

J. J. Strossmayer University of Osijek  Department of Mathematics
MATHOS
meet the team
THE PEOPLE BEHIND VIMS
Zoran Tomljanović
principal investigator
Abstract
keywords: mechanical system, vibration reduction, quadratic eigenvalue problem, frequency isolation, reducedorder 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 nonsmooth 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 MultipleInput MultipleOutput case. We will also study approaches for approximating the fullorder model with a reducedorder 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 IIII 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 fullorder model with a reducedorder 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 IIII 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
Samplingfree parametric model reduction for structured systems
Christopher Beattie, Serkan Gugercin, Zoran Tomljanović
 submitted 2020
Semiactive 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, 2427 February 2020
Z. Tomljanović, Samplingfree parametric model reduction for structured systems
ApplMath20, Brijuni, 1418 September 2020
S. Miodragović, Frequency isolation for the hyperbolic guadratic eigenvalue problem
M. Ugrica, Frequencyweighted damping via nonsmooth optimization and fast computation of QEPs with lowrank updates
Magdeburg Lectures on Optimization and Control, Magdeburg, 25 September 2020
Z. Tomljanović, Damping optimization in mechanical systems using samplingfree model reduction
News
Invited lectures & visiting fellows
Serkan GugercinVirginia Tech, USASerkan 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.
Department of Mathematics, J. J. Strossmayer University of OsijekTrg Ljudevita Gaja 6
HR31000 Osijek
Croatia