ASME International
Uncoupling of Linear Multi-Degree-of-Freedom Damped Gyroscopic Potential Systems
Abstract
This paper deals with the uncoupling of linear damped multi-degree-of-freedom gyroscopic potential systems in which the damping is taken to have a specifically chosen form. Necessary and sufficient conditions are obtained that guarantee the uncoupling of such damped systems into independent subsystems with at most two degrees-of-freedom. Along with several other results, it is shown that when the potential (stiffness) matrix of the damped system has distinct eigenvalues—a...
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2023
Ranislav M. Bulatovic
,
Firdaus E. Udwadia
ASME International
On the Generalization of Merkin’s Theorem for Circulatory Systems: A Rank Criterion
Abstract
This paper provides a generalization of the celebrated Merkin theorem. It provides new results on the destabilizing effect of circulatory forces on stable potential systems. Previous results are described and discussed, and the paper uncovers a deeper understanding of the fundamental reason for the destabilization. Instability results in terms of rank conditions that deal with the potential and circulatory matrices that describe the system are obtained, thereby generalizing...
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2020
Ranislav M. Bulatovic
,
Firdaus E. Udwadia