• Vibration Reduction in Mechanical Systems - VIMS

    IP-2019-04-6774

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

    MATHOS

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.

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

Semi-active H∞ damping optimization by adaptive interpolation

Zoran Tomljanović, Matthias Voigt

  • accepted for publication in Numerical Linear Algebra with Applications

Fast computation of optimal damping parameters for linear vibrational systems

Nevena Jakovčević Stor, Ivan Slapničar, Zoran Tomljanović

  • submitted

Dissemination

COST Action 18232 Zagreb meeting, 24-27 February 2020

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

91th Annual Meeting of the GAMM, Kassel, 16-20 March 2020

Z. Tomljanović, Frequency-weighted damping via non smooth optimization and fast computation of QEPs

ICCS 2020, Amsterdam, 3-5 June 2020

I. Kuzmanović Ivičić, Damping optimization of the excited mechanical system

S. Miodragović, Frequency isolation for the hyperbolic QEP

Visiting

Visiting fellows

Abstract. tba

tbalecture on Mathematical Colloquium

Trg Ljudevita Gaja 6
HR-31000 Osijek
Croatia

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