Frequency & Eigenvalue from dynamic eqn

AI Thread Summary
To find the natural period of a vertical cantilever beam, the user has formulated the equation [M]-w^2[K] = 0 using global mass (M) and stiffness (K) matrices, which are square symmetric but not diagonal. A numerical eigensolution is necessary for solving this characteristic polynomial, with various numerical analysis packages available, including MatLab. The user has identified that transforming the matrix into diagonal form simplifies the solution process. This approach is essential for determining the cyclic frequency (w). The discussion emphasizes the importance of numerical methods in structural dynamics analysis.
rk81
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Hi, i am trying to find the natural period of a vertical cantilever beam which is fixed at bottom and free at other end., i worked out the global M & K matrices and i have the eqn in the form [M]-w^2[K] = 0, the M & K are not diagonal matrices, but square symetric matrices of rank 6. i understand that w2 is the cyclic frequency, how do i solve this characteristic polynomial the matrix way.. thanks in advance,
 
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You need a numerical eigensolution, such as is available in many numerical analysis packages (NAG, EisPack, etc.). I think MatLab probably has one as well, and there are many other sources as well.
 
thanks, i think i found the answer.. i need to make the matrix to diagonal form, and then the soln is simple.
 

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