Linear Radom Vibration of Structural Systems with Singular Mass Matrices

Fragkoulis, Vasileios ORCID: 0000-0001-9925-9167, Kougioumtzoglou, Ioannis and Pantelous, Athanasios ORCID: 0000-0001-5738-1471 (2016) Linear Radom Vibration of Structural Systems with Singular Mass Matrices. Journal of Engineering Mechanics, 142 (2). 04015081-.

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Abstract

A framework is developed for determining the stochastic response of linear multi-degree-of-freedom (MDOF) structural systems with singular matrices. This system modeling can arise when using more than the minimum number of coordinates, and can be advantageous, for instance, in cases of complex multibody systems whose dynamics satisfy a number of constraints. In such cases the explicit formulation of the equations of motion can be a nontrivial task, whereas the introduction of additional/redundant degrees of freedom can facilitate the formulation of the equations of motion in a less labor-intensive manner. Relying on the generalized matrix inverse theory and on the Moore-Penrose (M-P) matrix inverse, standard concepts, relationships, and equations of the linear random vibration theory are extended and generalized herein to account for systems with singular matrices. Adopting a state-variable formulation, equations governing the system response mean vector and covariance matrix are formed and solved. Further, it is shown that a complex modal analysis treatment, unlike the standard system modeling case, does not lead to decoupling of the equations of motion. However, relying on a singular value decomposition of the system transition matrix significantly facilitates the efficient computation of the system response statistics. A linear structural system with singular matrices is considered as a numerical example for demonstrating the applicability of the methodology and for elucidating certain related numerical aspects.

Item Type:	Article
Uncontrolled Keywords:	structural systems, degrees of freedom, equations of motion, stochastic processes, vibration, matrix (mathematics), linear functions, numerical methods
Depositing User:	Symplectic Admin
Date Deposited:	17 May 2016 09:07
Last Modified:	14 Mar 2024 18:07
DOI:	10.1061/(ASCE)EM.1943-7889.0001000
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3001253