- Interactions between parametric and self-excited vibrations of mechanical systems, synchronisation phenomena and transitions from regular to chaotic motion. The impact of external force on the systems is considered in two variants: (a) ideal system - when exciting force is independent of the main structure and (b) non-ideal system - when the complete dynamical model i.e. the vibrating oscillator and the energy source interact.
- Nonlinear Normal Modes (NNM) of nonlinear lumped mass systems (e.g. coupled oscillators) or continuous system like cables, beams or plates. The existence and stability of various modes and their couplings to use them as natural forms of the structure response is studied.
- Dynamics and control of flexible systems made of composite material with embedded active elements. The specific control strategy, based often on nonlinear phenomena is imp[lemented to design the so called "smart structure" enable to behave properly to varied environmental conditions e.g. temperature, loadings, impacts etc.
- Theoretical models and a laboratory tests of rotating structures, e.g. composite beams, helicopter or wind turbine blades with embedded active elements.
- Self-excited chatter vibrations occurring in turning or milling processes and their mathematical models represented by differential equations with time delay.
- Delay differential equations and control of micro and macro electro-mechanical systems.
- Vibrations of human middle ear ossicles, the modelling of the system and its reconstruction by application of designed prostheses.
- Numerical methods, signal processing, phase-space reconstruction, bifurcation and chaos theory, continuation techniques..
- Analytical perturbation methods e.g. the multiple time scale method, Krylov-Bogolyubov-Mitropolski method, harmonic balance or Poincaré method.
