A REVIEW OF MASS MATRICES FOR EIGENPROBLEMS

Various nonconsistent mass matrices have been presented to achieve more accurate natural frequencies in eigenproblems of the finite element analysis. The matrices arc obtained as a linear combination of lumped and consistent mass matrices. For an improved accuracy, the consistent mass should be more weighted than the lumped mass. Instead of the mass combination, the interpolation functions can be combined to give nonconsistent mass matrices, which show the same tendency. To find a nonsingular lumped mass matrix for the bending vibration of beams, a translational inertia has been proposed for rotational degrees of freedom. The inertia effect is highly overestimated and hence lower natural frequencies are obtained. When combined with the consistent mass matrix, however, the modified lumped mass matrix gives a significant improvement for the natural frequencies of intermediate and higher modes. A simple corrective method was applied to get a better estimation of the natural frequencies through the use of the frequency dependent stiffness and mass matrices. The method shows high accuracy without complicated calculations.