Modeling of Complex Dynamic Systems

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

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• Inteligência artificial
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Abstract algebra; Aerospace engineering; Algorithms; Amplitude-frequency; Applied mechanics; Argument principle; Asymmetric stiffness; Axle; Beam; Beam with discontinuity; Beam-arch; Beam-arch; Bogie; Bounded noise excitation; Buckling; Cauchy integral; Chebyshev polynomial; Circular shells; Civil engineering; Complex analysis; Complex function; Complex numbers; Complex system; Computational engineering; Computational intelligence; Computational materials science; Computational mechanics; Computer science; Construction engineering; Continuous system; Contour integration method; Coupled system; Coupled vehicles; Cross-ply laminated plate; D-decomposition; Damage; Damage mechanics; Damaged beam; Damping; Dash-pot; Diffusion process; Discrete system; Displacement response; Double-beam system; Dynamic stability; Dynamical system; Elastic coupling; Engineering; Equation decoupling; Euler-Bernoulli; Forced vibrations; Foundation with discontinuity; Fourier integral transform; Fourier transform; Fractional viscoelastic system; Fracture mechanics; Free vibrations; Frequency response; Geophysics; Harmonic balance; Harmonic balance method; High-order beam; Infinite beam; Ito equation; Kelvin-Voigt model; Kirchhoff-Love plate; Laminated plate; Laplace integral transform; Laplace transform; Lyapunov exponent; Lyapunov exponents; MDOF; Machine learning; Machine learning markers; Markov process; Materials science engineering; Mathematics; Mechanical engineering; Mechanical system; Mechanical systems; Mechanics; Mode shape; Moment Lyapunov; Monte Carlo simulation; Monte-Carlo simulation; Moving mass; Multi-degree-of-freedom; Natural frequencies; Natural frequency; Newmark method; Newmark procedure; Newmark-beta; Nonlinear dynamics; Nonlinear mechanics; Nonlinear vibration; Nonlinear vibrations; Nonsymmetric amplitude; Numerical analysis; Orstein-Uhlenbeck; Oscillator