Abstract
Numerical analysis of discrete vibratory systems subjected to broad band excitation usually requires specification of a viscous damping matrix. A method of determining the entries in such matrices directly is presented in this paper. The modal damping ratios, which can normally be estimated, are used to produce a fully populated damping matrix. To facilitate numerical integration of the equations of motion, a procedure termed stripping has been established for reducing the matrix to banded form. Additionally, using a procedure termed replacement, small element matrices were identified, extracted from the fully populated damping matrix and utilized (much as element mass and stiffness matrices are) to construct the global damping matrix. The effects of stripping or replacement were evaluated for a number of boundary conditions on plates, beams, and shells. Errors caused by variation of the number of system degrees of freedom, the number of diagonal rows remaining in the stripped matrix, and the magnitude and mo dal distribution of damping ratios were studied. Results were, in general, good. Damping ratios, damped natural frequencies, and eigenvectors were closely approximated by both type of systems.
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