ON THE PERFORMANCE OF VARIOUS BEAM MASS MATRICES

摘要

A criteria using translational and rotational rigid-body modes to verify the conservation of mass, mass moment of inertia, and rotatory inertia in a beam element is presented. Conservation of element mass means convergence to the exact eigenvalue solutions of a Euler beam. Conservation of element mass and rotatory inertia means convergence to the exact solution of an Euler beam with rotatory inertia. Conservation of mass moment of inertia can be used to predict the performance of beam mass matrices in eigenvalue solutions with respect to their accuracy and consistency. Various kinds of lumped masses are tested to see if they meet the criteria. Then, four different beam models are used to test the various lumped mass matrices in free-vibration analysis. Natural frequencies are obtained and compared with exact natural frequencies. It is found that most of the results can be explained using the criteria for all lumped-mass models tested. The results also show that a block-diagonal lumped-mass matrix and a lumped mass matrix (a = -1/12) have advantages over the currently used lumped mass matrices. They give good consistent results as well as converge to the continuum solutions.