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How can I avoid 'and' in result? or any other way to solve
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I'm writing a code for vibration of beam, the problem is that after derivation and substituting boundary values the result contains 'and' relation between two equation. It maybe due to the assumption, but it is necessary. Is there a way to avoid 'and' in this result?
BC: (for cantilever beam, beam length = 4m)
Y(x=0)=0
Y'(x=0)=0
Y''(x=4)=0
Y'''(x=4)=0
code:
Y=A*sin(b*x)+B*cos(b*x)+C*sinh(b*x)+D*cosh(b*x);
Yx=[1 0;1 0;0 1;0 1];
% Yx(i,j)=> i=n, (n-1)th derivative of Y
% j=1, at x=0; j=2, at x=Length of beam
assume(b>0);
t=0;
for i=1:4
for j=1:2
if Yx(i,j)==0
continue
end
t=t+1;
dY=diff(Y(x,b),x,(i-1));
F=simplify(expand(subs(dY,x,Yx(5,j))==0,'ArithmeticOnly',true));
c=symvar(F);
if or(size(c,2)==1,c(1)~='b')
d=1;
else
d=2;
end
if t==4;
assume(c(d)~=0)
Y=simplify(expand(F,'ArithmeticOnly',true));
else
G=solve(F,c(d));
Y(x,b)=subs(Y,c(d),G);
end
end
end
disp(Y);
The final result is like this:
Y = sin(4*b) + sinh(4*b) ~= 0 and cosh(4*b)^2 + 2*cos(4*b)*cosh(4*b) + 1 == sinh(4*b)^2
I'm using Matlab R2013a
2 Comments
Walter Roberson
on 14 Apr 2018
You should be able to add an assume() that asserts the first relationship to be true and then it should simplify() out.
It does appear to be true for all positive b.
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