• Vibration Reduction in Mechanical Systems - VIMS

    IP-2019-04-6774

    funded by HRZZ
  • J. J. Strossmayer University of Osijek - Department of Mathematics

    MATHOS
  • Workshop on Optimal Control of Dynamical Systems and applications

    5-6 November 2020 at Department of Mathematics, J. J. Strossmayer University of Osijek

    Workshop

January 2020 – December 2023

meet the team

THE PEOPLE BEHIND VIMS

Serkan Gugercin

investigator

Serkan Gugercin

investigator

A.V. Morris Professor of Mathematics

Virginia Tech
Blacksburg, USA

Works on model reduction, dynamical systems, numerical analysis, and scientific computing.

Ivana Kuzmanović Ivičić

investigator

Ivana Kuzmanović Ivičić

investigator

Assistant Professor
Department of Mathematics, Josip Juraj Strossmayer University of Osijek
Osijek, Croatia

Works on parameter dependent problems, especially on damping optimization and matrix equations.

Suzana Miodragović

investigator

Suzana Miodragović

investigator

Assistant Professor
Department of Mathematics, Josip Juraj Strossmayer University of Osijek
Osijek, Croatia

Works on perturbation theory for eigenvalue problems and its applications.

Zoran Tomljanović

principal investigator

Zoran Tomljanović

principal investigator

Associate Professor
Department of Mathematics, Josip Juraj Strossmayer University of Osijek
Osijek, Croatia

Works on damping optimization in mechanical systems, matrix equations, perturbation theory, and its applications.

Matea Ugrica

Postdoc

Matea Ugrica

Postdoc

Postdoc
Department of Mathematics, Josip Juraj Strossmayer University of Osijek
Osijek, Croatia

Works on damping optimization in mechanical systems, matrix equations, perturbation theory for eigenvalue problems and its applications.

Marinela Pilj Vidaković

PhD student

Marinela Pilj Vidaković

PhD student

PhD student
Department of Mathematics, Josip Juraj Strossmayer University of Osijek
Osijek, Croatia

Works on damping optimization in mechanical systems and model reduction.

Abstract

keywords: mechanical system, vibration reduction, quadratic eigenvalue problem, frequency isolation, reduced-order model, parameter optimization

Vibration analysis and vibration reduction for mechanical systems are prominent problems in numerous research fields. Although the vibrations analysis is an intensively studied topic in recent decades, many problems still remain open. While the case without external excitation leads to the study of homogeneous systems, presence of an external forcing leads to the study of nonhomogeneous systems. Depending on the presence of an external excitation and applications, we will consider four different research themes.
Within the first research theme, we will study theoretical results that are relevant for vibration reduction. We plan to develop theoretical results that characterize important properties of the quadratic eigenvalue problem (QEP) arising from vibration analysis of mechanical systems. Within the second research theme we will develop new methods for frequency isolation and utilize methods which are based on algorithms for non-smooth optimization. For this case we will derive new algorithms that preserve the structure of the matrices and structural properties of the considered QEP. In the third research theme, we will consider vibration reduction based on criteria that use system norms (e.g. H2 and Hinf) for Multiple-Input Multiple-Output case. We will also study approaches for approximating the full-order model with a reduced-order model that retains the structure of parametric dependence. The new approaches will be well suited for computationally efficient parameter optimization and the study of important system properties. In the fourth research theme we will consider integrating research themes I-III and applications in real world examples.
Moreover, we will apply obtained new approaches and algorithms in various academic examples, but also in real life examples that arise, e.g., in car industry (such as disc brake problem) and civil engineering (such as beams, civil buildings), etc. Therefore, the results from this project could have wide applications.

Research themes

I - IV

RT I: homogeneous case

We develop theoretical results that characterize important properties of the Quadratic Eigenvalue Problem (QEP) that arise from vibration analysis of mechanical systems. In relative perturbation bounds typically relative gaps appear, which makes such bounds demanding to compute. We will approximate these perturbation bounds and develop new bounds that can be used for efficient vibration reduction.

RT II: case with given external force

We develop criterion that considers vibration isolation in order to avoid resonance in vibrational system. For this case we will derive new algorithms that preserve the structure of the matrices and structural properties of the considered QEP.

RT III: MIMO case

We consider a new measures that can ensure better robustness, stability and other important system properties. Within this case, to make the optimization algorithm computationally feasible, we will employ a novel approach to parametric model order reduction. We will also study approaches for approximating the full-order model with a reduced-order model that retains the structure of parametric dependence. The new approach will be well suited for computationally efficient parameter optimization and the study of important system properties.

RT IV: integrating research themes and applications

This is integrating research themes I-III and applications in real world examples. Firstly, we will employ the theoretical results obtained for the homogeneous case in the setting of the nonhomogeneous case as well. We propose new approaches that are based on criteria that are nonsmooth, such as Hinf criterion or criterion based on frequency isolation. We will test our new approaches and algorithms in various academic examples, but also in real life examples that arise, for example, in car industry (such as disc break problem) and civil engineering (such as beams, civil buildings), etc.

Publications

Sampling-free parametric model reduction for structured systems

Christopher Beattie, Serkan Gugercin, Zoran Tomljanović

  • submitted 2020

Semi-active H∞ damping optimization by adaptive interpolation

Zoran Tomljanović, Matthias Voigt

  • published in Numerical Linear Algebra with Applications 27/4 (2020)

Fast computation of optimal damping parameters for linear vibrational systems

Nevena Jakovčević Stor, Ivan Slapničar, Zoran Tomljanović

  • submitted 2020

Dissemination

COST Action 18232 Zagreb meeting, 24-27 February 2020

Z. Tomljanović, Sampling-free parametric model reduction for structured systems

ApplMath20, Brijuni, 14-18 September 2020

S. Miodragović, Frequency isolation for the hyperbolic guadratic eigenvalue problem

M. Ugrica, Frequency-weighted damping via nonsmooth optimization and fast computation of QEPs with low-rank updates

Magdeburg Lectures on Optimization and Control, Magdeburg, 25 September 2020

Z. Tomljanović, Damping optimization in mechanical systems using sampling-free model reduction

Workshop on Optimal Control of Dynamical Systems and applications

5-6 November 2020 at Department of Mathematics, J. J. Strossmayer University of Osijek

The goal of this workshop is to provide a coherent set of lectures that will adequately clarify the mathematical aspects of the (optimal) control of dynamical systems, with special emphasis on optimization and model reduction methods for large-scale systems.

INVITED LECTURES

Ivica Nakić, Department of Mathematics, University of Zagreb, Croatia

Abstract
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Luka Grubišić, Department of Mathematics, University of Zagreb, Croatia

Abstract
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Ivan Slapničar, Department of Mathematics, University of Zagreb, Croatia

Abstract
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Josip Tambača, Department of Mathematics, University of Zagreb, Croatia

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Domagoj Tolić, RIT Croatia, Dubrovnik, Croatia

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CONTRIBUTED TALKS

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Schedule

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News

Invited lectures & visiting fellows

Serkan Gugercin is our guest at the Optimization and application seminar on 10th June 2020. He will give a talk on An Introduction to Interpolatory Methods for Model Reduction.

Serkan GugercinVirginia Tech, USA

Trg Ljudevita Gaja 6
HR-31000 Osijek
Croatia

Department of Mathematics, J. J. Strossmayer University of Osijek