How to vary an element in a matrix?

I want to be able to vary a matrix element between a set of certain values. Below is my code:

% System parameters

k1=180; k2=50; k3=220;

m1=1.1; m2=3.4;

% Stiffness and mass matrices

K=[k1+k2,-k2;-k2,k2+k3];

M=[m1,0;0,m2];

% Eigenvalues and natural frequencies

lambda=eig(K,M);

omega_nf=sqrt(lambda); disp(sort(omega_nf))

However, I want k1 to vary between 0.5*180:1.5*180. I know this doesn't work due to the dimensions of the arrays not being consistent. How could I make this work? I want to plot the eigenvalues against the varying k1.

Thank you for any help, it is appreciated.

Answer 1

[Star Strider]

Use a for loop or arrayfun —

% System parameters
k1=180 * linspace(0.5, 1.5, 9);                             % Define 'k1' As A Vector
k2=50; 
k3=220;
m1=1.1; m2=3.4;
% Stiffness and mass matrices
K= @(k1) [k1+k2,-k2;-k2,k2+k3];                             % Create Anonymoous Function
M=[m1,0;0,m2];
% Eigenvalues and natural frequencies
lambda=arrayfun(@(k1)eig(K(k1),M), k1, 'Unif',0);           % Calculate 'lambda'
omega_nf=sqrt([lambda{:}]); disp(sort(omega_nf))

    8.2530    8.4101    8.5106    8.5791    8.6283    8.6651    8.6936    8.7163    8.7348
   11.7716   12.5063   13.2349   13.9444   14.6306   15.2929   15.9321   16.5497   17.1471

figure
plot(k1, omega_nf)
grid

.

Answer 2

[Bruno Luong]

If you have latest R2022a, use eig2 FEX (we are still waiting for TMW to implement pageeig)

% System parameters
k1=0.5*180:1.5*180; 
k2=50; k3=220;
m1=1.1; m2=3.4;
% Stiffness and mass matrices
K1=reshape(k1,1,1,[]);
K=[K1+k2,0*K1-k2;0*K1-k2,0*K1+k2+k3];
M=[m1,0;0,m2];
% Eigenvalues and natural frequencies
lambda=eig2(pagemldivide(K,M));
omega_nf=sqrt(lambda); 
plot(k1,sort(omega_nf)')

If not just do for-loop of k1

% System parameters
k1=0.5*180:1.5*180;
k2=50; k3=220;
m1=1.1; m2=3.4;
% Stiffness and mass matrices
omega_nf = zeros(2,length(k1));
for i=1:length(k1)
    K=[k1(i)+k2,-k2;-k2,k2+k3];
    M=[m1,0;0,m2];
    % Eigenvalues and natural frequencies
    lambda=eig(K,M);
    omega_nf(:,i)=sqrt(lambda);
end
plot(k1,sort(omega_nf)')

Answer 3

[Davide Masiello]

clear,clc

k1 = 0.5*180:1.5*180;
k2 = 50; 
k3 = 220;
m1 = 1.1; 
m2 = 3.4;

omega_nf = zeros(2,length(k1));

for idx = 1:length(k1)
K = [k1(idx)+k2,-k2;-k2,k2+k3];
M = [m1,0;0,m2];

lambda = eig(K,M);
omega_nf(:,idx) = sqrt(lambda);
end

plot(k1,omega_nf)