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Coding an Equation to be solved

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I would like some help in coding equation 14, in order to solve equation 15 to obtain the value of C. Is this possible to do? I am not able to do it.

Accepted Answer

Alan Stevens
Alan Stevens on 7 Apr 2021
This should do it, assuming you know the values of the other constants:
% Arbitrary data
L = 1;
rho = 1;
A = 1;
sigma = 1;
Mt = 1;
It = 1;
lambda = 1.162;
k = lambda/L;
% define functions without C
phia = @(x) (cos(k*x)-cosh(k*x)+sigma*(sin(k*x)-sinh(k*x)));
phiasq = @(x) phia(x);
dphidxa = @(x) -k*(sin(k*x)+sinh(k*x)-sigma*(cos(k*x)-cosh(k*x)));
S = rho*A*integral(phiasq,0,L) + Mt*phiasq(L) + It*dphidxa(L)^2;
C = sqrt(1/S);
Alan Stevens
Alan Stevens on 21 Apr 2021
Well, strictly, your value of L is outside the range of the values used for the curve fit, but the line is so straight I suspect this won't introduce a significant error here.

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