Development of rotationally consistent diagonal mass matrices for plate and beam elements

This paper presents a new diagonalization technique for mass matrices of finite elements that contain both translational and rotational degrees of freedom. The goal is to produce a diagonal mass matrix that maintains the translational and rotational rigid body inertias that are present in the consistent mass matrix. The technique is applied to moderately thick and thin Mindlin plate elements, Euler-Bernoulli beam elements, and Timoshenko beam elements. The accuracy of the new rotationally consistent diagonal mass matrices is demonstrated in a number of sample vibration problems, and the importance of accurate rotational inertia modeling in dynamic analyses is examined.