How to solve nonlinear equation?

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GUANGHE HUO
GUANGHE HUO il 20 Dic 2022
Commentato: GUANGHE HUO il 23 Dic 2022

Risposta accettata

Sam Chak
Sam Chak il 21 Dic 2022
The nonlinear matrix ODE with time-varying stiffness matrix K can be transformed into a nonlinear state-space model. See example below.
tspan = [0 40];
x0 = [1 0.5 0 0];
[t, x] = ode45(@odefcn, tspan, x0);
plot(t, x), grid on, xlabel('t')
function xdot = odefcn(t, x)
xdot = zeros(4, 1);
M = diag([3 5]);
C = 2*eye(2);
K = [1+0.5*sin(2*pi/40*t) 0; 0 1+0.5*sin(2*pi/40*t)]; % time-varying K
A = [zeros(2) eye(2); -M\K -M\C];
B = [zeros(2); eye(2)];
F = [0; 0]; % Requires your input
u = M\F;
xdot = A*x + B*u;
end
  4 Commenti
Sam Chak
Sam Chak il 23 Dic 2022
I use ordinary numeric array in my simulations. Perhaps you can try using the cell2mat() command to convert the selected cell array into the desired numeric array.
If your Force vector and the Stiffness matrix are time series data (cannot be expressed in any fundamental mathematical form), then you need to use the interp1() function to interpolate and to obtain the value of the time-dependent terms at the specified time.
Here is an example of using a data-driven Force to stabilize the Double Integrator system:
% Force data set recorded over some intervals of time
ft = linspace(0, 20, 2001);
f = 2*exp(-ft).*ft - exp(-ft).*(1 + ft); % made-up to generate the data
tspan = [0 20];
y0 = [1 0];
opts = odeset('RelTol', 1e-4, 'AbsTol', 1e-8);
[t, y] = ode45(@(t, y) doubleInt(t, y, ft, f), tspan, y0, opts);
plot(t, y), grid on, xlabel('t'), ylabel('Y(t)')
legend('y_{1}(t)', 'y_{2}(t)')
% Double Integrator system
function dydt = doubleInt(t, y, ft, f)
dydt = zeros(2, 1);
f = interp1(ft, f, t); % Interpolate the data set (ft, f) at time t
dydt(1) = y(2);
dydt(2) = f;
end
GUANGHE HUO
GUANGHE HUO il 23 Dic 2022
Thanks for your help.@Sam Chak, You give me a lot of help, because i am new for MATLAB

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Più risposte (1)

Torsten
Torsten il 20 Dic 2022
Write as
xdot = y
ydot = inv(M)*(F-c*y-K*x)
and use ode45 to solve.

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