Question

If the first and second mode shapes, normalised with respect to the mass matrix, of an undamped two degree of freedom system are given by: -0.009) (-O 015 01 = {0.0143; 02 = 0.012) and the stiffness matrix is: K = _4 24]* 106 N/m then, calculate the natural frequencies. (30%)

Answer 1

if we find the eigenvalues of K matrix then we can get the natural frequencies.

thus, finding eigenvalues we get, $\lambda^2 -12 \lambda +16 =0$

thus eigen values are 10.47 and 1.53

$\omega = \sqrt(\lambda)$

=3.23 and 1.236 are natural frequencies