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 consis...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2005-02, Vol.194 (6), p.675-689
Main Authors: Archer, Graham C., Whalen, Timothy M.
Format: Article
Language:English
Subjects:
Beam elements
Consistent mass matrices
Diagonal mass modeling
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Plate elements
Rotational inertia
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary: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.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2003.08.015