=5;

g(0)=3 et h'(2)=h(2)

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Lewis Fer 2021-6-11

I have post my question in this pub, but there is no answer

https://www.mathworks.com/matlabcentral/answers/853120-how-to-solve-a-system-of-second-order-nonlinear-differential-equations-with-boundary-conditions?s_tid=srchtitle#add_answer

Lewis Fer 2021-6-11