i'm trying to evaluate a G11 symfun in the code below but it fails and keep showing me the variable t that I choose to be set as specified in the code, I even tried to use the 'subs' command but it failed also. I define the necessary symbols and variables but the t variable does not evaluated in just 'G11' symfun, there are another similar symfun such G12 or K12 but the t variable evaluated in them here is my code
% Defining the variables as symbols.
clear all, close all
clc
syms x xi q_1 q_2 q_3 q_4 q_01 q_02 q_03 q_04 EI Mr M m L t Omega S1 S2 S3
...
S4 S5 S6 S7 S8 w L_dot U U_dot g L_ddot M11 M22
% Defining the general coordinates and the trial function.
L_ddot=0;
g=9.8;
Mr=M/(M+m);
PHI(x,t)=[sqrt(2).* sin(pi.*(xi)) sqrt(2).* sin(2*pi.*(xi)) sqrt(2).*
sin(3.*pi.*(xi)) sqrt(2).* sin(4.*pi.*(xi))];
q_1(t)= S1*exp(sqrt(-1)*w*t);
q_01(t)= S5*exp(sqrt(-1)*w*t);
q_2(t)= S2*exp(sqrt(-1)*w*t);
q_02(t)= S6*exp(sqrt(-1)*w*t);
q_3(t)= S3*exp(sqrt(-1)*w*t);
q_03(t)= S7*exp(sqrt(-1)*w*t);
q_4(t)= S4*exp(sqrt(-1)*w*t);
q_04(t)= S8*exp(sqrt(-1)*w*t);
Q_v(t) =[q_1;q_2;q_3;q_4];
Q_w(t) =[q_01;q_02;q_03;q_04];
V(x,t) = PHI*Q_v(t);
W(x,t) = PHI*Q_w(t);
% Defining the coeficients of the ODE.
U(x,t)=U;
L(x,t)=1+0.1*t;
L_dot(x,t)=diff(L,'t',1);
L_ddot=0;
M11=int(PHI'*PHI,'xi',[0 1]);
M22=M11;
G11=(2*(L_dot/L))* int((2-xi)*PHI'*diff(PHI,'xi',1),'xi',[0 1])+2*Mr*
(U/L)*int(PHI'*diff(PHI,'xi',1),'xi',[0 1]);
G12=-2*Omega*int(PHI'*PHI,'xi',[0 1]);
G21=-G12;
G22=G11;
K11=(EI/((M+m)*L^4))*int(PHI'*diff(PHI,'xi',4),'xi',[0 1])+ (L_dot/L)^2
*int((2-xi)^2 *...
PHI'*diff(PHI,'xi',2),'xi',[0 1])+ ((L_ddot*L-2*L_dot^2)/L^2)*int((1-
xi)*PHI'*diff(PHI,'xi',1),'xi',[0 1]) ...
+ 2*Mr*(L_dot*U/L^2)*int((2-xi)*PHI'*diff(PHI,'xi',2),'xi',[0 1])+ Mr*
(U/L)^2 *int(PHI'*diff(PHI,'xi',2),'xi',[0 1])-...
(g-((L_ddot-2*L_dot^2)/L))*int((1-xi)*PHI'*diff(PHI,'xi',2),'xi',[0 1])+
(g/L)*int(PHI'*diff(PHI,'xi',1),'xi',[0 1])-...
Omega^2 * int(PHI'*PHI,'xi',[0 1]);
K12= -2*Omega*(L_dot/L)*int((2-xi)*PHI'*diff(PHI,'xi',1),'xi',[0 1])-2*Mr*
((U*Omega)/L)*int(PHI'*diff(PHI,'xi',1),'xi',[0 1]);
K21=-K12;
K22=K11;
% evaluating the Coefficient matrices for the time history 1 to 80 seconds
by the stepping of 0.1 .
t=0:0.1:80;
m=8;
M=2;
Mr=0.2;
x=1;
U=2; % the flow velocity
Omega=90;
EI=8.9782;
FUNM11 = matlabFunction(M11);
Mmatrix11 = feval(FUNM11);
FUNG11 = matlabFunction(G11);
Gmatrix11 = feval(FUNG11,t,U,Mr,L_dot,L);
FUNG12 = matlabFunction(G12);
Gmatrix12 = feval(FUNG12, t,x,Omega);
FUNK11 = matlabFunction(K11);
Kmatrix11 = feval(FUNK11, t,M,x,Omega,m,U,EI);
FUNK12 = matlabFunction(K12);
Kmatrix12 = feval(FUNK12, t,M,x,U,m,Omega);
Mmatrix22=Mmatrix11;
Gmatrix21=-Gmatrix12;
Gmatrix22=Gmatrix11;
Kmatrix21=-Kmatrix12;
Kmatrix22=Kmatrix11;
% Assembling the Coeficient matrices
Q=[Q_v;Q_w];
Mmatrix=[Mmatrix11 ,zeros(size(Mmatrix11)); zeros(size(Mmatrix11))
Mmatrix22];
Gmatrix=[Gmatrix11 Gmatrix12; Gmatrix21 Gmatrix22];
Kmatrix=[Kmatrix11 Kmatrix12; Kmatrix21 Kmatrix22];
After assembling my coefficient matrices I try to solve this algebric equation for w:
eqn=det(-w^2.*Mmatrix+i*w.*Gmatrix+Kmatrix)==0;
which w is the frequency of the system.