Research Article
Apr 1963
Consistent mass Matrix for Distributed Mass Systems
Publication: Journal of the Structural Division
Volume 89, Issue 4
Abstract
A technique is developed for constructing a consistent mass matrix for vibration analysis of general structural configurations. The approach is consistent with standard procedures for stiffness matrix formulation of structural problems, but accounts for the actual mass distribution within the structure in a manner similar to the Rayleigh-Ritz formulation. The basic equation for computing the mass matrix coefficients is given a physical interpretation. It is shown that the natural frequencies obtained by using the consistent mass matrix are upper bounds to the exact solution. The procedure is applicable to general dynamic response analysis and is demonstrably superior to the usual procedure of physical mass lumping by application to frequency analysis of free-free and simply-supported prismatic beams with uniformly distributed mass. It is observed that if lateral translation coordinates alone are used to represent the distortion of a uniform beam, the number of individual beam segments must exceed by one the number of natural mode frequencies it is desired to closely approximate.
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Published In
Journal of the Structural Division
Volume 89 • Issue 4 • April 1963
Pages: 161 - 178
Copyright
© 1963 American Society of Civil Engineers.
History
Published in print: Apr 1963
Published online: Feb 1, 2021
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Authors
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John S. Archer, M.ASCE
Mgr., Dynamics Dept., Engrg. Mechanics Lab., Space Technology Laboratories, Inc., Redondo Beach, Calif.
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ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.