Nazad
ASME International
Uncoupling of Damped Linear Potential Multi-Degrees-of-Freedom Structural and Mechanical Systems
Ranislav M. Bulatovic , Firdaus E. Udwadia
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2024
Abstract This paper provides the necessary and sufficient conditions for a multi-degrees-of-freedom linear potential system with an arbitrary damping matrix to be uncoupled into independent subsystems of at most two degrees-of-freedom using a real orthogonal transformation. The incorporation of additional information about the matrices, which many structural and mechanical systems commonly possess, shows a reduction in the number of these conditions to three. Several new results are obtained and are illustrated through examples. A useful general form for the damping matrix is developed that guarantees the uncoupling of such systems when they satisfy just two conditions. The results provided herein lead to new physical insights into the dynamical behavior of potential systems with general damping matrices and robust computational procedures. It is shown that the dynamics of a damped potential system in which the damping matrix may be arbitrary is identical to that of a damped gyroscopic potential system with a symmetric damping matrix. This brings, for the first time, these two systems, which are seen today as belonging to different categories of dynamical systems, under a unified framework.
ASME International
Uncoupling of Damped Linear Potential Multi-Degrees-of-Freedom Structural and Mechanical Systems
Abstract This paper provides the necessary and sufficient conditions for a multi-degrees-of-freedom linear potential system with an arbitrary damping matrix to be uncoupled into independent subsystems of at most two degrees-of-freedom using a real orthogonal transformation. The incorporation of additional information about the matrices, which many structural and mechanical systems commonly possess, shows a reduction in the number of these conditions to three. Several new results are...
Download 2024 Ranislav M. Bulatovic , Firdaus E. Udwadia
ASME International
Decomposition and Uncoupling of Multi-Degree-of-Freedom Gyroscopic Conservative Systems
Abstract This paper explores the decomposition of linear, multi-degree-of-freedom, conservative gyroscopic dynamical systems into uncoupled subsystems through the use of real congruences. Two conditions, both of which are necessary and sufficient, are provided for the existence of a real linear coordinate transformation that uncouples the dynamical system into independent canonical subsystems, each subsystem having no more than two-degrees-of-freedom. New insights and conceptual simplifications...
Download 2023 Ranislav M. Bulatovic , Firdaus E. Udwadia
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...
Download 2023 Ranislav M. Bulatovic , Firdaus E. Udwadia
ASME International
Stability of Multidegree of Freedom Potential Systems to General Infinitesimal Positional Perturbation Forces
Abstract The stability of general linear multidegree of freedom stable potential systems that are perturbed by general arbitrary positional forces, which may be neither conservative nor purely circulatory/conservative, is considered. It has been recently recognized that such perturbed potential systems with multiple frequencies of vibration are susceptible to instability, and this paper is centrally concerned with the situation when potential systems have such multiple natural frequencies....
Download 2022 Ranislav M. Bulatovic , Firdaus E. Udwadia
The Royal Society
On the stability and instability of linear potential systems subjected to infinitesimal circulatory forces
The stability of linear multi-degree-of-freedom stable potential systems with multiple natural frequencies under the action of infinitesimal circulatory forces is considered. Contrary to the received view that such systems are inherently unstable, a careful study shows that such systems have a much more complex behaviour than previously recognized and could exhibit an alternation of stability and instability that depends on the structure of the potential system and its interaction with the circulatory...
Download 2021 Ranislav M. Bulatovic , Firdaus E. Udwadia
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Copyright © 2025 EmpowerHR4Inno. All right reserved.
Copyright © 2025 EmpowerHR4Inno. All rights reserved.