Modeling of Complex Dynamic Systems

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