Subscript indices must either be real positive integers or logicals always show up. what should i do?

%% Beam Properties

L = 0.35; % Length of the beam (m)

w = 0.02; % Width of the beam (m)

t = 0.002; % thickness of the beam (m)

m = 0.024; % Mass of the point mass (kg)

E = 200e6; % Young's Modulus (Pa)

rho = 7850; % Density of the material

Acs = w*t; %cross sectional area

I = w*t^3/12; %second moment of inertia

A = 2;

%% Calculation of Natural Frequencies and Mode Shapes

n = 4; % Number of modes to be calculated

beta = zeros(n,1);

for i = 1:n

beta(i) = (i*pi/L)^2;

end

omega = sqrt((beta.^4.*E*I)/rho.*Acs);

frequencies = omega/(2*pi); % Natural Frequencies in Hz

x = linspace(0,L,100); % Discretized beam length

mode_shape = zeros(n,length(x)); % Mode Shapes

for i = 1:n

mode_shape(i,:) = A(sin(beta*x)-sinh(beta*x)-((sin(beta*L)+sinh(beta*L))/(cos(beta*L)+cosh(beta*L)))*(cos(beta*x)-cosh(beta*x))); % Mode Shapes

mode_shape(i,:) = mode_shape(i,:)/max(abs(mode_shape(i,:))); % Normalize Mode Shapes

end

%% Plotting Mode Shapes

figure(1)

hold on

for i = 1:n

plot(x,mode_shape(i,:),'LineWidth',2)

end

xlabel('x (m)')

ylabel('Normalized Deflection')

title('Mode Shapes')

legend('Mode 1','Mode 2','Mode 3','Mode 4')

%% Displaying Natural Frequencies

disp('Natural Frequencies (Hz):')

disp(frequencies)

[Dyuman Joshi]

Do you mean to use beta(i) in this loop?

for i = 1:n
    mode_shape(i,:) = A(sin(beta*x)-sinh(beta*x)-((sin(beta*L)+sinh(beta*L))/(cos(beta*L)+cosh(beta*L)))*(cos(beta*x)-cosh(beta*x))); % Mode Shapes
    mode_shape(i,:) = mode_shape(i,:)/max(abs(mode_shape(i,:))); % Normalize Mode Shapes
end

[Nur Mufidatul]

yes

Answer 1

[VBBV]

%% Beam Properties
L = 0.35;      % Length of the beam (m)
w = 0.02;      % Width of the beam (m)
t = 0.002;     % thickness of the beam (m)
m = 0.024;     % Mass of the point mass (kg)
E = 200e6;     % Young's Modulus (Pa)
rho = 7850;    % Density of the material
Acs = w*t;     %cross sectional area
I = w*t^3/12;   %second moment of inertia
A = 2;
%% Calculation of Natural Frequencies and Mode Shapes
n = 4;      % Number of modes to be calculated
beta = zeros(n,1);

omega = sqrt((beta.^4.*E*I)/rho.*Acs);
frequencies = omega/(2*pi); % Natural Frequencies in Hz
x = linspace(0,L,100); % Discretized beam length
mode_shape = zeros(n,100);

M = {'--','-.','-',':'}; % set linestyles 
%% Plotting Mode Shapes
hold on
for i = 1:n
    beta(i) = (i*pi/L)^2;
    mode_shape(i,:) = A*(sin(beta(i)*x*pi/180)-sinh(beta(i)*x*pi/180)-((sin(beta(i)*L*pi/180)+sinh(beta(i)*L*pi/180))./(cos(beta(i)*L*pi/180)+cosh(beta(i)*L*pi/180))).*(cos(beta(i)*x*pi/180)-cosh(beta(i)*x*pi/180))); % Mode Shapes
    mode_shape(i,:) = mode_shape(i,:)./max(abs(mode_shape(i,:))); % Normalize Mode Shapes
    plot(x,mode_shape(i,:),'LineWidth',2,'LineStyle',M{i})
end
xlabel('x (m)')
ylabel('Normalized Deflection')
title('Mode Shapes')
legend('Mode 1','Mode 2','Mode 3','Mode 4'); grid

%% Displaying Natural Frequencies
disp('Natural Frequencies (Hz):')

Natural Frequencies (Hz):

disp(frequencies) 

     0
     0
     0
     0

[VBBV]

you can avoid multiple for loops to evaluate the mode shapes and plotting graphs

[Nur Mufidatul]

Thank you so much, this really help me. one more question, whay does the frequencies are zero?

[VBBV]

%% Beam Properties
L = 0.35;      % Length of the beam (m)
w = 0.02;      % Width of the beam (m)
t = 0.002;     % thickness of the beam (m)
m = 0.024;     % Mass of the point mass (kg)
E = 200e6;     % Young's Modulus (Pa)
rho = 7850;    % Density of the material
Acs = w*t;     %cross sectional area
I = w*t^3/12;   %second moment of inertia
A = 2;
%% Calculation of Natural Frequencies and Mode Shapes
n = 4;      % Number of modes to be calculated
beta = zeros(n,1);


 % Natural Frequencies in Hz
x = linspace(0,L,100); % Discretized beam length
mode_shape = zeros(n,100);

M = {'--','-.','-',':'}; % set linestyles 
%% Plotting Mode Shapes
hold on
for i = 1:n
    beta(i) = (i*pi/L)^2;
    omega(i) = sqrt((beta(i)^4.*E*I)/rho.*Acs);  % omega 
    frequencies(i) = omega(i)/(2*pi);  % frequencies 
    mode_shape(i,:) = A*(sin(beta(i)*x*pi/180)-sinh(beta(i)*x*pi/180)-((sin(beta(i)*L*pi/180)+sinh(beta(i)*L*pi/180))./(cos(beta(i)*L*pi/180)+cosh(beta(i)*L*pi/180))).*(cos(beta(i)*x*pi/180)-cosh(beta(i)*x*pi/180))); % Mode Shapes
    mode_shape(i,:) = mode_shape(i,:)./max(abs(mode_shape(i,:))); % Normalize Mode Shapes
    plot(x,mode_shape(i,:),'LineWidth',2,'LineStyle',M{i})
end
xlabel('x (m)')
ylabel('Normalized Deflection')
title('Mode Shapes')
legend('Mode 1','Mode 2','Mode 3','Mode 4'); grid

%% Displaying Natural Frequencies
disp('Natural Frequencies (Hz):')

Natural Frequencies (Hz):

disp(frequencies.') 

    0.0038
    0.0609
    0.3085
    0.9749

Answer 2

[Alan Stevens]

Well, this works, but you might want to check the correctness or otherwise of your mode_shape calculations (there are a lot of zeros there!)

%% Beam Properties
L = 0.35;      % Length of the beam (m)
w = 0.02;      % Width of the beam (m)
t = 0.002;     % thickness of the beam (m)
m = 0.024;     % Mass of the point mass (kg)
E = 200e6;     % Young's Modulus (Pa)
rho = 7850;    % Density of the material
Acs = w*t;     %cross sectional area
I = w*t^3/12;   %second moment of inertia
A = 2;
%% Calculation of Natural Frequencies and Mode Shapes
n = 4;      % Number of modes to be calculated
beta = zeros(n,1);
for i = 1:n
    beta(i) = (i*pi/L)^2;
end
omega = sqrt((beta.^4.*E*I)/rho.*Acs);
frequencies = omega/(2*pi); % Natural Frequencies in Hz
x = linspace(0,L,100); % Discretized beam length
mode_shape = zeros(n,100);

for i = 1:n

    mode_shape(i,:) = A*(sin(beta(i)*x)-sinh(beta(i)*x)-((sin(beta(i)*L)+sinh(beta(i)*L))./(cos(beta(i)*L)+cosh(beta(i)*L))).*(cos(beta(i)*x)-cosh(beta(i)*x))); % Mode Shapes
    mode_shape(i,:) = mode_shape(i,:)./max(abs(mode_shape(i,:))); % Normalize Mode Shapes
    
end


%% Plotting Mode Shapes
figure(1)
hold on
for i = 1:n
    plot(x,mode_shape(i,:),'LineWidth',2)
end
xlabel('x (m)')
ylabel('Normalized Deflection')
title('Mode Shapes')
legend('Mode 1','Mode 2','Mode 3','Mode 4')
%% Displaying Natural Frequencies
disp('Natural Frequencies (Hz):')
disp(frequencies)

[Nur Mufidatul]

Thank you for te correction.

Answer 3

[Image Analyst]

See the FAQ for a thorough discussion of what causes the error and how to fix it:

https://matlab.fandom.com/wiki/FAQ#%22Subscript_indices_must_either_be_real_positive_integers_or_logicals.%22