Actually I have calculated stiffness matrix , but I want know how to calculate the modal frequencies and mode shapes using MATLAB ........
% 'modal.m'
%
% This program calculates the natural frequencies and mode shapes for
% a multi-degree-of-freedom system. Then it uses the mode shapes to
% calculate the modal mass, modal damping and modal stiffness matrices.
% Inputs: [m], the mass matrix
% [c], the damping matrix
% [k], the stiffness matrix
% Outputs: {fn}, the vector of natural frequencies
% [phi], the mode shape matrix
% [\M\], the modal mass matrix
% [\C\], the modal damping matrix
% [\K\], the modal stiffness matrix
clear
% Enter the mass, damping and stiffness matrices %%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Enter the mass matrix. For example, at the prompt, type:')
disp('[1 0 0 ')
disp('0 3 0 ')
disp('0 0 5] ')
disp(' ')
m=input(' Enter mass matrix m: ')
c=input(' Enter damping matrix c: ')
k=input(' Enter stiffness matrix k: ')
% Calculate eigenvectors and eigenvalues %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[P,lamda]=eig(m^(-1)*k);
[wn,kk]=sort(sqrt(diag(lamda)));
P=P(:,kk);
% Make sure the first entry of every column is positive
for i=1:length(m)
if P(1,i)
You need to calculate the mass matrix as well. With it and the stiffness matrix you can form the dynamical matrix and either extract its eigenvalues (reciprocal of the squared angular eigenfrequencies) or use vector iteration to find the modes first and from them the eigenvalues.
Check out this link, it might help you for the case of eigenvalues in Matlab.
http://www.mathworks.com/help/matlab/ref/eig.html
% 'modal.m'
%
% This program calculates the natural frequencies and mode shapes for
% a multi-degree-of-freedom system. Then it uses the mode shapes to
% calculate the modal mass, modal damping and modal stiffness matrices.
% Inputs: [m], the mass matrix
% [c], the damping matrix
% [k], the stiffness matrix
% Outputs: {fn}, the vector of natural frequencies
% [phi], the mode shape matrix
% [\M\], the modal mass matrix
% [\C\], the modal damping matrix
% [\K\], the modal stiffness matrix
clear
% Enter the mass, damping and stiffness matrices %%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Enter the mass matrix. For example, at the prompt, type:')
disp('[1 0 0 ')
disp('0 3 0 ')
disp('0 0 5] ')
disp(' ')
m=input(' Enter mass matrix m: ')
c=input(' Enter damping matrix c: ')
k=input(' Enter stiffness matrix k: ')
% Calculate eigenvectors and eigenvalues %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[P,lamda]=eig(m^(-1)*k);
[wn,kk]=sort(sqrt(diag(lamda)));
P=P(:,kk);
% Make sure the first entry of every column is positive
for i=1:length(m)
if P(1,i)
You can obtain the dynamical matrix (D = inv[M].[K]) from the stiffness [K] and mass matrix [M]. The eigen values and eigen vecors of [D] correspond to the mode shapes and square of modal frequencies of the system respectively.
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