Part I: Fundamental mathematical background of dynamics and vibrations: Overview of numerical methods and recent improvements 1. Mathematical methods and procedures in the analysis of stability of vibrations of complex moving objects 2. Mathematical methods and applications in the analysis of nonlinear vibrations 3. Mathematical methods in stochastic stability of mechanical systems Part II: Stability of vibrations of complex moving objects: Modeling and applications 4. Stabilization and critical velocity of a moving mass 5. Stability of vibration of a complex discrete oscillator moving at an overcritical speed 6. Vibrational benefits of a new stabilizer in moving coupled vehicles 7. Dynamics and stability of a complex rail vehicle system 8.
Modeling of a three-part viscoelastic foundation and its effect on dynamic stability 9. Vibrational instability in a complex moving object: Innovative approaches to elastically damped connections between car body components and supports Part III: Nonlinear vibrations: Stabilizing phenomena and applications 10. Nonlinear amplitude analysis of shear deformable beams supported by an elastic foundation with variable discontinuity 11. Nonlinear vibrational characteristics of damaged beams resting on a Pasternak foundation 12. The purpose of an arch in the stability of nonlinear vibrations of coupled structures 13. Quantitative effect of an axial load on the amplitude stability of rotating nano-beams 14. Coupled multiple plate systems and their stability characteristics Part IV: Stochastic stability of structures and mechanical systems: Methodology and examples 15. Moment Lyapunov exponents and stochastic stability of vibrationally isolated laminated plates 16.
Higher-order stochastic averaging method in fractional stochastic dynamics 17. Parametric stochastic stability of viscoelastic rotating shafts 18. Stochastic stability of circular cylindrical shells 19. Generalized transformations for MDOF stochastic systems Part V: From traditional methods to Artificial Intelligence 20. Modeling and applications of markers in machine learning and technical practice.