Change Input Force to Input Displacement ODE Solver

I have the following ODE solution:
N = 100;
m = 0.1*ones(N,1);
c = 0.1;
b = 0.1;
k = 4;
gamma = 0.1;
X0 = zeros(2*N, 1);
dt = 0.91; % [s]
scale = 0.0049/2;
epsilon = 0.5; % [m]
escale = 10^-2;
rd = 1;
f = @(t,rd) rd.*scale.*square(t) + epsilon.*escale; % [N]
fun = @(t, X) odefun(t, rd, X, N, marray(m), make_diagonal(X,c,b,N),…
make_diagonal(X, k, gamma, N),f);
tspan_train = [0:dt:100];
[t, X] = ode45(fun, tspan_train, X0);
function dX = odefun(t, rd, X, N, M, C, K, f)
%% Definitions
x = X(1:N); % position state vector
dx = X(N+1:2*N); % velocity state vector
%% Force vector
f_reservoir = f(t,rd);
F = [f_reservoir; zeros(98,1); f_reservoir];
%% Equations of Motion
ddx = M(F – K*x – C*dx);

%% State-space model
dX = [dx; …
ddx];
end
function out = make_diagonal(x, k, gamma, N)
x = x(:);
x = [x(1:N); 0];
ck = circshift(k, -1);
cg = circshift(gamma, -1);
cx = circshift(x, -1);
ccx = circshift(x, 1);
d1 = -3 .* ck .* cg .* cx .^ 2 – ck;
d2 = (k .* gamma + ck .* cg) .* x .^ 2 + k + ck;
d3 = -3 .* k .* ccx .^ 2 – k;
out = full(spdiags([d1 d2 d3], -1:1, N, N));
end
function M = marray(m)
M = diag(m);
end
I would like to change my input force f in Newtons to an input displacement in meters. How do I do this?I have the following ODE solution:
N = 100;
m = 0.1*ones(N,1);
c = 0.1;
b = 0.1;
k = 4;
gamma = 0.1;
X0 = zeros(2*N, 1);
dt = 0.91; % [s]
scale = 0.0049/2;
epsilon = 0.5; % [m]
escale = 10^-2;
rd = 1;
f = @(t,rd) rd.*scale.*square(t) + epsilon.*escale; % [N]
fun = @(t, X) odefun(t, rd, X, N, marray(m), make_diagonal(X,c,b,N),…
make_diagonal(X, k, gamma, N),f);
tspan_train = [0:dt:100];
[t, X] = ode45(fun, tspan_train, X0);
function dX = odefun(t, rd, X, N, M, C, K, f)
%% Definitions
x = X(1:N); % position state vector
dx = X(N+1:2*N); % velocity state vector
%% Force vector
f_reservoir = f(t,rd);
F = [f_reservoir; zeros(98,1); f_reservoir];
%% Equations of Motion
ddx = M(F – K*x – C*dx);

%% State-space model
dX = [dx; …
ddx];
end
function out = make_diagonal(x, k, gamma, N)
x = x(:);
x = [x(1:N); 0];
ck = circshift(k, -1);
cg = circshift(gamma, -1);
cx = circshift(x, -1);
ccx = circshift(x, 1);
d1 = -3 .* ck .* cg .* cx .^ 2 – ck;
d2 = (k .* gamma + ck .* cg) .* x .^ 2 + k + ck;
d3 = -3 .* k .* ccx .^ 2 – k;
out = full(spdiags([d1 d2 d3], -1:1, N, N));
end
function M = marray(m)
M = diag(m);
end
I would like to change my input force f in Newtons to an input displacement in meters. How do I do this? I have the following ODE solution:
N = 100;
m = 0.1*ones(N,1);
c = 0.1;
b = 0.1;
k = 4;
gamma = 0.1;
X0 = zeros(2*N, 1);
dt = 0.91; % [s]
scale = 0.0049/2;
epsilon = 0.5; % [m]
escale = 10^-2;
rd = 1;
f = @(t,rd) rd.*scale.*square(t) + epsilon.*escale; % [N]
fun = @(t, X) odefun(t, rd, X, N, marray(m), make_diagonal(X,c,b,N),…
make_diagonal(X, k, gamma, N),f);
tspan_train = [0:dt:100];
[t, X] = ode45(fun, tspan_train, X0);
function dX = odefun(t, rd, X, N, M, C, K, f)
%% Definitions
x = X(1:N); % position state vector
dx = X(N+1:2*N); % velocity state vector
%% Force vector
f_reservoir = f(t,rd);
F = [f_reservoir; zeros(98,1); f_reservoir];
%% Equations of Motion
ddx = M(F – K*x – C*dx);

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