MATLAB: Change of surface in a rectangular tank

Question

I am plotting a change of surface in terms of beta

The thing is I see no change in the figure when I change the values of beta

Can you help me please

here is the code

clear

x=pi

x0=0.05;

omega=3;

beta0=0.1;

g=10;

z0=(1-(beta0*g)*omega^(-2))^0.5;

h=1;

b=4*(omega^(2))*x0*(g*pi)^(-1)

h=1;

g=10 ;

N=2;

syms t x z0

z0=0;

for n=0:N;

Z=((2*n+1)^(-2))*cos((2*n+1)*x)*cosh(z0*(2*n+1)*((cosh((2*n+1)*z0*h)-g*(2*n+1)*sinh((2*n+1)*z0*h)*(pi^(2)*z0)^(-1))^(-1)))*sin(t);

Zf=z0+Z;

end

Z=simplify(Zf);

Z1=subs(Z,x,pi);

t=0:0.02:20;

x=0:0.02:pi;

[T,X]=meshgrid (t,x);

for n=0:N;

Z=((2*n+1)^(-2))*cos((2*n+1).*X)*cosh(z0*(2*n+1)*((cosh((2*n+1)*z0*h)-g*(2*n+1)*sinh((2*n+1*z0)*h)*(pi^(2)*z0)^(-1))^(-1))).*sin(T);

Zf=z0+Z;

end

a=(omega^(2))*x0*(X-0.5*pi)*g^(-1);

Z=a.*sin(T)+b*Z;

mesh(T,X,Z)

grid on

title('evolution spaciotemporelle de la surface libre');

Answer 1

I suggest you to clarify your code. There are some errors i think

x=pi
x0=0.05;
omega=3;
beta0=0.1;
g=10;
z0=(1-(beta0*g)*omega^(-2))^0.5;
h=1;
b=4*(omega^(2))*x0*(g*pi)^(-1)
h=1;                    % again
g=10 ;                  % declaring the same variable
N=2;
syms t x z0             % declaring symbolic variable
                        % and re-write them?
    z0=0;               % re-write z0? It's symbolic
for n=0:N;
    Z=((2*n+1)^(-2))*cos((2*n+1)*x)*cosh(z0*(2*n+1)*((cosh((2*n+1)*z0*h)-g*(2*n+1)*sinh((2*n+1)*z0*h)*(pi^(2)*z0)^(-1))^(-1)))*sin(t);
    Zf=z0+Z;            % you mean Zf=Zf+Z ?
end
Z=simplify(Zf);
Z1=subs(Z,x,pi);        % substitute only x variable (t remains)
t=0:0.02:20;
x=0:0.02:pi;
[T,X]=meshgrid (t,x);
for n=0:N;
        % overwrite Z variable? Z has some value already
    Z=((2*n+1)^(-2))*cos((2*n+1).*X)*cosh(z0*(2*n+1)*((cosh((2*n+1)*z0*h)-g*(2*n+1)*sinh((2*n+1*z0)*h)*(pi^(2)*z0)^(-1))^(-1))).*sin(T);
    Zf=z0+Z;
end

Pay attention to warnings