Dr. Vasileios Fragkoulis
Research Fellow
Institute for Risk and Reliability
Leibniz Universität Hannover
Wednesday, May 23, 2018, 10:00, Room 116, Institute for Risk and Reliability, LUH
Deterministic and stochastic analysis of complex engineering dynamical systems: Singular matrices and fractional derivatives
Abstract
For many cases of complex engineering systems, analytical as well as numerical methodologies are required, firstly for the purposes of characterizing and quantifying uncertainties associated with excitations and system parameters, and subsequently for efficiently determining/predicting the system stochastic response. In stochastic engineering dynamics, in particular, the study and mathematical modeling of complex nonlinear systems with potential singularities arising either naturally (e.g. coupled electro-mechanical devices), or from an unconventional formulation of the system governing equations, are of high interest. In addressing the above challenges, a novel approach for determining the stochastic response of complex multi-body systems with singularities has been proposed. The singularities can either appear naturally in the governing equations of motion (e.g. smart materials, mathematically ill-conditioned engineering models, energy harvesting problems), or relate to a redundant coordinates modeling scheme (e.g. multi-body, robotic systems). Specifically, it can be argued that utilizing a redundant coordinates modeling scheme generates less complex and more computationally efficient techniques for formulating the equations of motion. In this context, based on the concept of the Moore-Penrose generalized matrix inverses, a generalized random vibration theory and computational framework have been developed to account for stochastically excited systems with singular matrices. Further, a generalization of the widely utilized statistical linearization approximate methodology for determining the stochastic response of nonlinear dynamical systems with singular matrices has also been developed. In this talk, the aforementioned framework for treating linear and nonlinear systems, as well as its potential extension to systems endowed with fractional derivative terms will be discussed.
Biography
Dr. Vasileios Fragkoulis is a Research Fellow in the Institute for Risk and Reliability at the Leibniz University of Hanover. He received his Ph.D. from the Department of Mathematical Sciences at the University of Liverpool. He also holds a M.Sc. degree and a 5-year Diploma from the School of Applied Mathematical and Physical Sciences at the National Technical University of Athens, both in the area of Applied Mathematical Sciences. Dr. Fragkoulis’ research interests focus on the general area of Applied Mathematics and Uncertainty Quantification and primarily, on mathematical modeling and analysis of (stochastic) dynamical systems with diverse applications in civil/mechanical engineering as well as theoretical and applied mechanics. Specifically, the development of analytical/numerical mathematical techniques in the fields of nonlinear stochastic dynamics constitutes one of his main research themes. In particular, part of his Ph.D. research focused on developing efficient solution methodologies for determining the response statistics of nonlinear and complex systems. The complexity relates to the governing (stochastic) equations of motion that include hysteretic operators, fractional derivatives, as well as singular matrices. Such unconventional and challenging modeling is associated with developing transformative technologies and devices, such as robotic systems, energy harvesters, and nano-materials.
