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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v1.i23.110
22 pages

A Robust Simulation Algorithm for Conservative Linear Mechanical Systems

Khalid Al-Widyan
Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, Canada
Jorge Angeles
Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, Canada
Svetlana Ostrovskaya
Department of Mechanical Engineering and Centre for Intelligent Machines, McGill University, Montreal, Canada

ABSTRACT

Proposed in this article is an inherently conservative simulation scheme, based on the zero-order hold and a closed-form time response of the system at hand. It is shown that the simulation algorithm can be cast in a form in which the state-transition matrix, mapping a state at instant tk into a state at instant tk+1, is proper orthogonal. Hence, for an n-degree-of-freedom (dof) system, this matrix represents a rotation in the 2n-dimensional space of state variables. As a result, the numerical damping required in the simulation of undamped systems is obviated. The performance of the algorithm is illustrated with two examples drawn from engineering systems.


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