Jerzy Warminski, Ph.D., D.Sc., Eng.
Professor of Theoretical and Applied Mechanics
The main attention of my research is paid to
non-linear dynamics of mechanical systems including the latest trends in
mechanics like: non-linear vibrations, chaos theory, bifurcation and stability
- Particularly I am interested in interactions
between parametric and self-excited vibrations of mechanical systems,
synchronisation phenomena and transitions from regular to chaotic motion.
I consider influence of external force on the systems in two variants: (a)
ideal system - when exciting force is independent on excited structure
response and (b) non-ideal system - when the complete dynamical model i.e.
the vibrating oscillator and the energy source interact.
- Another important subject of my research concerns
Nonlinear Normal Modes of nonlinear lumped mass systems (e.g. coupled
oscillators) or continuous system like cables, beams or plates. I am
interested in study of existence and stability of various modes and their
couplings in order to use them as natural gains to control structure
- I intensively work on dynamics and control of
flexible structures made of composite material with embedded active
elements. By introducing specific control strategy, often based on
nonlinear phenomena I try to design a so called "smart
structure" able to behave properly to varied environmental conditions
e.g. temperature, loadings, impacts etc.
- I develop theoretical models and laboratory
set-up for testing rotating structures, like composite beams or more
advanced helicopter or wind turbine blades. In the study I consider
orthotropic properties of the material and variable angular velocity of
- Next subject of my interest is related to
machining processes. I study self-excited chatter vibrations
occurring in turning or milling processes. Their mathematical models
are represented by differential equations with time delay.
- I analyse the delay differential equations
considering their possible applications to design control strategy, to
model MEMS dynamics and others.
- Last but not least is dynamics of human middle
ear ossicles. I work on the modelling of the system including its a
reconstruction by application of especially designed prostheses. I take
part in experimental tests of samples of taken from human bodies or tests
performed directly during medical surgeries. The collected experimental
data requires intensive signal analysis. Thus, I use signal processing
adopted from nonlinear dynamics, phase-space reconstruction and
bifurcation and chaos theory.
In the research I apply analytical perturbation
methods e.g. the multiple time scale method, Krylov-Bogolyubov-Mitropolski
method, harmonic balance or Poincaré method. The transition from regular to
chaotic vibrations I predict numerically by bifurcation diagrams, Poincaré
maps, Lyapunov exponents or in some specific cases by analytically by Melnikov
method. Having a mathematical model I use continuation methods to find
bifurcation points and to verify stability of the solution. In the numerical
investigations I use original differential equations or modulation equations
(slow-flow) obtained by analytical methods.