RESEARCH AREA

Jerzy Warminski, Ph.D., D.Sc., Eng.
Professor of Theoretical and Applied Mechanics

The main attention of my research is paid to
nonlinear dynamics of mechanical systems including the latest trends in
mechanics like: nonlinear vibrations, chaos theory, bifurcation and stability
analysis.
 Particularly I am interested in interactions
between parametric and selfexcited 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) nonideal 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
response.
 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
setup 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
the system.
 Next subject of my interest is related to
machining processes. I study selfexcited 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, phasespace reconstruction and
bifurcation and chaos theory.
In the research I apply analytical perturbation
methods e.g. the multiple time scale method, KrylovBogolyubovMitropolski
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
(slowflow) obtained by analytical methods.