Can anybody help me in simplifying the final solution of 'y' in terms of variable? It can be easily solve by hand and we can get values as a factor of '(1/l)*sqrt(T/rho)'.

clc;
clear all;
close all;

syms T h l rho F1 F2 omega
mem=4 %number of elements
h=l/mem
%element k matrix
k=h\T*[1 -1;-1 1];
m=(rho*h/6)*[2 1;1 2]

% assembling global matrix
tightwire=importdata('TightWire.xlsx');
S=zeros(mem+1,'sym');
M=zeros(mem+1,'sym');
U=sym('U%d',[mem+1 1])
F=sym('F%d',[mem+1 1])
for t=2:mem
F(t)=tightwire(mem,t);
end

%elementnumbering
nod=[1:1:mem+1];
c=cell(mem,1);
for t=1:mem
    c{t,1}=[nod(t) nod(t)+1];
end

for r=1:mem
    l=c{r};
    for i=1:mem+1
        for j=1:mem+1
            for o=1:2
                for p=1:2
                    if i==l(o)
                        if j==l(p)
                            S(i,j)=S(i,j)+k(o,p);
                            M(i,j)=M(i,j)+m(o,p);
                        end
                    end
                end
            end
        end
    end
end

determinant=S(2:mem,2:mem)-omega^2*M(2:mem,2:mem)
y=solve(det(determinant),omega)

Answer 1

[Walter Roberson]

Change

syms T h l rho F1 F2 omega

to

syms T h l rho F1 F2 omega real

Change

y=solve(det(determinant),omega)

to

y = simplify(solve(det(determinant),omega))

[Prateek jain]

Thanks it helps but still it is giving weird roots. What I can do if I need values in decimals? Other than this I want to know two more things. First, when I am using mem=8 there is a constant 'z' is coming in the solution what is the value of that z? Second, how to resolve the warning 'Specify the return condition option.'

[Walter Roberson]

You are probably hoping for something more like this:

%clc;
%clear all;
close all;

syms omega real
syms L rho T positive
mem=8 %number of elements
h=L/mem;
%element k matrix
k=h\T*[1 -1;-1 1];
m=(rho*h/6)*[2 1;1 2]

% assembling global matrix
%tightwire=importdata('TightWire.xlsx');
tightwire = zeros(mem, mem);
S=zeros(mem+1,'sym');
M=zeros(mem+1,'sym');
U=sym('U%d',[mem+1 1]);
F=sym('F%d',[mem+1 1]);
for t=2:mem
F(t)=tightwire(mem,t);
end

%elementnumbering
nod=1:1:mem+1;
c=cell(mem,1);
for t=1:mem
    c{t,1}=[nod(t) nod(t)+1];
end

for r=1:mem
    l=c{r};
    for i=1:mem+1
        for j=1:mem+1
            for o=1:2
                for p=1:2
                    if i==l(o)
                        if j==l(p)
                            S(i,j)=S(i,j)+k(o,p);
                            M(i,j)=M(i,j)+m(o,p);
                        end
                    end
                end
            end
        end
    end
end

determinant=S(2:mem,2:mem)-omega^2*M(2:mem,2:mem);
y = solve(det(determinant),omega, 'MaxDegree', 4, 'ReturnConditions',true);
ysim = simplify(real(vpa(y.omega)))

[Prateek jain]

Awesome!! Thanks, it works better.Can you please tell me how to arrange 'ysim' in descending order with only positive omega values.

[Walter Roberson]

ch = children(ysim);
constant_is_in_column = 4;
constants = cellfun(@(C) C(constant_is_in_column), ch);
sorted_constants = sort(constants(constants>0));

There is a possibility that you might need to change the column number for the constants. When I ran, the entries looked like

[ 1/L, T^(1/2), 1/rho^(1/2), 6.4456627293774011978986902055451958164659195481673]

but it would not surprise me if the order was not always that -- in particular it would not surprise me if the constant was in the first column.

[Prateek jain]

now code is working great but still it is showing error in last line.'undefined function 'gt' for input argument of type 'cell'.

ch = children(ysim);
constant_is_in_column = 4;
constants = cellfun(@(C) C(constant_is_in_column), ch,'uniformoutput',false);
sorted_constants = sort(constants(constants>0));

[Walter Roberson]

You should not use uniform 0 there unless you are using older MATLAB versions that do not permit you to create symbolic output from a cellfun. But if you are then

   constants = [constants{:}]