How can I avoid 'and' in result? or any other way to solve

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Tarsem Singh Khalsa 2018-4-14

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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

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Walter Roberson 2018-4-14

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.

Tarsem Singh Khalsa 2018-4-15

Thanx that worked perfectly.

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