How can plot individual mode shapes of a cantilever beam with a tip mass?

I have been given code by my professor to solve for the roots of the characteristic equation of a cantilever beam.

% Material and geometric properties -- correct these!
EI = .75897;                 % Young's modulus * moment of inertia
rhoA = .1192506;               % density * cross-sectional area
L = .613;                  % length
M = .0053;                  % tip mass

BL = 0:0.01:15;         % array of beta*L values
mu = M / rhoA / L;      % normalized tip mass
for iB = 1:length(BL)   % loop over all values of beta*L
	s=sin(BL(iB)); c=cos(BL(iB));       % just saving space in next
	sh=sinh(BL(iB)); ch=cosh(BL(iB));   % by using s, c, sh, ch
	c1=mu*BL(iB)*s-c; c2=s+mu*BL(iB)*c;
   c3=ch+mu*BL(iB)*sh; c4=sh+mu*BL(iB)*ch;
    chareq(iB) = det([ 0  1  0  1;      % from zero disp at x=0
                       1  0  1  0;      % from zero slope at x=0
                      -s -c  sh ch;     % from zero moment at x=L
                      c1  c2  c3 c4]);   % from tip mass force at x=L
end
plot(BL,chareq);  axis([0 15 -10 10]);  grid on
xlabel('\betaL');  ylabel('det[A]')

I have also been instructed to plot the first three mode shapes (corresponding to the first three Beta-L values). This is my attempt:

B1=1.752;
X=0:.05:.7;
s=sin(B1*X); c=cos(B1*X);
sh=sinh(B1*X); ch=cosh(B1*X);
c1=mu*B1*s-c; c2=s+mu*B1*c;
c3=ch+mu*B1*sh; c4=sh+mu*B1*ch;

f=s+(c2*c)+(c3*sh)+(c4*ch);

plot(x,f)

I am getting this error and I am not exactly sure why:

Error using *

Inner matrix dimensions must agree.

Error in PL4Starter (line 39)

f=s+(c2*c)+(c3*sh)+(c4*ch);

This is in the same file as the previous code, so existing variables are still defined. Can anyone offer some help here?

I am not too familiar with MATLAB and understanding syntax, even with the help of documentation, is a struggle. I have coded in C and python, so I am familiar with typical programming syntax.

Answer 1

[Star Strider]

You need to use element-wise operations (.* for element-wise multiplication instead of * that is used for matrix multiplication):

f=s+(c2.*c)+(c3.*sh)+(c4.*ch);

See Array vs. Matrix Operations for details.

Also, MATLAB is case sensitive, so change your plot arguments to:

plot(X,f)

[Star Strider]

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