On the Quasi-Diagonalization and Uncoupling of Gyroscopic Circulatory Multi-Degree-of-Freedom SystemsSource: Journal of Applied Mechanics:;2024:;volume( 092 ):;issue: 002::page 21005-1DOI: 10.1115/1.4067148Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: A new central result that gives the necessary and sufficient conditions for two n by n skew-symmetric matrices and one symmetric matrix to be simultaneously quasi-diagonalized by a real orthogonal congruence is proved. Based on this result, the decomposition of linear multi-degree-of-freedom dynamical systems with gyroscopic, circulatory, and potential forces is investigated through a real linear coordinate transformation generated by an orthogonal matrix. Several sets of conditions, applicable to real-life structural and mechanical systems arising in aerospace, civil, and mechanical engineering, under which such a coordinate transformation exists are found, thereby allowing these systems to be decomposed into independent, uncoupled subsystems, each with a maximum of two degrees of freedom. The conditions are expressed in terms of the coefficient matrices of the system. A specific form for the circulatory (gyroscopic) matrix is posited, and when the gyroscopic (circulatory) matrix is simple—a situation that commonly appears in real-life applications—it is shown that just a single necessary and sufficient condition is required for the decomposition of the multi-degree-of-freedom system. Numerical examples are provided throughout to demonstrate the analytical results.
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contributor author | Bulatovic, Ranislav M. | |
contributor author | Udwadia, Firdaus E. | |
date accessioned | 2025-04-21T09:58:30Z | |
date available | 2025-04-21T09:58:30Z | |
date copyright | 12/17/2024 12:00:00 AM | |
date issued | 2024 | |
identifier issn | 0021-8936 | |
identifier other | jam_92_2_021005.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4305227 | |
description abstract | A new central result that gives the necessary and sufficient conditions for two n by n skew-symmetric matrices and one symmetric matrix to be simultaneously quasi-diagonalized by a real orthogonal congruence is proved. Based on this result, the decomposition of linear multi-degree-of-freedom dynamical systems with gyroscopic, circulatory, and potential forces is investigated through a real linear coordinate transformation generated by an orthogonal matrix. Several sets of conditions, applicable to real-life structural and mechanical systems arising in aerospace, civil, and mechanical engineering, under which such a coordinate transformation exists are found, thereby allowing these systems to be decomposed into independent, uncoupled subsystems, each with a maximum of two degrees of freedom. The conditions are expressed in terms of the coefficient matrices of the system. A specific form for the circulatory (gyroscopic) matrix is posited, and when the gyroscopic (circulatory) matrix is simple—a situation that commonly appears in real-life applications—it is shown that just a single necessary and sufficient condition is required for the decomposition of the multi-degree-of-freedom system. Numerical examples are provided throughout to demonstrate the analytical results. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | On the Quasi-Diagonalization and Uncoupling of Gyroscopic Circulatory Multi-Degree-of-Freedom Systems | |
type | Journal Paper | |
journal volume | 92 | |
journal issue | 2 | |
journal title | Journal of Applied Mechanics | |
identifier doi | 10.1115/1.4067148 | |
journal fristpage | 21005-1 | |
journal lastpage | 21005-13 | |
page | 13 | |
tree | Journal of Applied Mechanics:;2024:;volume( 092 ):;issue: 002 | |
contenttype | Fulltext |